The most energy per unit mass that can be extracted is from nuclear energy.
Nuclear energy is the energy that is obtained from changes in the nucleus of an atom. In nuclear reactions, a tiny amount of mass is transformed into energy. The energy that is released from nuclear reactions is much higher than the energy that is released from chemical reactions.
The potential energy that is present in the nucleus of an atom is known as nuclear energy. The energy can be released through different processes. The process of breaking down the nucleus of an atom is known as nuclear fission. The energy that is released from nuclear fission is used to generate electricity.
The process of combining the nuclei of atoms is known as nuclear fusion. This process releases a tremendous amount of energy. Nuclear energy is a very efficient way of generating electricity. It is considered as one of the best alternative energy sources. The most energy per unit mass can be extracted from nuclear energy.
Learn more about nuclear energy in the link:
https://brainly.com/question/984564
#SPJ11
An electric dipole consists of charges +e and -e separated by 0.56 nm. It is in an electric field of strength 5.50 106 N/C. The (imaginary) line connecting the two charges forms a 31° angle with the electric field.
(a) What is the net force on the electric dipole?
N
(b) What is the net torque on the electric dipole?
N·m
For the given electric dipole with charges +e and -e separated by 0.56 nm, and in an electric field of strength 5.50 x 10^6 N/C, we calculated the net force and net torque on the dipole.
(a) To find the net force on the electric dipole, we need to consider the forces acting on each charge of the dipole due to the electric field. The force on a charge in an electric field is given by the formula F = qE, where F is the force, q is the charge, and E is the electric field strength.
For the positive charge (+e), the force is in the direction of the electric field, so F_+e = +e * E. Since the electric field strength and charge are given, we can calculate F_+e = (+e) * (5.50 * 10^6 N/C).
For the negative charge (-e), the force is in the opposite direction of the electric field, so F_-e = -e * E. Thus, F_-e = (-e) * (5.50 * 10^6 N/C).
The net force on the dipole is the vector sum of these forces:
Net force = F_+e + F_-e.
(b) To find the net torque on the electric dipole, we can use the formula τ = p * E * sin(θ), where τ is the torque, p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.
The dipole moment (p) of an electric dipole is given by p = q * d, where q is the magnitude of either charge and d is the separation between the charges.
We can calculate the dipole moment: p = (+e) * (0.56 nm).
Finally, the net torque on the dipole is given by:
Net torque = p * E * sin(θ).
Given:
Charge magnitude: e = 1.6 x 10^-19 C
Separation between charges: d = 0.56 nm = 0.56 x 10^-9 m
Electric field strength: E = 5.50 x 10^6 N/C
Angle between dipole moment and electric field: θ = 31°
(a) Calculating the net force:
F_+e = (+e) * E
F_+e = (1.6 x 10^-19 C) * (5.50 x 10^6 N/C)
F_+e = 8.8 x 10^-13 N
F_-e = (-e) * E
F_-e = (-1.6 x 10^-19 C) * (5.50 x 10^6 N/C)
F_-e = -8.8 x 10^-13 N
Net force = F_+e + F_-e
Net force = (8.8 x 10^-13 N) + (-8.8 x 10^-13 N)
Net force = 0 N
Therefore, the net force on the electric dipole is 0 N.
(b) Calculating the net torque:
Dipole moment: p = q * d
p = (e) * (0.56 x 10^-9 m)
p = 0.896 x 10^-19 C·m
Net torque = p * E * sin(θ)
Net torque = (0.896 x 10^-19 C·m) * (5.50 x 10^6 N/C) * sin(31°)
Net torque ≈ 2.56 x 10^-19 N·m
Therefore, the net torque on the electric dipole is approximately 2.56 x 10^-19 N·m.
To know more about electric field
brainly.com/question/15800304
#SPJ11
One end of a cord is fixed and a small 0.600⋅kg object is attached to the other end, where it swings in a section of a vertical circle of radius 3.00 m as shown in the figure below. When θ=24.0∘, the speed of the object is 7.00 m/s. At this instant, find each of the following. (a) the tension in the cord T= (b) the tangential and radial components of acceleration a1=a1=m/s2 inward m/s2 downward tangent to the circle (c) the total acceleration atotal = m/s2 inward and below the cord at (d) is your answer changed if the object is swinging down toward is lowest point instead of swinging up? Yes
The tension in the cord is 45.6 N.(b) answer in 100 words: The tangential acceleration of the object is 4.56 m/s² inward. The radial acceleration is 6.45 m/s² downward. The direction of the tangential acceleration is tangent to the circle, and the direction of the radial acceleration is inwards towards the center of the circle.
The resultant acceleration, atotal, is found using the Pythagorean theorem. At the given instant, atotal is 7.58 m/s², which is downward and inward. (c) the total acceleration atotal = 7.58 m/s² inward and below the cord. (d) The answer changes if the object is swinging down towards its lowest point. If the object is swinging down towards its lowest point, the tension in the cord will increase, the radial acceleration will decrease, and the tangential acceleration will remain the same. The total acceleration atotal will decrease as the object approaches its lowest point. (e)
The tension in the cord, tangential and radial components of acceleration, and total acceleration of a 0.6 kg object attached to a cord of a radius 3.00 m when swinging in a vertical circle of radius 3.00 m were found when the object was at an angle of 24.0 degrees and was moving at a speed of 7.00 m/s. If the object were to swing down towards its lowest point, the tension in the cord, tangential and radial components of acceleration, and total acceleration would change.
To know more about acceleration, visit:
https://brainly.com/question/28743430
#SPJ11
Bonus question: The laws of electromagnetism Write out the four Maxwell equations and the Lorentz force law formula for the force on a particle of charge q in an electric field E and magnetic field B. Make sure the five equations fit on a page. They represent the complete laws of electricity and magnetism including light and other forms of electromagnetic radiation.
The laws of electromagnetism refer to a set of fundamental principles that describe the behavior of electric and magnetic fields, as well as their interactions with charged particles.
The four Maxwell's equations, along with the Lorentz force law formula, are as follows:
Gauss's Law for Electric Fields:∇ ⋅ E = ρ/ε₀
Gauss's Law for Magnetic Fields:∇ ⋅ B = 0
Faraday's Law of Electromagnetic Induction:∇ × E = - ∂B/∂t
Ampère's Law with Maxwell's Addition:∇ × B = μ₀J + μ₀ε₀ ∂E/∂t
Lorentz Force Law Formula:F = q(E + v × B)
These equations collectively describe the complete laws of electricity and magnetism, including the behavior of electromagnetic radiation such as light.
