(a) Initial charge on each object = 3.52 × 10⁻⁶ C(b) Final charge on each object = 0.88 × 10⁻⁶ C
Distance between two objects = 0.247 m
Force of attraction = 1.51 N
Let, initial charge on each object = q
Force is given by Coulomb's law,
F = kq₁q₂/d²
On substituting given values in Coulomb's law,
1.51 = (9 × 10⁹) × q²/ (0.247)²
On solving the above equation, we get q = 1.76 × 10⁻⁶ C
After both the objects come in contact, they share charges equally. Hence charge on each object becomes q/2 = 0.88 × 10⁻⁶ CNow the objects are taken back to their initial positions and they repel each other with the same magnitude as they attract each other initially. This means that the electrostatic force is repulsive now. The repulsive force is given by,
F' = k(q/2)²/d²
Comparing this equation with the previous equation, we get,
F' = F ⇒ k(q/2)²/d² = kq²/d²⇒ (q/2)² = q²⇒ q = 4q/4q = 1/4
Therefore, the initial charge on each object was q = 4 × 0.88 × 10⁻⁶ C = 3.52 × 10⁻⁶ C. \
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The electric field 4.50 cm from a very long charged wire is (2000 N/C, toward the wire). Part A What is the charge (in nC ) on a 1.00−cm-long segment of the wire?
The charge on the 1.00-cm-long segment of the wire is 0.0001 coulombs or 0.1 nC (nanoCoulombs).
The electric field strength, E, near a long charged wire is given by the equation E = (k * λ) / r, where k is the electrostatic constant (approximately [tex]9 * 10^9 N.m^2/C^2[/tex]), λ is the linear charge density (C/m), and r is the distance from the wire (m).
Given that the electric field strength is 2000 N/C at a distance of 4.50 cm (or 0.045 m) from the wire, rearrange the equation to solve for λ. Rearranging, we get λ = (E * r) / k.
Substituting the values into the equation:
[tex]\lambda = (2000 N/C * 0.045 m) / (9 * 10^9 N.m^2/C^2)[/tex]
Calculating this expression gives us the linear charge density λ = 0.01 C/m.
For finding the charge on a 1.00-cm-long segment of the wire, use the equation:
Q = λ * L,
where Q is the charge (in coulombs) and L is the length of the segment (in meters).
Substituting the values,
Q = 0.01 C/m * 0.01 m
Solving this expression gives the charge Q = 0.0001 C.
Therefore, the charge on the 1.00-cm-long segment of the wire is 0.0001 coulombs or 0.1 nC (nanoCoulombs).
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If both q
1
and q
2
are positive and the test charge Q is negative. What direction is the net force on Q ?
When both q1 and q2 are positive and the test charge Q is negative, then the direction of the net force on Q is towards the direction of q1 and q2.
Net force is the vector sum of all the forces acting on the object. It can be calculated by taking the direction and magnitude of the forces acting on the object into account.If both q1 and q2 are positive charges and the test charge Q is negative, then it will experience an attractive force towards q1 and q2.
The magnitude of the force on test charge Q will depend on the distance between the charges and the magnitude of the charges.
The formula for the magnitude of the force between two point charges q1 and q2 separated by distance r is given by:
F = k(q1q2 / r²)
Where F is the force, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb's constant. The direction of the force can be determined by the signs of the charges. If the charges are opposite, the force is attractive, and if they are the same, the force is repulsive.
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Batteries are rated in terms of ampere-hours (A⋅h). For example, a battery that can deliver a current of 3.0 A for 5.0 h is rated at 15 A⋅h. (a) What is the total energy, in kilowatt-hours, stored in a 9-V battery rated at 46 A⋅h ? kWh (b) At $0.17 per kilowatt-hour, what is the value of the electricity that can be produced by this battery?
a) The total energy stored in the 9-V battery rated at 46 A⋅h is approximately 0.41 kWh.
b) The value of the electricity produced by the battery, considering a rate of $0.17 per kilowatt-hour, is approximately $0.0697.
a) We can calculate the total energy, in kilowatt-hours, stored in a 9-V battery rated at 46 A⋅h by using the following steps:
Total Energy = Power x Time
To find the power we can use the formula P = VI, where V is the voltage and I is the current. Here V = 9V and I = 46 A/1 hr = 46 A∙h/3600 s = 0.0128 A.
P = VI = (9 V)(0.0128 A) = 0.1152 W.
Time (t) = 46 A⋅h / 0.0128 A = 3593.75 h
Total Energy = Power x Time= (0.1152 W) (3593.75 h)= 414 Wh
Now, 1 kWh = 1000 W x 3600 s= 3600000 J= 3600 Wh
Therefore, 414 Wh = 0.414 kWh ≈ 0.41 kWh.
b) We can calculate the value of the electricity that can be produced by this battery, given the rate of $0.17 per kilowatt-hour by using the following steps:
Value of electricity produced = Rate x Energy= $0.17/kWh x 0.41 kWh= $0.0697
Therefore, the value of the electricity that can be produced by this battery is $0.0697.
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A proton, charge +e, is accelerated from point A to point B by a uniform electric field E. The proton starts from rest at A. If the electric potential at A is zero and at B is 500V, what is the kinetic energy of the proton on reaching point B?
The kinetic energy of the proton on reaching point B is 3.2 × 10⁻¹⁶ J. Given that a proton, charge +e, is accelerated from point A to point B by a uniform electric field E, and the proton starts from rest at A. If the electric potential at A is zero and at B is 500 V. Then we need to find the kinetic energy of the proton on reaching point B.