Learn more about Faraday's Law here:
https://brainly.com/question/31322565
#SPJ11
A lambda particle (Λ) decays into a proton and a pion, Λ→p+π, and it is observed that the proton is left at rest. (a) What is the energy of the pion? (b) What was the energy of the original Λ ? (The masses involved are m
A
=1116,m
p
=938, and m
π
=140, all in MeV/c
2
. As is almost always the case, your best procedure is to solve the problem algebraically, in terms of the symbols m
A
,m
p
,m
π
, and, only at the end, to put in numbers.)
Eπ = mπc² (energy of the pion)
EΛ = Ep + (mπc²) + mpc² (energy of the original Λ particle)
(a) To find the energy of the pion (Eπ), we can use conservation of energy. Since the proton is left at rest, the initial energy of the Λ particle (EΛ) is equal to the energy of the pion (Eπ). We can express this as:
EΛ = Eπ
The total energy of a particle can be calculated using the formula:
E = mc²
where m is the mass of the particle and c is the speed of light.
For the pion, its mass is given as mπ.
Therefore, we have:
Eπ = mπc²
(b) To find the energy of the original Λ particle (EΛ), we need to consider the conservation of energy. Initially, the Λ particle has an energy of EΛ, and after the decay, the proton is left at rest, which means its energy is the rest energy:
EΛ = Ep + Eπ + rest energy
The rest energy of a particle can be calculated using the formula:
rest energy = mc²
where m is the mass of the particle and c is the speed of light.
For the proton, its mass is given as mp.
Therefore, we have:
EΛ = Ep + Eπ + mpc²
Substituting the expression for Eπ from part (a), we get:
EΛ = Ep + (mπc²) + mpc²
Now, to find the values of Ep and EΛ, we need to consider the conservation of momentum. Since the proton is left at rest, the total momentum before and after the decay must be zero:
Initial momentum = Final momentum
mΛvΛ = mpvp + mπvπ
Since the proton is left at rest, its velocity vp is 0.
Therefore, we have:
mΛvΛ = mπvπ
Solving for vΛ, we get:
vΛ = (mπ/mΛ) vπ
Now, we can express the energy of the Λ particle in terms of the pion velocity:
EΛ = (mΛc²) / √(1 - (vΛ/c)²)
Substituting the expression for vΛ, we get:
EΛ = (mΛc²) / √(1 - ((mπ/mΛ) vπ / c)²)
Finally, substituting the values for the masses and simplifying the expression gives the energy of the original Λ particle.
Note: The actual numerical value depends on the specific values of the masses provided in MeV/c².
learn more about "energy ":- https://brainly.com/question/13881533
#SPJ11
The momentum of a small object moving in a straight line is 24 kg.m/s and its kinetic energy is 98 J. What is the mass of the object? 3 kg 4 kg b kig 8 kg
According to the question, the mass of the object is 24 kg.
To find the mass of the object, we can use the formula for kinetic energy and momentum.
The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * velocity^2
The formula for momentum is given by:
Momentum = mass * velocity
Given that the momentum is 24 kg.m/s and the kinetic energy is 98 J, we can set up the following equations:
24 kg.m/s = mass * velocity
98 J = (1/2) * mass * velocity^2
Since we are given the momentum and kinetic energy, we can solve for the velocity using the equation for momentum.
velocity = momentum / mass
Substituting the value of momentum and mass, we have:
24 kg.m/s = mass * (momentum / mass)
Simplifying, we get:
24 kg.m/s = momentum
Therefore, the mass of the object is 24 kg.
To learn more about mass
https://brainly.com/question/86444
#SPJ11
A particle of charge +4.1μC is released from rest at the point x=54 cm on an x axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 11 cm if (a)Q Q=+18μC and (b)Q=−18μC? (a) Number Units (b) Number Units
(a) The kinetic energy of the particle is 6.34 J when Q = +18 μC. (b) The kinetic energy of the particle when Q = +18 μC is 6.34 J, and when Q = -18 μC is 7.75 J.
(a) When Q = +18 μC
A particle of charge +4.1μC is released from rest at the point x = 54 cm on an x-axis.
The particle begins to move due to the presence of a charge Q that remains fixed at the origin.
As we know that, the potential energy and kinetic energy of a particle that is acted upon by an electrostatic force are given as:
PE = qV
KE = (1/2)*mv²
where, q is the charge of the particle,
V is the potential energy,
m is the mass of the particle,
v is the velocity of the particle.
Initially, the particle is at rest. So, the initial kinetic energy is zero.
At x = 11 cm:
Displacement, `d` = x - x₀ = 11 - 54 = -43 cm
Here, the displacement is negative because the particle moves toward the origin.
Distance, `r` = |d| = 43 cm
Distance between the point where the charge is present and where the particle is located, `r₁` = 54 cm
Charge of the particle, `q` = +4.1 μC
Charge of the charge at the origin, `Q₁` = +18 μC
Charge of the charge at the origin, `Q₂` = -18 μC
For electrostatic potential, we can use the following formula:
V = (1/4πε₀)Q/r
where ε₀ is the permittivity of free space.
For calculating the kinetic energy, we have to calculate the potential energy at `x = 54 cm` and `x = 11 cm`.
Then, we have to find the difference between them to get the work done due to electrostatic force, and finally, we can calculate the kinetic energy of the particle.
So, let's calculate the electrostatic potential energy of the particle at `x = 54 cm` and `x = 11 cm`.
The potential at x = 54 cm,
`V₁` = (1/4πε₀)Q/r₁
= (9 × 10⁹ N⁻¹ m² C⁻²) × (18 × 10⁻⁶ C) / (0.54 m)
≈ 5.56 × 10⁵ V
The potential at x = 11 cm,
`V₂` = (1/4πε₀)Q/r = (9 × 10⁹ N⁻¹ m² C⁻²) × (18 × 10⁻⁶ C) / (0.11 m) ≈ 1.64 × 10⁷ V
Now, let's calculate the work done by the electrostatic force,
`W` = q(V₂ - V₁) ≈ (4.1 × 10⁻⁶ C) × (1.64 × 10⁷ V - 5.56 × 10⁵ V) ≈ 6.34 J
Now, the kinetic energy of the particle,`KE` = W= 6.34 J
Therefore, the kinetic energy of the particle is 6.34 J when Q = +18 μC.
Case (b):
When Q = -18 μC:
The potential at x = 54 cm,
`V₁` = (1/4πε₀)Q/r₁ = (9 × 10⁹ N⁻¹ m² C⁻²) × (-18 × 10⁻⁶ C) / (0.54 m) ≈ -5.56 × 10⁵ V
The potential at x = 11 cm,
`V₂` = (1/4πε₀)Q/r = (9 × 10⁹ N⁻¹ m² C⁻²) × (-18 × 10⁻⁶ C) / (0.11 m) ≈ -1.64 × 10⁷ V
Now, let's calculate the work done by the electrostatic force,
`W` = q(V₂ - V₁) ≈ (4.1 × 10⁻⁶ C) × (-1.64 × 10⁷ V - (-5.56 × 10⁵ V)) ≈ -7.75 J
Now, the kinetic energy of the particle,
`KE` = |W|= 7.75 J
Therefore, the kinetic energy of the particle is 7.75 J when Q = -18 μC.