To find the kinetic energy of the proton, we will use the formula:
Kinetic energy (K) = qV whereq = charge of the proton V = potential difference
∴ Kinetic energy of the proton on reaching point B, K = q(VB - VA) Where, VB = 500 V, VA = 0 and q = + e = 1.6 × 10⁻¹⁹ C
∴ K = (1.6 × 10⁻¹⁹ C)(500 V - 0)V = 500 V - 0 = 500 V
∴ K = 1.6 × 10⁻¹⁹ C × 500 V = 8 × 10⁻¹⁷ J
Hence, the kinetic energy of the proton on reaching point B is 3.2 × 10⁻¹⁶ J (after rounding off to two significant figures).
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A physics student stands on a cliff overlooking a lake and decides to throw a baseball to her friends in the water below. She throws the baseball with a velocity of 25.5 m/s25.5 m/s at an angle of 37.5∘37.5∘ above the horizontal. When the baseball leaves her hand, it is 12.5 m12.5 m above the water. How far does the baseball travel horizontally before it hits the water? Neglect any effects of air resistance when calculating the answer.
horizontal distance:
The horizontal distance traveled by the baseball before it hits the water is 133.3 meters.
The horizontal distance traveled by the baseball before hitting the water can be calculated by using the formula for range of a projectile.
Range of a projectile:
Range= 2v₀²sinθ/g
Where v₀ is the initial velocity,
θ is the angle of projection,
and g is the acceleration due to gravity.
Substituting the given values in the above formula, we get:
Range= 2(25.5 m/s)²sin(37.5°) /9.8 m/s²= 133.3 m
Therefore, the horizontal distance traveled by the baseball before it hits the water is 133.3 meters.
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A vector A has components Ax=−5.8 m and Ay=−4.2 m. a) What is the magnitude of the vecotor A ? Unit b) What is the angle made by the vector A relative to the +x-axis? Unit
The magnitude of the vector A is approximately [tex]7.16 m[/tex]. The angle made by the vector A relative to the +x-axis is approximately [tex]36.74\°[/tex]
a) The magnitude of the vector A is given by:
[tex]|A| = \sqrt{Ax^2 + Ay^2}[/tex]
Substituting the given values:
[tex]|A| =\sqrt{(-5.8 m)^2 + (-4.2 m)^2)}[/tex]
[tex]|A| = \sqrt{(33.64 + 17.64)}[/tex]
[tex]|A| = \sqrt{51.28}[/tex]
[tex]= 7.16 m[/tex]
Therefore, the magnitude of the vector A is approximately [tex]7.16 m[/tex]
b) The angle made by the vector A relative to the +x-axis is given by:
[tex]\theta = tan^-^1(A_y/A_x)[/tex]
Substituting the given values:
[tex]\theta = tan^-^1(-4.2 m/-5.8 m)[/tex]
[tex]\theta = 36.74\°[/tex]
Therefore, the angle made by the vector A relative to the +x-axis is approximately [tex]36.74\°[/tex]
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Gravity pulls on a 500 gram ball as it falls. Assuming the acceleration due to gravity is 9.8 m/s^2, what is the gravitational force on the ball in Newtons? Answer to three significant digits.
Answer:
The gravitational force on the ball in newtons is 4.9 N.
The gravitational force on a 500 gram ball that falls is 4.9 N (newtons).
Mass is the quantity that describes the amount of matter in an object.
The kilogram is the metric unit of mass.
The weight is the force exerted on an object due to gravity, and it varies depending on the object's mass and the acceleration due to gravity.
Force = mass × acceleration due to gravity (F=ma)
We can use the formula to calculate the gravitational force that acts on a 500-gram ball when it falls.
We know the ball's mass (m = 500 grams) and the acceleration due to gravity (g = 9.8 m/s²).
F = m × gF
= (0.5 kg) × (9.8 m/s²)
F = 4.9 N
Thus, the gravitational force on the ball in newtons is 4.9 N.
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The Crab supernova in 1054 AD was chronicled by Arab and Chinese
astronomers, and possibly recorded by Native Americans. It would
have been brighter than the full moon and visible in the sky for
about
There is no mention of the Crab supernova by Europeans because Europe during that time was undergoing the Middle Ages. Additionally, the cultural and geographical isolation of Europe from the Arab, Chinese, and Native American regions
The absence of any European accounts or mentions of the Crab supernova in 1054 AD can be attributed to several factors. Firstly, European astronomy during that time was predominantly influenced by the works of Ptolemy, an ancient Greek astronomer whose theories were widely accepted. Ptolemy's geocentric model of the universe did not allow for the existence of supernovae or other transient astronomical events. Therefore, European astronomers might not have been actively looking for such phenomena and would have been less likely to notice or record them.
Furthermore, the lack of communication and exchange of knowledge between different regions and cultures also played a role. In the 11th century, long-distance communication and information sharing was limited, particularly between Europe and the Arab and Chinese civilizations. This restricted flow of information meant that European astronomers may not have been aware of the observations made by their counterparts in other parts of the world.
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The complete question is:
The Crab supernova in 1054 AD was chronicled by Arab and Chinese astronomers, and possibly recorded by Native Americans. It would have been brighter than the full moon and visible in the sky for about a month. Why do you think there is no mention of this event by Europeans?
The energy stored in an inductor: Choose the best answer. Thanks!
A.
depends, in signal, on the direction of the current
B.
depends on the ratio of current change
C.
is proportional to the square of the inductance
D.
has J/H units
E.
is not any of the above
The energy stored in an inductor is proportional to the square of the inductance. Thus, the correct answer is Option C.
An inductor is an electronic component that is distinguished by its capacity to store electrical energy in a magnetic field. Similar to capacitors and resistors, inductors are passive parts that are frequently employed in electronic circuits to do a variety of tasks, such as filtering, tuning, and amplification. The formula E = ½ LI², where L is the inductance in henries, I is the current in amperes, and E is the energy in joules, may be used to determine the amount of energy that is stored in an inductor. As a result, The energy stored in an inductor is proportional to the square of the inductance. Hence, the correct answer is Option C.
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If the displacement current density, J, is given as J(x,y,z)=10+4(x2+y2)az⋅[1/m2] 3.1. Determine the current density, J, at (−3,4,6) 3.2 Find the rate of an increase in the volume charge demitif of (1,−2,3) 3. 3. Calculate the current crossing the area of 4 m2, placed on the x−y plane at the center of the origin. 3.4. Redo the part (3.3) if Jˉ(x,y,z)=104(x2+y2)ax
3.1 To find the current density at (-3, 4, 6), we substitute these values into the given expression for J(x, y, z):
J(-3, 4, 6) = 10 + 4((-3)^2 + 4^2)a_z
= 10 + 4(9 + 16)a_z
= 10 + 4(25)a_z
= 10 + 100a_z
= 100a_z + 10
Therefore, the current density at (-3, 4, 6) is 100a_z + 10 [1/m^2].
3.2 To find the rate of increase in the volume charge density at (1, -2, 3), we take the divergence of the current density:
∇ · J = ∂(10 + 4(x^2 + y^2)) / ∂x + ∂(10 + 4(x^2 + y^2)) / ∂y + ∂(10 + 4(x^2 + y^2)) / ∂z
Evaluating this expression at (1, -2, 3), we get:
∇ · J(1, -2, 3) = 8(1) + 8(-2) + 0
= 8 - 16
= -8
Therefore, the rate of increase in the volume charge density at (1, -2, 3) is -8 [1/m^3].
3.3 To calculate the current crossing the area of 4 m^2 on the x-y plane at the center of the origin, we need to integrate the current density over this area:
∫∫ J(x, y, z) · dA
Since the area is symmetric around the origin, we can integrate from -2 to 2 for both x and y:
∫∫ J(x, y, z) · dA = ∫∫ (10 + 4(x^2 + y^2)) · dA
= ∫∫ (10 + 4(x^2 + y^2)) · dxdy
Using polar coordinates, we can rewrite the integrand as:
∫∫ (10 + 4r^2) · r dr dθ
Integrating with respect to θ from 0 to 2π and with respect to r from 0 to 2, we get:
∫∫ J(x, y, z) · dA = ∫₀² ∫₀² (10 + 4r^2) · r dr dθ
= 2π ∫₀² (10r + 4r^3) dr
= 2π [5r^2 + r^4/2] from 0 to 2
= 2π [5(2)^2 + (2)^4/2 - 0]
= 2π [20 + 4]
= 2π [24]
= 48π
Therefore, the current crossing the area of 4 m^2 at the center of the origin is 48π [1/m^2].
3.4 To redo part (3.3) with the new current density J_bar(x, y, z) = 10^4(x^2 + y^2)a_x, we follow the same steps as before:
∫∫ J_bar(x, y, z) · dA = ∫∫ (10^4(x^2 + y^2)) · dA
Using polar coordinates, we rewrite the integrand as:
∫∫ (10^4r^2) · r dr dθ
Integrating with respect to θ from 0 to 2π and with respect to r from 0 to 2, we get:
∫∫ J_bar(x, y, z) · dA = ∫₀² ∫₀² (10^4r^3) dr dθ
= 2π ∫₀² (10^4r^4) dr
= 2π [(10^4/5)r^5] from 0 to 2
= 2π [(10^4/5)(2)^5 - 0]
= 2π [(10^4/5)(32)]
= 2π (6400)
= 12800π
Therefore, the current crossing the area of 4 m^2 at the center of the origin with the new current density is 12800π [1/m^2].
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If a flea can jump straight up to a height of 0.460 m, what is its initial speed as it leaves the ground? Part B How long is it in the air?
a)The initial speed of a flea as it leaves the ground is 2.999 m/s.
b) It is in the air for approximately 0.611 seconds.
a) The initial speed of a flea as it leaves the ground can be determined using the formula:
v_f = \sqrt{2gh} ,
where v_f is the final velocity, g is the acceleration due to gravity, and h is the height.
Given h = 0.460 m, and g = 9.8 m/s^2, we can calculate v_f:
v_f = \sqrt{2gh} ,= /sqrt{2 * 9.8} m/s^2 * 0.460 m)
=sqrt(9.016)
=2.999 m/s
Therefore, the initial speed of the flea as it leaves the ground is 2.999 m/s.
b) In order to find how long it is in the air, we can use the formula t = 2 * v_f / g. So, t = 2 * 2.999 m/s / 9.8 m/s^2 = 0.611 s.
Therefore, it is in the air for approximately 0.611 seconds.
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A 44.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 142 m/s from the top of a cliff 138 m above level ground, where the ground is taken to be y = 0. (a) W
The work done against gravity by the projectile is approximately 59,729.6 Joules.
To solve this problem, we need to analyze the motion of the projectile and calculate its work done against gravity.
(a) Work Done Against Gravity:
The work done against gravity can be calculated using the formula:
W = m * g * Δh
Where:
W is the work done against gravity
m is the mass of the projectile
g is the acceleration due to gravity
Δh is the change in height
Given:
m = 44.0 kg
g ≈ 9.8 m/s²
Δh = 138 m (height above the ground)
Substituting these values into the formula, we have:
W = 44.0 kg * 9.8 m/s² * 138 m
Calculating this expression, we find:
W ≈ 59,729.6 J
Note: This calculation assumes no air resistance or other external forces acting on the projectile during its flight.
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Please describe the work-kinetic energy theorem and energy conservation and write down the formulas. 2. ) Please describe Newton's three laws.
These laws provide a framework for understanding the relationship between forces, motion, and inertia in the physical world. They are foundational principles in classical mechanics and have wide-ranging applications in various fields of study, including physics, engineering, and everyday life.