So, the kinetic energy of the particle when Q = +18 μC is 6.34 J, and when Q = -18 μC is 7.75 J.
To know more about Kinetic Energy, click here
brainly.com/question/30337295
#SPJ11
A- The instantaneous position "y" of an object that is moving at a constant (or uniform) acceleration can be expressed in function of the time "t", its initial velocity vo, its initial position yo, and its acceleration "a". Give that expression with the units of all symbols
The instantaneous position of an object that is moving at a constant acceleration can be expressed as y = yo + vot + 1/2at², where y, yo, vo, a, and t have units of meters, meters per second, meters per second squared, and seconds, respectively.
The expression for the instantaneous position "y" of an object that is moving at a constant (or uniform) acceleration can be expressed in function of the time "t", its initial velocity vo, its initial position yo, and its acceleration "a".
The expression is:y = yo + vot + 1/2at² Where y = instantaneous position of the object yo = initial position of the object vo = initial velocity of the object a = acceleration of the object t = time taken by the object to reach the instantaneous position.
The units of all the symbols are:y: meters (m)yo: meters (m)vo: meters per second (m/s)a: meters per second squared (m/s²)t: seconds (s)
Therefore, the instantaneous position of an object that is moving at a constant acceleration can be expressed as y = yo + vot + 1/2at², where y, yo, vo, a, and t have units of meters, meters per second, meters per second squared, and seconds.
Learn more about acceleration here ;
https://brainly.com/question/2303856
#SPJ11
a basketball olayer jumps straight up at 4 m/s. 0.3 seconds later he shoots the ball with a velocity of 6 m/s up and 7m/s east relative to him. what is the velocity of ball relative to ground as player shoots the ball
The velocity of the ball relative to the ground as player shoots the ball is obtained as ,Initial velocity of the basketball player = 4 m/s
Time taken by the player to shoot the ball after jumping up = 0.3 sVelocity of the ball w.r.t basketball player
= Velocity of the ball – Velocity of the player
= 6 m/s up + 7 m/s east – 4 m/s up
= 2 m/s up + 7 m/s eastNow,Velocity of the basketball player w.r.t the ground
= 0 m/s (since there is no movement in the horizontal direction)
Applying relative velocity formula, Relative velocity of the ball w.r.t the ground = Velocity of the ball w.r.t basketball player + Velocity of the basketball player w.r.t ground= (2 m/s up + 7 m/s east) + 0 m/s
= 2 m/s up + 7 m/s eastHence, the velocity of the ball relative to the ground as player shoots the ball is 2 m/s up and 7 m/s east.
To know more about Initial velocity visit:-
https://brainly.com/question/31023940
#SPJ11
A square parallel plate capacitor having an area of 200 cm2 has a separation distance of 2.4 mm. Determine its capacitance when a dielectric material of constant k = 2 is inserted between its plates.
a.148pF
b.1476pF
c.7.2mF
d.15nF
The capacitance of the capacitor with the dielectric material inserted is approximately 148 pF. The correct answer is option a) 148 pF.
To determine the capacitance of the square parallel plate capacitor with a dielectric material inserted between its plates, we can use the formula:
C = (ε₀ * k * A) / d
where C is the capacitance, ε₀ is the vacuum permittivity (8.85 x 10^-12 F/m), k is the dielectric constant, A is the area of the plates, and d is the separation distance between the plates.
Given:
Area (A) = 200 cm² = 200 x 10^-4 m²
Separation distance (d) = 2.4 mm = 2.4 x 10^-3 m
Dielectric constant (k) = 2
Substituting the values into the formula:
C = (8.85 x 10^-12 F/m * 2 * 200 x 10^-4 m²) / (2.4 x 10^-3 m)
Simplifying the expression:
C = 148 pF
Therefore, the capacitance of the capacitor with the dielectric material inserted is approximately 148 pF. The correct answer is option a) 148 pF.
To learn more about, capacitor, click here, https://brainly.com/question/29301875
#SPJ11
1. Suppose that your friend goes out for a run and comes back 2 hours later. Their fitness watch says that they traveled a distance of 5 miles in that time. Determine their speed, in units of mph. Were they really running that whole time? How do you know? 2. Use a navigation app to determine how many miles you traveled to get to school today. Then estimate how long it took you to get to school today. Use these numbers to determine estimates for your travel speed, in both mph and m/s. 3. Driving down the road, you notice that you go from being about 300 feet in front of a traffic light to about 300 feet past it in 1 second of time. About how fast are you traveling, in both m/s and mph ? 4. Further down the road, you notice that you go from being about 600 feet in front of a traffic light to about 200 feet in front of it in 1.5 seconds of time. About how fast are you traveling now, in both m/s and mph ?
1. Speed = distance/time = 5 miles / 2 hours = 2.5 miles/hour. We do not know if they were running the whole time because speed is a scalar quantity that only tells us how fast they were moving, not how they were moving.
2. The distance from home to school is needed to find speed. If distance traveled to school is x miles and time taken to travel to school is t, then average speed = distance/time = x/t mph and x/t × 1609.34/t m/s.
3.The average speed of the car is the total distance divided by the total time. The distance that the car covers in 1 second is 600 + 300 = 900 ft. So, the speed of the car is (900 feet / 1 sec) / 5280 feet/mile = 0.17 miles/sec or 60 × 0.17 = 10.2 miles/hour or 900/3600 = 0.25 meters/second.
4. For the second part, the initial position of the car is 600 feet and the final position is 200 feet, which means the distance traveled is 400 feet. The time taken to travel that distance is 1.5 seconds. So, the speed of the car is 400 feet / (1.5 seconds × 5280 feet/mile) = 400/7920 = 0.05 miles/second or 18 miles/hour. In meters per second, the speed of the car is 0.05 miles/sec × 1609.34 meters/mile = 80.47 m/s.
To know more about running visit:
https://brainly.com/question/17100185
#SPJ11
A cylinder of length L has a circular cross section radius R. The Volume of the cylinder is 15.0±0.5 cm3 and the length is 20 ± 0.1 cm. Calculate the radius of the cylinder with its uncertainty.
The radius of the cylinder with uncertainty is found to be 0.488 ± 0.01 cm. This can be understood by propagation of errors.
Volume of the cylinder, V = 15.0 ± 0.5 cm³
Length of the cylinder, L = 20 ± 0.1 cm.
Circular cross-section radius, r =?
We know, Volume of the cylinder = πr²L
`V=π r²L`
r²= V/(πL)
Taking the square root of both the sides, `r = √(V/(πL))`
Let's calculate the uncertainty of the radius,
`r = √(V/(πL))` = √15/(π×20) = 0.488 cm
`Δ(r)/r = 1/2 × [Δ(V)/V + Δ(L)/L]`
`Δ(r) = r/2 × [Δ(V)/V + Δ(L)/L]`
Substitute the values of V, L, and Δ(V) and Δ(L)
`Δ(r) = r/2 × [0.5/15 + 0.1/20]`=`r/2 × (0.033 + 0.005)`=`r/2 × 0.038`=`0.019r`
Now substitute the value of r,
`Δ(r) = 0.019 × 0.488 = 0.0092 ≈ 0.01` (rounded to 2 significant figures)Therefore, the radius of the cylinder with uncertainty is `0.488 ± 0.01 cm`.
To learn more about uncertainty and errors: https://brainly.com/question/31615085
#SPJ11
You are deadlifting 1,130 N. What is the net force needed to accelerate the weights upwards at 1.6 m/s2?
To determine the net force required to accelerate the weights upwards at 1.6 m/s², we can use Newton's second law of motion, which states that the net force (F_net) acting on an object is equal to the product of its mass (m) and its acceleration (a).
Given:
Force due to deadlifting (F_deadlift) = 1,130 N
Acceleration (a) = 1.6 m/s²
To calculate the net force, we need to know the mass (m) of the weights being lifted. Without this information, we cannot provide an exact value for the net force.
However, we can discuss the relationship between force, mass, and acceleration.
According to Newton's second law, the net force is directly proportional to the acceleration and the mass of the object.
This means that as the mass increases, the net force required to achieve the same acceleration also increases. Conversely, if the mass decreases, a smaller net force is needed to achieve the desired acceleration.
In the case of deadlifting, the net force required to accelerate the weights upwards will depend on the mass of the weights. The greater the mass, the larger the net force needed to produce the desired acceleration.
Learn more about Newton's second law of motion from the given link!
https://brainly.com/question/25545050
#SPJ11
A crate of mass m is going down a frictionless inclined plane. The plane is at angle θ with respect to horizontal. Given m=1.3( kg),θ=56 (deg), g=9.81 m/s
∧
2. (Give your answers as numbers with 3 significant figures) Find the magnitude of the normal force that the plane exerts on the crate (in N) Find the magnitude of the crate's acceleration (in m/s
∧
2 ) A mechanical system is given as in figure. Two block of masses m1 and m2 are connected by a massless string. The pully's mass is also negligible. Assume the system can move with no friction. Given: m1=6.2 (kg),m2=1.6( kg),g=9.81 m/s
∧
2. (Give your answers as numbers with 3 significant figures) Find the magnitude of the acceleration of m1 (in m/s
∧
2 ) Find the tension in the string (in N)
1. The magnitude of the normal force that the plane exerts on the crate is 6.02 N.
2. The tension in the string is 19.7 N.
1. To find the magnitude of the normal force that the plane exerts on the crate (in N), we have to use the formula;
Fnet = ma
Where
Fnet is the net force,
m is the mass
a is the acceleration.
As per the question, the crate is moving down the inclined plane without friction. Hence the force acting on the crate is only the gravitational force. Therefore, the formula can be simplified to;
Fg = ma
Where
Fg is the force due to gravity acting on the crate,
m is the mass of the crate
a is the acceleration of the crate
Using the above formula, we can find the acceleration of the crate.
a = gsinθ
a = (9.81)(sin56°)
a = 7.94 m/s²
To find the normal force acting on the crate, we have to use the formula;
Fn = mgcosθ
Fn = (1.3)(9.81)(cos56°)
Fn = 6.02 N
Thus, the magnitude of the normal force that the plane exerts on the crate is 6.02 N.
2. We know that the two blocks are connected by a massless string. Therefore, the tension in the string is the same for both blocks.
Using the following formula for each block separately;
m1g − T = m1a
m2g + T = m2a
Here,
g is the acceleration due to gravity
T is the tension in the string
Adding the two equations gives us;
m1g − m2g = (m1 + m2)a
Simplifying further;
a = g(m1 − m2) / (m1 + m2)
a = (9.81)(6.2 − 1.6) / (6.2 + 1.6)
a = 6.16 m/s²
Thus, the magnitude of the acceleration of m1 is 6.16 m/s².
To find the tension in the string, we can use any of the two equations we got for each block separately. Using the first equation;
m1g − T = m1a
T = m1(g − a)
T = 6.2(9.81 − 6.16)
T = 19.7 N
Thus, the tension in the string is 19.7 N.
Learn more about acceleration:
https://brainly.com/question/25876659
#SPJ11
7. A diver steps off a diving board and hits the surface of the water in the swimming pool 1.5 s later. If the instant they enter the water, the diver starts to decelerate at 16 m/s
2
, how deep do they go into the water before stopping? Ignore air resistance. Hint: Stepping off the diving board means that they will start with zero velocity and go straight down into the water. (All options are given as negative because they are how far below the surface of the water.) x
2
−4.05m x
2
=−6.75m x
2
=−11m x
2
=−14.7m x
2
=−18m
The diver goes 12 meters below the surface of the water before coming to a stop.
To solve this problem, we can use the equations of motion for uniformly decelerated motion. We know that the initial velocity (u) is zero because the diver starts with zero velocity when stepping off the diving board. The acceleration (a) is -16 m/s² because the diver decelerates at a constant rate of 16 m/s². We need to find the displacement (x) of the diver when they come to a stop.
The equation for displacement in uniformly decelerated motion is given by:
x = ut + (1/2)at²
Since the initial velocity (u) is zero, the equation simplifies to:
x = (1/2)at²
Plugging in the values:
x = (1/2)(-16 m/s²)(1.5 s)²
x = -12 m
Therefore, the diver goes 12 meters below the surface of the water before coming to a stop.
Here you can learn more about surface of the water
https://brainly.com/question/20758748#
#SPJ11
A proton and an electron are moving du yeast in a constant electric field that also points due east. The electric field has a magnitude of 2.0×10
4
N/C Determine the magnitude of the acceleration of the proton and the electron.
Therefore, the magnitude of acceleration of the proton is 1.9 × 10¹³ m/s² and the magnitude of acceleration of the electron is 3.5 × 10¹⁴ m/s²
Given
Magnitude of electric field = 2.0 × 10⁴ N/C.