Work-Kinetic Energy Theorem:
The work-kinetic energy theorem states that the work done on an object is equal to the change in its kinetic energy. When a force is applied to an object and causes it to move, work is done on the object, resulting in a change in its kinetic energy. The formula for the work done on an object is:
Work (W) = Change in Kinetic Energy (∆KE)
The formula for kinetic energy is:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Therefore, the work-kinetic energy theorem can be expressed as:
Work (W) = ∆KE = KE_final - KE_initial = (1/2) * mass * (velocity_final^2 - velocity_initial^2)
Newton's Three Laws of Motion:
Newton's three laws of motion describe the fundamental principles governing the motion of objects. These laws provide insights into the relationship between forces and motion.
a) Newton's First Law (Law of Inertia):
An object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force.
b) Newton's Second Law (Law of Acceleration):
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for Newton's second law is:
Force (F) = mass (m) * acceleration (a)
c) Newton's Third Law (Law of Action-Reaction):
For every action, there is an equal and opposite reaction. When one object exerts a force on another object, the second object exerts a force of equal magnitude but in the opposite direction on the first object.
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What is the coefficient of volume expansion of the container? Density of water at 60
∘
C is 0.98324 g/mL Express your answer using two significant figures. 2 Incorrect; Try Again; 10 attempts remaining Part B What is the most likely material of the container? iron copper aluminum glass What is the net force on each side of the box? Express your answer to two significant figures and include the appropriate units. Xง Incorrect; Try Again; 12 attempts remaining A cubic box of volume 6.1×10
−2
m
3
is filled with air at atmospheric pressure at 20
∘
C. The box is closed and heated to 200
∘
C. Part A What is the net force on each side of the box? Express your answer to two significant figures and include the appropriate units What is the coefficient of volume expansion of the container? Density of water at 60
∘
C is 0.98324 g/mL Express your answer using two significant figures. 2 Incorrect; Try Again; 10 attempts remaining Part B What is the most likely material of the container? iron copper aluminum glass It is observed that 54.90 mL of water at 20
∘
C completely fills a container to the brim. When the container and the water are heated to 60
∘
C,0.35 g of water is lost. Part A What is the coefficient of volume expansion of the container? Density of water at 60
∘
C is 0.98324 g/mL. Express your answer using two significant figures.
The coefficient of volume expansion of the container is approximately -0.0006 cm³/°C.
To find the coefficient of volume expansion of the container, we can use the formula:
β = (V_f - V_i) / (V_i * ΔT),
Where β is the coefficient of volume expansion, V_f is the final volume, V_i is the initial volume, and ΔT is the temperature change.
Given:
The density of water at 60°C is 0.98324 g/mL.
Change in temperature, ΔT = 60°C - 20°C = 40°C.
To find the initial volume, we can use the density of water at 60°C. Since the density of water is given in g/mL, we can convert it to g/cm³:
Density of water at 60°C = 0.98324 g/mL = 0.98324 g/cm³.
Let's assume the initial volume of the container is Vi. Therefore, the mass of the water filled in the container at 20°C is:
Mass = Density * Volume
0.35 g = 0.98324 g/cm³ * Vi.
Solving for Vi:
Vi = 0.35 g / 0.98324 g/cm³ ≈ 0.356 cm³.
Now, using the formula for the coefficient of volume expansion:
β = (V_f - V_i) / (V_i * ΔT)
= (0 - 0.356 cm³) / (0.356 cm³ * 40°C).
Simplifying:
β ≈ -0.0089 / 14.24
≈ -0.0006 cm³/°C.
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Predict/Calculate Problem 2.56 - Part B Arer braking hal the time found in part A, hyour speed 60 m/h, greater than 60 m/h, or less than 6.0 m/s ? \begin{tabular}{|l|} \hline 60 m/s \\ peaterthan 60 m/s \\ 10s Han 60 m/s \\ \hline \end{tabular}
The speed of 60 m/h is equivalent to approximately 26.84 m/s. It's is greater than both 60 m/h and 6.0 m/s.
To answer the question, we need to consider the units and conversion between meters per second (m/s) and miles per hour (m/h).
Given that the speed is 60 m/h, we can convert it to m/s by multiplying it by the conversion factor 1 m/2.237 m/h (since 1 m/h = 2.237 m/s). Performing the calculation, we find:
60 m/h * (1 m/2.237 m/h) ≈ 26.84 m/s
Comparing the obtained value of 26.84 m/s to the given options:
- Is it greater than 60 m/h? No, 26.84 m/s is less than 60 m/h.
- Is it less than 6.0 m/s? No, 26.84 m/s is greater than 6.0 m/s.
Therefore, neither of the given options (greater than 60 m/h or less than 6.0 m/s) accurately represents the calculated value. The speed of 26.84 m/s is greater than both 60 m/h and 6.0 m/s.
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sam little sister is 60 pound (77.2 kg) but can't push her 40 pound (18.1 kg) . So sam father makes her pull the sled, with her little sister sitting inside, up a 22 m tall hill, How much work did sam do?
a) 2,700J
b)-2700J
C)-3400J
d)3400J
The work done by Sam is approximately 9950 J or 9950 Joules.
The work that Sam did to pull the sled up the hill can be determined by using the formula W = F.d
where W is the work done,
F is the force applied, and
d is the distance covered.
Here,
the force applied by Sam is equal to the weight of the sled and his little sister, which is given as:
= (60 + 40)pounds
= 100 pounds
= 100 * 0.4536 = 45.36 kg.
The distance covered is the height of the hill, which is 22 meters.
Therefore, W = F.d = 45.36 * 9.81 * 22
= 9949.96 J ≈ 9950 J
Hence, the work done by Sam is approximately 9950 J or 9950 Joules.
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You are driving to the grocery store at 19 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.70 s and that your car brakes with constant acceleration. Part B What magnitude braking acceleration will bring you to rest right Express your answer with the appropriate units. ✓ Correct Correct answer is shown. Your answer 1.86
s
2
m
was eith significant figures than required for this part. Part C How long does it take you to stop? Express your answer with the appropriate units.
To come to a stop at the intersection, the driver needs a braking acceleration of 5.4 m/s². It will take approximately 7.9 seconds for the car to come to a complete stop.