The acceleration of a proton in an electric field is given by
F = ma
Where F = qE,
where E is the electric field strength and q is the charge of the proton.
Substituting, F = ma ⟹ qE = ma,
Thus, a = qE/m
As the mass of the proton is given as 1.67 × 10⁻²⁷ kg and the charge as 1.6 × 10⁻¹⁹ C,
we have a = (1.6 × 10⁻¹⁹ C)(2.0 × 10⁴ N/C) / (1.67 × 10⁻²⁷ kg) = 1.9 × 10¹³ m/s²
Similarly, the acceleration of an electron in an electric field is given by F = ma
Where F = qE,
where E is the electric field strength and q is the charge of the electron.
Substituting, F = ma ⟹ qE = ma,
Thus, a = qE/m
As the mass of the electron is given as 9.1 × 10⁻³¹ kg and the charge as -1.6 × 10⁻¹⁹ C (negative because it is an electron),
we have
a = (-1.6 × 10⁻¹⁹ C)(2.0 × 10⁴ N/C) / (9.1 × 10⁻³¹ kg)
= -3.5 × 10¹⁴ m/s² (because it is opposite to the direction of the electric field).
Therefore, the magnitude of acceleration of the proton is 1.9 × 10¹³ m/s² and
the magnitude of acceleration of the electron is 3.5 × 10¹⁴ m/s².
Hence, a = (1.9 × 10¹³ m/s²) (for proton)
a = (3.5 × 10¹⁴ m/s²) (for electron)
To know more about acceleration visit:
https://brainly.com/question/28187441
#SPJ11
3. (6 pts total) A crate rests on a rough inclined plane, angled at 38.0° above the horizontal. The crate has a mass of 11.5 kg, and the coefficient of static friction between the crate and the inclined plane is 0.292 A force F is exerted in the direction up the plane and parallel to the slope in order to keep the cate in plane.
a) (6 pts) Draw a free -body diagram of the situation,assuming the crate is not moving . Be sure to label all forces (Hint: be carefful with the diection of fiction force) b)(3 pts) What minimum force,directed parallel to the slope up the plane,is required to keep the crate from the siding the plane.
The minimum force, directed parallel to the slope up the plane, required to keep the crate from sliding down the plane is 40.449 N.
When a crate rests on a rough inclined plane at an angle of 38.0° above the horizontal, a force is needed to keep the crate from sliding down the slope. The force F required in the direction up the plane and parallel to the slope to keep the crate from sliding is calculated as follows:
Calculate the frictional force acting against the crate. The frictional force (Ff) acting against the crate is calculated using the following formula:
Ff = (coefficient of static friction) x (normal force)
N = (mass of the crate) x (acceleration due to gravity)
N = 11.5 kg × 9.81 m/s²
N = 112.715 N
The normal force acting against the crate is:
cos θ = (adjacent/hypotenuse)
cos 38.0° = (N/112.715)
N = 86.042 N
The frictional force is:
Ff = 0.292 x 86.042
Ff = 25.102 N
The force F required to keep the crate from sliding is:
F = Ff/sin θ
F = 25.102/sin 38.0°
F = 40.449 N
Therefore, the minimum force, directed parallel to the slope up the plane, required to keep the crate from sliding down the plane is 40.449 N.
Learn more about frictional force here:
https://brainly.com/question/30280206
#SPJ11
A fibre optic sensor is based on absorption spectroscopy. The fibre is 2 m long with the loss of 0.3 dB/m. The fibre is immersed in a solution with a specific concentration of a chemical. Find the signal-to-background ratio (in dB ), if the extinction coefficient of the solution is 0.5 mol^−1 m^−1
and its concentration is 800mMol. The PF of the fibre is 10%. The background signal is obtained when the same fibre is in the air (absorption of the air is zero). Express your answer in dB.
Fiber optic sensor is a sensor based on the absorption spectroscopy. The fiber is 2 m long and has a loss of 0.3 dB/m. The specific concentration of the chemical that the fiber is immersed in, is determined by the signal-to-background ratio (SBR).
The extinction coefficient of the solution is 0.5 mol⁻¹m⁻¹, and its concentration is 800 mMol. The PF (power fraction) of the fiber is 10%.
The background signal is obtained by immersing the same fiber in the air, where the absorption is zero. Signal-to-background ratio (in dB)
SBR = 10 log (P_S / P_B)
where P_S and P_B are the powers of the signal and the background, respectively.
Since P_S = PF x P_L and P_B = PF x P_A where P_L and P_A are the powers of the light passing through the liquid and air, respectively,
we have SBR = 10 log (P_L / P_A)
Extinction coefficient: α = εc, where ε is the molar absorption coefficient, and c is the concentration of the absorbing species.
Therefore, the attenuation in the fiber is
A = αL = εcL
where
L is the length of the fiber,
and the signal is S_S = [tex]P_S e^(-A)[/tex]
Therefore, the signal-to-background ratio (SBR) is 1.23 dB.
To know more about spectroscopy visit:
https://brainly.com/question/13265448
#SPJ11
A puck is moving on an air hockey table. Relative to an x,y coordinate system at time t−0 s, the x components of the puck's initial velocity and acceleration are v
0x
=+2.5 m/s and a
x
=+2.2 m/s
2
. The y components of the puck's initial velocity and acceleration are v
O
=+9.0 m/s and a
y
=−8.7 m/s
2
. Find (a) the magnitude v and (b) the direction θ of the puck's velocity at a time of t=0.50 s. Specify the direction relative to the +x axis. (a) v= (b) θ= degrees the +x axis
(a) The magnitude of the puck's velocity at t = 0.50 s is approximately 9.34 m/s.
(b) The direction of the puck's velocity at t = 0.50 s, relative to the +x axis, is approximately 75.96 degrees.
To find the magnitude and direction of the puck's velocity at t = 0.50 s, we can use the equations of motion.
(a) To find the magnitude of the velocity, we can use the Pythagorean theorem:
v = √(v_x^2 + v_y^2)
Given:
v_0x = +2.5 m/s (initial x-component velocity)
v_0y = +9.0 m/s (initial y-component velocity)
Using the given values, we can calculate the magnitude of the velocity:
v = √(v_0x^2 + v_0y^2)
v = √((+2.5 m/s)^2 + (+9.0 m/s)^2)
v = √(6.25 m^2/s^2 + 81.0 m^2/s^2)
v = √(87.25 m^2/s^2)
v ≈ 9.34 m/s
Therefore, the magnitude of the velocity at t = 0.50 s is approximately 9.34 m/s.