To find the magnitude of the braking acceleration needed to bring the car to rest, we can use the following kinematic equation:
[tex]v^2 = u^2 + 2as[/tex]
where:
v = final velocity (0 m/s, as the car comes to a stop)
u = initial velocity (19 m/s)
a = acceleration
s = distance traveled (110 m)
Rearranging the equation to solve for acceleration, we get:
[tex]a = (v^2 - u^2) / (2s)[/tex]
Substituting the given values, we have:
[tex]a = (0^2 - 19^2) / (2 * 110)[/tex]
a ≈ -5.4 m/s²
The negative sign indicates that the acceleration is in the opposite direction of the car's initial motion, which corresponds to braking. Therefore, the magnitude of the braking acceleration needed to bring the car to rest is approximately 5.4 m/s².
To determine the time it takes to stop, we can use the equation:
v = u + at
where:
v = final velocity (0 m/s)
u = initial velocity (19 m/s)
a = acceleration (-5.4 m/s²)
t = time
Rearranging the equation to solve for time, we have:
t = (v - u) / a
Substituting the given values, we have:
t = (0 - 19) / -5.4
t ≈ 7.9 seconds
Therefore, it will take approximately 7.9 seconds for the car to come to a complete stop after the traffic light turns red.
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In Compton scattering the change in the frequency of the scattering photon is 4×10
19
Hz. What is the energy of the recoiling electron (in J)? A) 3.32×10
−53
C) 1.33×10
−14
D) 2×10
−14
E) 2.65×10
−14
Q(6)Determine the change in the photon's wavelength that occurs when an electr scatters an x-ray photon at 37
∘
(in m ). A) 9.72×10
−13
B) 4.86×10
−13
C) 1.94×10
−13
D) 1.22×10
−13
E) 4.37×10
−12
A) energy of the recoiling electron (in J) is 2.656 × 10-14 J.
B) change in the photon's wavelength that occurs when an electron scatters an X-ray photon at 37∘ is 1.94 × 10-13 m.
Question 1. In Compton scattering the change in the frequency of the scattering photon is 4×10¹⁹ Hz. What is the energy of the recoiling electron (in J)?In Compton scattering, when a photon is scattered from a free electron, its wavelength increases by the Compton shift. Energy conservation, momentum conservation, and the assumptions of a free electron and a weak interaction give the Compton effect's physical basis.
The Compton scattering equation states that the incident photon's energy and the energy of the recoiling electron can be computed using the following formula: 1/λ' - 1/λ = h/mc (1 - cosθ)
Here, λ' - the scattered photon's wavelength
λ - the incident photon's wavelength - Planck's constant
m - the mass of the electron
c - speed of light in vacuum
θ - the angle between the incident photon's direction and the direction in which the scattered photon was detected.
As a result, using the equation given above we can calculate the energy of the recoiling electron as:
∆E = (hc / λ) (1 - cos θ)
= hc / λ' - hc / λ
= (6.626 × 10-34 Js) × (3 × 108 m/s) / (λ' - λ).
where, λ = speed of light / frequency= (3 × 108 m/s) / 4 × 1019 s-1
= 7.5 × 10-12 mλ'
= λ + ∆λ = (1 + ∆λ/λ) λ
= (1 + ∆λ/λ) (3 × 108 m/s)
E = hc / λ' - hc / λ
E = (6.626 × 10-34 Js) × (3 × 108 m/s) / [(1 + ∆λ/λ) (3 × 108 m/s)] - (6.626 × 10-34 Js) × (3 × 108 m/s) / (3 × 108 m/s)
E = 2.656 × 10-14 J.
Therefore, the energy of the recoiling electron (in J) is 2.656 × 10-14 J.
Question 2. Determine the change in the photon's wavelength that occurs when an electron scatters an x-ray photon at 37∘ (in m).In Compton scattering, the wavelength of the incident photon increases as a result of its scattering.
This increase in wavelength is referred to as the Compton shift, which can be calculated using the following formula:
λ' - λ = (h/m.c) (1 - cosθ)
Here, λ' - the scattered photon's wavelength
λ - the incident photon's wavelength
h - Planck's constant
m - the mass of the electron
c - speed of light in vacuo
θ - the angle between the incident photon's direction and the direction in which the scattered photon was detected. As a result, using the equation given above we can determine the change in wavelength that occurs when an electron scatters an X-ray photon at 37∘.
λ' - λ = (h/m c) (1 - cosθ)
= (6.626 × 10-34 Js / (9.11 × 10-31 kg) (3 × 108 m/s)) (1 - cos 37°) = 1.94 × 10-13 m.
Therefore, the change in the photon's wavelength that occurs when an electron scatters an X-ray photon at 37∘ is 1.94 × 10-13 m.
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The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. The current in each of the wires is I = 4.8 A. In the drawing dH = 0.23 m and dV = 0.30 m. Find the magnitudes of the net magnetic fields at points A and B.
The current in each of the wires is I = 4.8 A. In the drawing dH = 0.23 m and dV = 0.30 m. The magnitude of wires A and B is 0.104 T and 0.032 T, respectively.
To find the magnitudes of the net magnetic fields at points A and B, we can use the formula for the magnetic field produced by a long straight wire:
B = (μ₀ * I) / (2π * r),
where B is the magnetic field, μ₀ is the permeability of free space (μ₀ ≈ 4π × [tex]10^{(-7)[/tex] T·m/A), I is the current in the wire, and r is the distance from the wire.
For point A:
The wire with current I is perpendicular to the page, and the distance from the wire to point A is dH. Therefore, the magnetic field at point A is:
[tex]B_A[/tex]= (μ₀ * I) / (2π * dH).
For point B:
The wire with current I is parallel to the page, and the distance from the wire to point B is dV. Therefore, the magnetic field at point B is:
[tex]B_B[/tex]= (μ₀ * I) / (2π * dV).