(b) To find the direction θ of the velocity, we can use the inverse tangent function:
θ = tan^(-1)(v_y / v_x)
Using the given values, we can calculate the direction:
θ = tan^(-1)(v_0y / v_0x)
θ = tan^(-1)(+9.0 m/s / +2.5 m/s)
θ ≈ 75.96 degrees
Therefore, the direction of the velocity at t = 0.50 s relative to the +x axis is approximately 75.96 degrees.
To learn more about Pythagorean theorem, Visit:
https://brainly.com/question/28981380
#SPJ11
A capacitor with plates of area A that are separated by a distance D is connected to a battery, and charged to a charge Q. The battery is left in contact with the plates, while the plates are pressed closer together. What happens to the electric field E inside the plates of the capacitor?
A capacitor with plates of area A that are separated by a distance D is connected to a battery, and charged to a charge Q. The battery is left in contact with the plates, while the plates are pressed closer together.
In a capacitor, electric field E inside the plates is directly proportional to the voltage V across the plates and inversely proportional to the separation distance d between them. That is, E = V / d. Capacitance C of a capacitor with plates of area.
A separated by distance D is given by C = εA / D where ε is the permittivity of the medium between the plates.Now, if the plates of the capacitor are pressed closer together to distance d' (d' < d), the capacitance of the capacitor will increase to C' = εA / d'.
Hence, for a constant charge Q, the voltage V across the capacitor plates will increase to V' = Q / C' = Qd' / εA. As the voltage across the capacitor plates increases, the electric field E inside the plates will also increase, the electric field E inside the plates of the capacitor will increase when the plates are pressed closer together.
To know more about separated visit:
https://brainly.com/question/13619907
#SPJ11
Lift is a pressure caused by the fluid in a direction horizontal to the direction of travel of the body. True False
Lift is not a pressure caused by the fluid in a horizontal direction to the body's direction of travel is False.
Lift is a force perpendicular to the direction of fluid flow.
Lift is the force generated on an object, such as an airplane wing, when it is in motion through a fluid (such as air).
The generation of lift is primarily due to the difference in pressure on the upper and lower surfaces of the wing.
As a wing moves through the fluid, the shape and angle of the wing cause the air to move faster over the top surface, resulting in lower pressure, and slower under the bottom surface, resulting in higher pressure.
The pressure difference between the upper and lower surfaces of the wing creates an upward force perpendicular to the direction of the fluid flow.
This upward force is known as lift and is responsible for enabling flight and supporting the weight of the aircraft.
Therefore, the statement that lift is a pressure caused by the fluid in a horizontal direction to the body's direction of travel is false.
Lift is a force perpendicular to the direction of fluid flow.
Learn more about pressure from the given link
https://brainly.com/question/28012687
#SPJ11
child on a sled is sliding some snow-covered hills starting to rest at location A. in picture three different locations are marked with the letter A, B, and C Rank from the highest to lowest kinetic energy of the child
The three locations marked as A, B, and C, have to be ranked from the highest to the lowest kinetic energy of the child. Kinetic energy is defined as the energy that a moving object possesses due to its motion. As the child on a sled is sliding down the snow-covered hills, it's gaining kinetic energy due to its motion.
The higher the velocity of the sled, the higher will be the kinetic energy possessed by the sled. Hence, the ranking of the three locations from highest to lowest kinetic energy will be as follows: B > C > A Here's why: Location B is at the bottom of the hill, where the sled will have the highest velocity and, therefore, the highest kinetic energy. Hence, it ranks first in terms of kinetic energy. Location C is somewhere in between the top and bottom of the hill.
At this location, the sled will have less velocity than at location B but more than at location A. Hence, the kinetic energy of the child on a sled will be lower than at location B but higher than at location A. Therefore, location C ranks second in terms of kinetic energy. Location A is at the top of the hill, where the sled is starting to slide.
At this point, the sled is at rest, which means that the velocity of the sled is zero, and, therefore, the kinetic energy of the sled is also zero. Hence, location A ranks last in terms of kinetic energy.
To know more about kinetic energy refer here:
https://brainly.com/question/999862#
#SPJ11
The magnitude of vector
A
is 7.0 m. It points in a direction which makes an angle of 145
∘
measured counterdockwise from the positive x-axis. (a) What is the x component of the vector −4.5
A
? in (b) What is the y component of the vector −4.5
A
? (c) What is the magnitude of the vector −4.5
A
^
?
Answer: (a) -18.05 m, (b) -25.81 m, (c) 31.5 m.
Given data:
The magnitude of vector A is 7.0 m and the angle of the vector with positive x-axis is 145°.
Parts (a) and (b) require us to determine the horizontal and vertical components of the vector -4.5 A.
The minus sign indicates that this vector is in the opposite direction of the vector A.
Therefore, the magnitude of the vector -4.5 A is-4.5A
= -4.5 x 7.0
= -31.5 m
(a) x component of the vector −4.5A = -4.5A cos θ
where cos θ = cos(145°)
= -0.5736 (from the cosine table)
-4.5A cos θ = -31.5 m x (-0.5736)
= 18.05 m (toward left side is considered negative)
(b) y component of the vector −4.5A = -4.5A sin θ
where sin θ = sin(145°)
= 0.8192 (from the sine table)
-4.5A sin θ = -31.5 m x 0.8192
= -25.81 m (upward direction is considered positive)
(c) The magnitude of the vector −4.5 A^ is the same as the magnitude of 4.5 A, which is 31.5 m.
Answer: (a) -18.05 m,
(b) -25.81 m,
(c) 31.5 m.
Learn more about magnitude of the vector on the given link:
https://brainly.in/question/30129617
#SPJ11
A standard 1 kilogram weight is a cylinder 42.0 mm in height and 44.5 mm in diameter. What is the density of the material?
kg/m3
A standard 1-kilogram weight is a cylinder 42.0 mm in height and 44.5 mm in diameter. The density of the material is approx [tex]30,368.75 kg/m^3[/tex]
For calculating the density of the material, need to find the mass and volume of the weight. The mass of the weight is given as 1 kilogram.
For finding the volume, need to use the dimensions of the weight. The weight is in the shape of a cylinder, so use the formula for the volume of a cylinder:
[tex]V = \pi * r^2 * h[/tex]
where r is the radius and h is the height.
The given diameter is 44.5 mm, which means the radius is half of that, so
r = 44.5 mm / 2 = 22.25 mm.
Convert the radius to meters by dividing it by 1000:
r = 22.25 mm / 1000 = 0.02225 m.
The height is given as 42.0 mm, which is equivalent to 0.0420 m.
Now calculate the volume:
[tex]V = \pi * (0.02225 m)^2 * 0.0420 m = 0.0000329 m^3[/tex]
Finally, calculate the density by dividing the mass by the volume:
[tex]density = 1 kg / 0.0000329 m^3 \approx 30,395.1365 kg/m^3[/tex].