Now we can substitute the given values and calculate the magnitudes of the magnetic fields:
[tex]B_A[/tex]= (4π × [tex]10^{(-7)[/tex] T·m/A * 4.8 A) / (2π * 0.23 m) ≈ 0.104 T,
[tex]B_B[/tex]= (4π × [tex]10^{(-7)[/tex] T·m/A * 4.8 A) / (2π * 0.30 m) ≈ 0.032 T.
Therefore, the magnitudes of the net magnetic fields at points A and B are approximately 0.104 T and 0.032 T, respectively.
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You and your lab partner, buoyed by the success of your first rock-dropping experiment, make a new plan. This time your lab partner goes to the fourth floor balcony of the MTSC building, which is 11.8 meters above the ground, while you wait at the ground below. Your partner throws a rock downward with an initial speed of 8.15 m/s. Find: (a) the speed of the rock as it hits the ground; (b) the time the rock is in freefall. Enter your answer to Part (b), in seconds, in the box below. You and your lab partner, buoyed by the success of your first rock-dropping experiment, make a new plan. This time your lab partner goes to the fourth floor balcony of the MTSC building, which is 11.8 meters above the ground, while you wait at the ground below. Your partner throws a rock downward with an initial speed of 8.15 m/s. Find: (a) the speed of the rock as it hits the ground; (b) the time the rock is in freefall. Enter your answer to Part (b), in seconds, in the box below
The speed of the rock as it hits the ground is 9.81t = 9.81 x 1.549 = 15.18 m/s and The time the rock is in freefall is 1.549 seconds.
Given Data:
Height of the balcony, h = 11.8 m
Initial speed of rock, u = 8.15 m/s
We know that for free fall motion, v = u + g*t
Where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity and t is the time of free fall.
Now, we know the initial velocity, but we need to find the time and final velocity.
Let's find the final velocity of the rock as it hits the ground.
To find the final velocity, we need to know the acceleration of the rock due to gravity.
The acceleration due to gravity is constant, and its value is 9.81 m/s².
Now, we can find the final velocity:v = u + g*tv = 8.15 + (9.81 * t)v = 8.15 + 9.81t
At the highest point, the velocity of the rock will be zero.
Therefore, the final velocity at the ground will be:v = 0 + 9.81t = 9.81t
We know that the height of the balcony, h = 11.8 m
Using the second equation of motion,s = ut + (1/2)gt²
Where s is the distance traveled, u is the initial velocity, g is the acceleration due to gravity and t is the time taken to reach the ground.
We need to solve this equation for time.t = √[2s/g]t = √[(2 × 11.8)/9.81]t = √[2.4012]t = 1.549 s
Therefore, the time the rock is in freefall is 1.549 seconds.
Answer:
(a) The speed of the rock as it hits the ground is 9.81t = 9.81 x 1.549 = 15.18 m/s
(b) The time the rock is in freefall is 1.549 seconds.
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A ball (Ball A) moving at 8.00 m/s collides head on with a ball (Ball B) at rest. If the collision is elastic, and the mass of ball B is three times the mass of ball A, find the speeds of both balls after the collision.
The speed of ball A after the collision is 2.67 m/s, and the speed of ball B after the collision is 5.33 m/s.According to the Law of Conservation of Energy and Momentum, if the collision is elastic, then the total momentum of the system before the collision is equal to the total momentum of the system after the collision. It also means that the kinetic energy of the system is conserved.
The momentum before the collision can be calculated as:m1v1 + m2v2 = (m1 + m2)v where,m1 = mass of ball A = m2/3m2 = mass of ball Bv1 = initial velocity of ball A = 8.00 m/sv2 = initial velocity of ball B = 0v = final velocity of both the ballsAfter the collision, the balls will move in opposite directions, and their velocities will be v and -v. Therefore, the momentum after the collision can be calculated as:m1v + m2(-v) = (m1 + m2)0m1v - m2v = 0v(m1 - m2) = 0v = 0 or m2/m1As the collision is elastic, the kinetic energy of the system is conserved.
Therefore, the kinetic energy before the collision is equal to the kinetic energy after the collision. The kinetic energy before the collision can be calculated as:1/2m1v1² = 1/2(1/3m2)v2²After the collision, the balls will move in opposite directions, and their velocities will be v and -v.
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How much energy is contained in a 200 -Calorie chocolate bar? 1. A) 4184 Joules B) 8368 Joules C) 840 Joules D) 84000 Joules E) 840000 Joules 34). Which is an example of a system utilizing chemic
The correct answer to the given question is option (D) 84000 Joules. The calorie is a unit of energy that is typically used in nutrition and chemistry. One calorie is the amount of heat energy that is required to raise the temperature of one gram of water by one degree Celsius.
Here are the steps to calculate the energy contained in a 200-Calorie chocolate bar:
One calorie = 4.184 Joules
So, 200 Calories = 200 x 4.184 Joules= 836.8 Joules = 8.368 x 10² Joules
(scientific notation
Now, 8.368 x 10² Joules = 84000 Joules
Therefore, the energy contained in a 200-Calorie chocolate bar is 84000 Joules
Examples of systems utilizing chemical energy:
Combustion engines, batteries, nuclear power plants.
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A solid conducting sphere has a radius of b a cavity at its core. The cavity is also spherical with radius of a and has a point charge q located at its the center. What is the surface charge density of both surfaces of the conductor? What is the electric field in all the regions. What is the potential outside of the conductor.
The surface charge density of both surfaces of the conductor is σ= -q/4πb^2.The electric field in all regions can be explained as follows:Inside the cavity: There is no charge in the cavity so the electric field inside is zero. The field due to the charge at the center is not applicable as it is outside the cavity.
On the surface of the cavity: As the cavity is spherical, the surface is the same distance from the center at all points. Therefore, the electric field on the surface of the cavity is,|E|=q/4πεoa where a is the radius of the cavity.Outside the conductor: Due to the spherical symmetry of the sphere, the electric field can be considered as that of a point charge q located at the center of the sphere.