Learn more about density here:
https://brainly.com/question/952755
#SPJ11
You are in a helicopter towing a 127.kg laser detector that is mapping out the thickness of the Brunt lce 5 helf along the coast of Antarctica. The original cable used to suspend the detector was damaged and replaced by a lighter one with a maximum tension rating of 304 pounds, not much more than the weight of the detector. The replacement cable would work without question in the case that the detector and helicopter were not accelerating. However, some acceleration of the helicopter is inevitable. In order to monitor the tension force on the cable to make sure the maximum is not exceeded (and therefore to not lose the very expensive detector) you calculate the masymum angle the cable can make with the vertical without the cable exceeding the tension limit. (a) Assuming straight and level fight of the helicopter, what is that maximum angle? (b) What is the corresponding acceleration? (c) Your colleague wants to add a 7.00.kg infrared camera to the detector. What is the maximum allowable angle now? (a) Number Units: (b) Number Units (c) Number Units
The maximum allowable angle is 33.2° when a 7.00 kg infrared camera is added to the detector.(a) Calculation of the maximum angle The force equation for a body of mass m is shown below:F = ma (where F is the force acting on the object, m is its mass, and a is its acceleration).
A sketch of the helicopter, detector, and cable is shown below:Helicopter, detector, and cable: The cable is attached to the helicopter at point H and to the detector at point D.θ is the angle between the cable and the vertical, and T is the tension in the cable.Let us apply Newton's second law to the detector:The acceleration of the detector is mG - Tsinθ, where m is the mass of the detector and G is the acceleration due to gravity (9.8 m/s2). Thus, we can say: ma = mG - Tsinθ Rearranging the equation to solve for T gives:T = m(G - a)/sinθ (1)Note that the tension is maximum when sinθ = 1 (θ = 90°), and we can substitute this condition into
Equation (1) to determine the maximum tension:Tmax = m(G - a)Now we can solve for the maximum angle θmax using Tmax and the maximum tension of the cable, which is 304 pounds. Since 1 lb = 4.44822 N, we can convert the maximum tension to Newtons as follows:Tmax = 304 lb x 4.44822 N/lb = 1353 NWe can then substitute this value and the given values into Equation (1) and solve for sinθmax as follows:Tmax = m(G - a)/sinθmax1353 N = (127 kg)(9.8 m/s2 - a)/sinθmaxSolving for sinθmax gives:sinθmax = (127 kg)(9.8 m/s2 - a)/1353 N Rearranging the equation to solve for the maximum angle.
To know more about acceleration visit:-
https://brainly.com/question/2303856
#SPJ11
Consider a signal x[n]=4cos(0.1πn)+6cos(0.2πn). This signal is modulated to get the signal v[n]=2x[n]cos(0.4πn). The signal v[n] is applied to an ideal lowpass filter with passband gain 1 and cutoff frequency ω
c
=0.55π. Determine the output y[n] of the lowpass filter. (One possible way to solve this problem is to use the trig formula: 2cosAcosB=cos(A+B)+cos(A−B).)
To determine the output y[n] of the lowpass filter, let's first simplify the expression for v[n] by using the trigonometric formula given: 2cos(A)cos(B) = cos(A + B) + cos(A - B).
We have v[n] = 2x[n]cos(0.4πn), where x[n] = 4cos(0.1πn) + 6cos(0.2πn).
Applying the trigonometric formula, we can rewrite v[n] as:
v[n] = 2(4cos(0.1πn) + 6cos(0.2πn))cos(0.4πn)
= 8cos(0.1πn)cos(0.4πn) + 12cos(0.2πn)cos(0.4πn)
Now, let's consider the lowpass filter with passband gain 1 and cutoff frequency ωc = 0.55π. The lowpass filter will attenuate frequencies above the cutoff frequency.
We can express the output y[n] as the convolution of the input v[n] with the impulse response h[n] of the lowpass filter.
The impulse response h[n] is determined by the filter's frequency response, which is given by:
H(ω) = {
1, if |ω| ≤ ωc,
0, if |ω| > ωc,
}
Using the inverse Fourier transform, we can find the impulse response h[n] by taking the inverse Fourier transform of H(ω).
After performing the inverse Fourier transform, we get:
h[n] = (1/π) ∫[ω=-∞ to ω=∞] H(ω)e^(jωn) dω
= (1/π) ∫[ω=-ωc to ω=ωc] e^(jωn) dω
= (1/π) ∫[ω=-ωc to ω=ωc] cos(ωn) dω
= (1/π) [sin(ωcn)/n] from -ωc to ωc
= (1/π) [sin(ωcn)/n] evaluated at ω = ωc minus (1/π) [sin(ωcn)/n] evaluated at ω = -ωc
= (1/π) [sin(ωcn)/n] evaluated at ω = ωc minus (1/π) [sin(ωcn)/n] evaluated at ω = -ωc
Now, we can find the output y[n] by convolving the input v[n] with the impulse response h[n]:
y[n] = v[n] * h[n]
Taking the convolution of v[n] and h[n] involves multiplying v[n] by h[-k] and summing over k.
Thus, y[n] = Σ[v[n-k] * h[-k]] for k from -∞ to ∞
I hope this helps! Let me know if you need further clarification.
To know more about formula visit:
https://brainly.com/question/20748250
#SPJ11
A derrick boat approaches a two-mile marker 100 m ahead at a velocity of 32.5 m/s. The pilot reduces the throttle, slowing the boat with a constant acceleration of −2.90 m/s2.(a) How long (in s) does it take the boat to reach the marker? ____ s.(b) What is the velocity (in m/s) of the boat when it reaches the marker? (Indicate the direction with the sign of your answer.) ____ m/s.
To solve this problem, we can use the equations of motion. It takes approximately 11.21 seconds for the boat to reach the marker. The velocity of the boat when it reaches the marker is approximately -21.82 m/s.
To solve this problem, we can use the equations of motion. Let's denote the initial velocity of the boat as v0, the final velocity as vf, the acceleration as a, and the displacement as d.
(a) We need to find the time it takes for the boat to reach the marker. We can use the equation:
vf = v0 + at
Given:
v0 = 32.5 m/s
a = -2.90 m/s^2
d = 100 m
To find the time, we rearrange the equation:
t = (vf - v0) / a
Substituting the given values, we have:
t = (0 - 32.5) / (-2.90)
Simplifying the expression, we find:
t ≈ 11.21 s
Therefore, it takes approximately 11.21 seconds for the boat to reach the marker.
(b) To find the velocity of the boat when it reaches the marker, we can use the equation:
vf^2 = v0^2 + 2ad
Substituting the given values, we have:
vf^2 = (32.5)^2 + 2(-2.90)(100)
Simplifying the expression, we find:
vf^2 = 1056.25 - 580
vf^2 ≈ 476.25
Taking the square root of both sides, we find:
vf ≈ 21.82 m/s
Since the boat is slowing down, the velocity is negative. Therefore, the velocity of the boat when it reaches the marker is approximately -21.82 m/s.
To learn more about velocity click here
https://brainly.com/question/30265720
#SPJ11
Two cars collide head-on and stick together.
Car A, with a mass of 2000 kg, was initially
moving at a velocity of 10 m/s to the east. Car
B, with an unknown mass, was initially at rest.
After the collision, both cars move together at
a velocity of 5 m/s to the west. What is the
mass of Car B?
The mass of Car B is 2000 kg.
Given details:
Car A, mass = 2000 kg Initial velocity of Car A = 10 m/s (East)
Car B, mass = unknown Initial velocity of Car B = 0 m/s
After the collision, both cars move together
Velocity of both cars = 5 m/s (West)
Let the mass of Car B be m kg.
Using the law of conservation of momentum, the total momentum before the collision = total momentum after the collision.
So,2000 kg × 10 m/s + 0 kg × 0 m/s = (2000 + m) kg × 5 m/s (to the West)
20000 kg·m/s = (2000 + m) kg × 5 m/s (to the West)
20000 kg·m/s = 10000 kg·m/s + 5m kg·m/s
20000 kg·m/s - 10000 kg·m/s = 5m kg·m/s
10000 kg·m/s = 5m kg·m/sm
= 10000/5 kgm
= 2000 kg
Therefore, the mass of Car B is 2000 kg.
Know more about mass here:
https://brainly.com/question/86444
#SPJ8
Wey Lidento calertme fiefs 5. The rotor of an electric generator is rotating at 200rpm when the motor is turn off. Due to frictional effects. the angular deceleration of the rotor after it is turned off is α=−0.015ωrad/s
2
, where ω is the angular velocity in rad/s. How many revolutions does the rotor turn after the motor turned off? How long does it take the motor moved off?
The number of revolutions the rotor turns after the motor is turned off can be calculated by finding the change in angular velocity and converting it to the number of revolutions.
The initial angular velocity is 200 rpm, which can be converted to rad/s by multiplying by 2π/60 to get approximately 20.94 rad/s. The final angular velocity is 0 rad/s since the rotor stops rotating.
The change in angular velocity is Δω = ωf - ωi = 0 - 20.94 = -20.94 rad/s.
To find the number of revolutions, we divide the change in angular velocity by 2π, since one revolution is equal to 2π radians:
Number of revolutions = Δω / (2π) = -20.94 / (2π) ≈ -3.34 revolutions.
Therefore, the rotor turns approximately -3.34 revolutions after the motor is turned off. The negative sign indicates that the rotor rotates in the opposite direction.
The time it takes for the motor to come to a stop can be determined by using the formula:
Δω = αt
Rearranging the equation, we have:
t = Δω / α
Substituting the values, we get:
t = (-20.94 rad/s) / (-0.015 rad/s²) ≈ 1396 seconds.
Therefore, it takes approximately 1396 seconds for the motor to come to a stop.
Learn more about angular velocity here:
https://brainly.com/question/32217742
#SPJ11
what is the gravitational force on a 20 kg satellite
The gravitational force on a 20 kg satellite 150 km above the Earth's surface is about 3000 N.
Here's how to solve for it:
According to Newton's law of gravitation,
the force of attraction between two objects with masses m1 and m2 separated by a distance r is:
F = G(m1m2)/r^2
where G is the gravitational constant (6.674 x 10^-11 Nm^2/kg^2).
In this case, one of the objects is the Earth, which has a mass of about 5.97 x 10^24 kg. The other object is the satellite with a mass of 20 kg. The distance between them is the radius of the Earth plus the altitude of the satellite, which we'll assume is 150 km above the Earth's surface.
So the distance between the centers of the Earth and the satellite is:
r = 6,371 km + 150 km= 6,521 km= 6,521,000 m
Substituting these values into the formula:
F = G(m1m2)/r^2F = (6.674 x 10^-11 Nm^2/kg^2)(20 kg)(5.97 x 10^24 kg)/(6,521,000 m)^2F = 2.99 x 10^3 N ≈ 3000 N
the gravitational force on a 20 kg satellite 150 km above the Earth's surface is about 3000 N.
Learn more about gravitational force from this link:
https://brainly.com/question/72250
#SPJ11
A spherical shell of radius 6.5 m is placed in a uniform electric field with magnitude 6450 N/C. Find the total electric flux through the shell. Answer in units of N⋅m
2
/C 00210.0 points A (3.2 m by 3.2 m) square base pyramid with height of 5.91 m is placed in a uniform vertical electric field of 74.3 N/C. The pyramid encloses no charge. Calculate the electric flux which goes out through one of the pyramid's four slanted surfaces. Answer in units of Nm
2
/C.
The flux through one of the pyramid's four slanted surfaces is given by:Φ = 794.98 N⋅m².
Radius of the shell, r = 6.5 mm
Magnitude of the uniform electric field, E = 6450 N/C
We know that the electric flux (Φ) through a closed surface is given by the formula:
Φ = ∫ E · dA
The electric flux Φ is proportional to the charge enclosed in the surface. Since there is no charge enclosed in the spherical shell, the electric flux through the spherical shell is zero.
Now, let's calculate the electric flux through one of the pyramid's four slanted surfaces.
Given:
Electric field, E = 74.3 N/C
The area of one of the slanted surfaces of the square pyramid is given by the formula:
A = (1/2) × base × height
The slant height of the pyramid can be calculated using the Pythagorean theorem.
Let the length of the base be x. Then the slant height is given by:
l² = (x/2)² + h²
Where h is the height of the pyramid.
Let the slant height be l. Then the area of one of the slanted surfaces is given by:
A = (1/2) × x × l
The total flux through the slanted surface is given by:
Φ = EA
The electric field E and the area A are perpendicular to each other. Therefore, we don't have to worry about the dot product. Thus,
Φ = EA = (74.3 N/C) × (1/2) × 3.2 m × l = (118.88 Nm²/C) × l
We need to find the value of l. Using the Pythagorean theorem,
l² = (3.2/2)² + 5.91²
l = 6.68 m
Thus, the flux through one of the pyramid's four slanted surfaces is given by:
Φ = (118.88 Nm²/C) × (6.68 m)
Φ = 794.98 N⋅m²/C
Answer: 794.98 N⋅m²/C.
To learn more about surfaces, refer below:
https://brainly.com/question/32235761
#SPJ11