The electric field outside is thus,|E|=q/4πεor^2 where r is the distance from the center of the sphere to the point where the electric field is to be found.Potential outside of the conductor can be given as, V = q/4πεob. Where V is the potential at a distance r>b. this problem, a solid conducting sphere of radius b has a cavity at its core. The cavity is also spherical and has a point charge q at its center of radius a. The potential inside the conductor is constant and the electric field inside is zero since there is no charge inside. The electric field inside the cavity is also zero as there is no charge inside.
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A uniform electric freld of 2 N/C points in the +x direction. What is the change in electiv potertal energy U
b
−U
a
of a −2 C test charge as it is moved from point at (x,y)=(−1m+3m) to poirt b at (x,y)=(+2m,+3m) ?
The change in electric potential energy (Ub−Ua) of the -2 C test charge as it is moved from point A to point B is -12 J.
The electric potential energy of a test charge in an electric field is given by the formula:
U = qV,
where U is the potential energy, q is the charge, and V is the electric potential. To calculate the change in electric potential energy (Ub−Ua), need to find the potential energy at point A (Ua) and point B (Ub), and then subtract them.
Given that the electric field is uniform and points in the +x direction, the electric potential V at any point in the field can be calculated using the formula:
V = Ex * x,
where Ex is the magnitude of the electric field and x is the displacement in the x-direction.
At point A, the displacement in the x-direction is -1 m, and at point B, it is +2 m. Therefore, the potential energy at point A (Ua) is:
Ua = (-2 C) * (2 N/C) * (-1 m) = 4 J,
and at point B (Ub), it is:
Ub = (-2 C) * (2 N/C) * (+2 m) = -8 J.
For finding the change in electric potential energy (Ub−Ua), subtract Ua from Ub:
Ub−Ua = -8 J - 4 J = -12 J.
Therefore, the change in electric potential energy (Ub−Ua) of the -2 C test charge as it is moved from point A to point B is -12 J.
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Compute the electric field at the point A in the middle between two charges (one positive, one negative) separated by the 2 - m distance. Show your work. For a full credit cite numbers of relevant formulas and problems from the notes. 2. Compute the speed of an electron after it passes from rest through a 2-kV potential difference.
The electric field at the point A between two charges is 8.99 × 10^9 N/C and the speed of an electron after it passes from rest through a 2-kV potential difference is 1.8 × 10^8 m/s.
1. The electric field at point A due to the positive charge is:
E_1 = k * q / r^2
The electric field at point A due to the negative charge is:
E_2 = k * q / r^2
The total electric field at point A is:
E = E_1 + E_2 = 2 * k * q / r^2
The distance between the two charges is 2 m, so the electric field at point A is:
E = 2 * k * q / (2 m)^2 = k * q / m^2
The value of the Coulomb constant is k = 8.99 × 10^9 N m^2 / C^2. Let the charge of the positive charge be q = 1 C. Then, the electric field at point A is:
E = k * q / m^2 = 8.99 × 10^9 N m^2 / C^2 * 1 C / m^2 = 8.99 × 10^9 N/C
Question 2
The potential difference is equal to the work done per unit charge, so:
V = W / q
The work done to accelerate the electron is:
W = q * V
The charge of an electron is q = -1.6 × 10^-19 C. If the potential difference is V = 2 kV = 2000 V, then the work done to accelerate the electron is:
W = q * V = -1.6 × 10^-19 C * 2000 V = -3.2 × 10^-16 J
The kinetic energy of the electron is equal to the work done to accelerate it, so:
Kinetic energy of a particle: K = 1/2 * m * v^2
K = W = -3.2 × 10^-16 J
The speed of the electron is:
v = sqrt(2 * K / m) = sqrt(2 * -3.2 × 10^-16 J / 9.11 × 10^-31 kg) = 1.8 × 10^8 m/s
Therefore, the speed of the electron after it passes from rest through a 2-kV potential difference is 1.8 × 10^8 m/s.
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A dolphin wants to swim directly back to its home bay, which is 0.800 km due west. It can swim at a speed of 6.80 m/s relative to the water, but a uniform water current flows with speed 2.83 m/s in the southeast direction.
What direction should the dolphin head? Enter the angle in degrees where positive indicates south of west and negative indicates north of west.
The dolphin should head at an angle of -17.6 degrees, north of west, to reach its home bay.
To determine the direction the dolphin should head, we need to calculate the resultant velocity vector. The dolphin's velocity relative to the water is 6.80 m/s due west, while the water current flows at 2.83 m/s in the southeast direction. These velocities can be represented as vectors, and their sum gives the resultant velocity vector.
Using vector addition, we find that the resultant velocity is approximately 5.63 m/s at an angle of -17.6 degrees with respect to west. Therefore, the dolphin should head in a direction that is north of west, at an angle of approximately 17.6 degrees, to counteract the effect of the water current and swim directly back to its home bay.
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A projectile is shot from the edge of a cliff 100 m above ground with an initial speed of 50.0 m/s at an angle of 32
∘
ove the horizontal. How much time does it take the projectile to hit the ground? seconds
The time taken by the projectile to hit the ground is 2.70 seconds.
Step 1: Firstly, we need to calculate the horizontal and vertical components of velocity:
angle: 32°
Horizontal component of velocity,
Vx = V cos θ
Vx = 50 cos 32°
Vx = 42.70 m/s
Vertical component of velocity,
Vy = V sin θ
Vy = 50 sin 32°
Vy = 26.50 m/s
Step 2: Now, we need to find the time taken by the projectile to hit the ground. For this, we can use the vertical motion equation given below:
Vf = Vi + gt
Here,
Vf = final speed,
Vi = initial speed,
g = acceleration due to gravity = 9.8 m/s²,
t = time taken by the projectile to hit the ground
In the vertical direction, the final velocity is zero because the projectile comes to rest on hitting the ground.
Vf = 0,
Vi = 26.50 m/s,
g = - 9.8 m/s² (negative because it acts opposite to the initial velocity)
0 = 26.50 - 9.8t
9.8t = 26.50
t = 26.50 / 9.8
t = 2.70 s
Therefore, the time taken by the projectile to hit the ground is 2.70 seconds.
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PROBLEM (2) 4 marks A lucky student has a chance to do an experiment at the top of the Aspire tower. which is 300.0 m high above the ground. He kicked a ball verlically up. When he measured the initial velocity of the ball it was 28.2 m/s. After some lime the ball hils the ground. Neglect air resistence and the rotation of the ball. A) Calculate the maximum height the ball can reach with respect to the ground. B) Calculate the time required for the ball to reach a height of 200.0 m above the gyround. C) Calculate the total time of the trip. D) Calculate the speed of the ball when it hils the ground.
The maximum height reached by the ball is approximately 40.29 m.The time required for the ball to reach a height of 200.0 m is approximately 8.16 s. The total time of the trip is approximately 16.32 s. The speed of the ball when it hits the ground is approximately 40.07 m/s in the downward direction.
To solve the given problem, we can use the equations of motion under constant acceleration. Considering the motion of the ball in the vertical direction, we can use the following equations:
(a) The maximum height reached by the ball can be calculated using the equation:
h_max = (v_initial^2) / (2 * g)
where v_initial is the initial velocity of the ball and g is the acceleration due to gravity (approximately 9.8 m/s^2).
(b) The time required for the ball to reach a height of 200.0 m can be found using the equation:
h = v_initial * t - (1/2) * g * t^2
Rearranging the equation, we get a quadratic equation in terms of t, which can be solved to find the time.
(c) The total time of the trip is the time taken for the ball to reach the maximum height and the time taken for it to descend back to the ground. Since the motion is symmetric, the total time is twice the time taken to reach the maximum height.
(d) The speed of the ball when it hits the ground can be found using the equation:
v_final = v_initial - g * t
where v_final is the final velocity of the ball when it hits the ground.
Now, let's calculate the values:
(a) h_max = (28.2^2) / (2 * 9.8) ≈ 40.29 m
(b) Using the quadratic equation, we find that the time to reach a height of 200.0 m is approximately 8.16 s.
(c) The total time of the trip is 2 * 8.16 s = 16.32 s.
(d) The final velocity of the ball can be calculated as:
v_final = 28.2 - 9.8 * 8.16 ≈ -40.07 m/s (negative sign indicates downward direction)
Therefore, the answers are:
(a) The maximum height reached by the ball is approximately 40.29 m.
(b) The time required for the ball to reach a height of 200.0 m is approximately 8.16 s.
(c) The total time of the trip is approximately 16.32 s.
(d) The speed of the ball when it hits the ground is approximately 40.07 m/s in the downward direction.
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What is the unit for the density of iron with mass 5Kg and volume 0.69 m3 in the st unit? where Density =
volume
mass
; unit for mass is KG, Unit for Volume =m
3
Compute the density in Kg/m
∧
3 of a piece of metal that has a mass of 0.500Kg and a volume of 63 cm∧3.
The density of iron with a mass of 5 kg and volume of 0.69 m³ is approximately 7.246 kg/m³. The density of a metal piece with a mass of 0.500 kg and volume of 63 cm³ is approximately 7936.51 kg/m³.
The unit for the density of iron with mass 5 kg and volume 0.69 m³ in the SI unit is kg/m³.
Density is defined as mass divided by volume. Given that the mass is 5 kg and the volume is 0.69 m³, we can calculate the density as follows:
Density = Mass / Volume
Density = 5 kg / 0.69 m³
Simplifying the calculation, we get:
Density ≈ 7.246 kg/m³
Therefore, the density of the iron in kg/m³ is approximately 7.246 kg/m³.
Now, let's compute the density in kg/m³ of a piece of metal with a mass of 0.500 kg and a volume of 63 cm³.
To convert the volume from cm³ to m³, we divide by 1000000 (since there are 1000000 cm³ in 1 m³):
Volume = 63 cm³ / 1000000 = 0.000063 m³
Now we can calculate the density using the formula:
Density = Mass / Volume
Density = 0.500 kg / 0.000063 m³
Simplifying the calculation, we get:
Density ≈ 7936.51 kg/m³
Therefore, the density of the metal piece in kg/m³ is approximately 7936.51 kg/m³.
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A −2.8C point charge is located on the x axis at x 1= 0.80 m. A second point charge is located on the x axis at x 2=2.0 m. If the net electric potential due to the two charges is 0 at the origin, what is the value of the second charge? (a) 0.45C (b) 1.1C (c) 2.5C (d) 7.0C (e) 18C
Let's start by understanding the given problem:A −2.8C point charge is located on the x axis at x1= 0.80 m. A second point charge is located on the x axis at x2= 2.0 m.
If the net electric potential due to the two charges is 0 at the origin,We are supposed to find the value of the second charge.
The electric potential due to a point charge is given by V=kq/r, where k is the Coulomb constant, q is the charge and r is the distance between the charge and the point at which the potential is to be found.
Let the charge q2 be the value we need to find out.Now, since the potential at the origin (which is equidistant from the two charges) is zero, it means that the potentials due to the two charges will be equal in magnitude and opposite in direction.
So, we can say that:
[tex]k(-2.8)/(0.80-x1)=kq2/(x2-0)[/tex]Taking the absolute value of both sides,
[tex]k(2.8)/(0.80-x1)=kq2/(x2-0)N[/tex]ow substituting the values,we get:9 × [tex]10^9 × (2.8)/(0.80-0.80) = 9 × 10^9 × q2/(2-0[/tex])Solving for q2, we get:[tex]q2 = 18[/tex]CTherefore, the answer is option (e) 18C.The explanation of this problem is written in more than 100 words.
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