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

To determine the time it takes for the current through the coil to drop from 90% to 10% of the maximum current, we need to consider the time constant of the RL parallel circuit formed by the resistor and the inductance coil.

The time constant (τ) of an RL circuit is given by the formula:

τ = L / R

τ = (0.001H) / 10Ω

= 0.0001 seconds

The time constant is 0.0001 seconds or 0.1 ms (milliseconds).

To determine the time it takes for the current through the coil to drop from 90% to 10% of the maximum current, we need to find the time it takes for the current to decrease by a factor of 10.

The time it takes for the current to decrease by a factor of 10 is approximately equal to 2.3 times the time constant (τ).

Therefore, the time it takes for the current to drop from 90% to 10% is:

t = 2.3 * τ

= 2.3 * 0.1 ms

≈ 0.23 ms

So, it takes approximately 0.23 ms for the current through the coil to drop from 90% to 10% of the maximum current.

Learn more about current here : brainly.com/question/31315986
#SPJ11

While the butterfly may be rare and fragile, it does not have a great enough mass to exert a significant force in a collision with a large, fast-moving object like a car. The car has a much greater mass, and therefore a much greater force, than the butterfly.

The car exerts a greater force than the butterfly in this scenario. This is because force is determined by the mass of an object and the acceleration that is applied to it, as defined by Newton's second law of motion. F=ma, where F is force, m is mass, and a is acceleration.

In this situation, the car has a much greater mass than the butterfly, which means that it requires a greater force to accelerate or decelerate it compared to the butterfly.Therefore, when the car hits the butterfly, it applies a force that is much greater than the force that the butterfly applies back.

The butterfly's force is so small that it is negligible compared to the car's force. Additionally, the car is traveling at a high speed, which increases its momentum and therefore the force it exerts on the butterfly when it hits it. This is due to the fact that force and momentum are directly proportional to one another.

In summary, while the butterfly may be rare and fragile, it does not have a great enough mass to exert a significant force in a collision with a large, fast-moving object like a car. The car has a much greater mass, and therefore a much greater force, than the butterfly.

For more such questions on butterfly, click on:

https://brainly.com/question/22952049

#SPJ8

Both the car and the butterfly exert equal force on each other according to Newton's Third Law of Motion. However, due to the car's significantly larger mass and speed, the effect of this force is drastically different for the two objects.

The force applied by the butterfly and the car on each other will be equal according to Newton's Third Law of Motion. This law states that every action has an equal and opposite reaction. So, when the car hits the butterfly, the butterfly also applies an equal force back to the car.

However, because of the vast difference in the mass and speed (momentum) of the car and the butterfly (nearly 0 for the butterfly), the impact of this force on the butterfly will be far more severe, causing it to smash against the windshield, but it won't affect the car to any noticeable extent.

https://brainly.com/question/2057822

#SPJ2

The electric potential energy of the system is

The acceleration of sphere A isa = [tex]F/m= (5.63\times10^{-2})/7.11\times10^{-3}= 7.92[/tex]m/s²

The acceleration of sphere B will be the same as the acceleration of sphere A, but in the opposite direction.

The speed of sphere A isv = u + at= 0 + 7.92×0.166= 1.31 m/s

The speed of sphere B will be the same as the speed of sphere A, but in the opposite direction.

(a) Electric potential energy of the system: We can calculate the electric potential energy of the system using the formula, U = q²/(4πε₀d)Where, q is the charge of each sphere, d is the separation distance between two spheres, and ε₀ is the permittivity of free space.

So, the electric potential energy of the system isU = [tex]6.67^{2} \times(10^{-6})^{2} /(4\times3.14\times8.85\times10^{-12}\times0.876)= 2.41\times10^{-3} J[/tex]

(b) Acceleration of sphere A:When the string is cut, the spheres will experience a force of attraction towards each other, so they will move towards each other.

We can calculate the acceleration of sphere A using the formula,F = maWhere, F is the force acting on sphere A due to the attraction with sphere B.

m is the mass of sphere A.a is the acceleration of sphere A.

So, the force acting on sphere A isF = k(q²/d²)= [tex](9\times10^9)\times(6.67\times10^-6)^{2} /(0.876)^{2} = 5.63\times10^{-2} N[/tex]

Thus, the acceleration of sphere A isa = F/m=  [tex]F/m= (5.63\times10^{-2})/7.11\times10^{-3}= 7.92[/tex] m/s²

(c) Acceleration of sphere B:The acceleration of sphere B will be the same as the acceleration of sphere A, but in the opposite direction.

(d) Speed of sphere A:We can calculate the speed of sphere A using the formula, v = u + at Where, u is the initial velocity of sphere A, which is zero.

v is the final velocity of sphere A.

t is the time taken by sphere A to reach the final velocity.a is the acceleration of sphere A, which we have already calculated.

So, the time taken by sphere A to reach the final velocity ist = √(2d/a)= √(2×0.876/7.92)= 0.166 s

Thus, the speed of sphere A isv = u + at= 0 + 7.92×0.166= 1.31 m/s(e) Speed of sphere B:

The speed of sphere B will be the same as the speed of sphere A, but in the opposite direction.

For more questions on   electric potential energy

https://brainly.com/question/26978411

#SPJ8

Heat is 87.89°F

Airflow rate calculation:

Given: Cross-sectional area of the duct (A) = 2 sq ft, Velocity of the air (V) = 300 ft/min

Airflow rate (Q) = A * V = 2 * 300 = 600 cfm (cubic ft/min)

Heat added to the air calculation:

Given: Mass flow rate (m) = 0.083 lb/ft³, Temperature differential (t2 - t1) = 5°F, Specific heat (q) = 0.24 Btu/lb.°F

Mass flow rate (m) = (0.083 * 2 * 300) = 49.8 lb/hr

Heat added to the air (Q) = m * A * (t2 - t1) = 49.8 * 5 * 0.24 = 59.76 BTU/hr

Wattage input to the heater:

Given: Voltage (V) = 110 volts

Wattage input to the heater (W) = V * A = 2 * 110 = 220 watts

Conversion of heat added to watts:

Conversion: 1 kW = 3412 BTU/hr, 1 hour = 3600 seconds

Heat added to the air in watts = 59.76 * (1 kW/3412 BTU/hr) * 3600 sec/hr = 0.052 kW

Heat added per unit mass of air calculation:

Heat added per unit mass of air (q) = Q/m = 59.76/49.8 = 1.2 BTU/lb.°F

Calculation of temperature difference at different velocities:

For V = 0 ft/min:

Heat added (Q) = 0 cfm, Power input (W) = 0 watts, Heat per unit mass (q) = 0.69 Btu/lb.°F

Temperature difference (t2 - t1) = W/[(m)(q)] = 0/[(49.8)(0.69)] = 0°F

For V = 150 ft/min:

Heat added (Q) = 300 cfm, Power input (W) = 330 watts, Heat per unit mass (q) = 0.69 Btu/lb.°F

Temperature difference (t2 - t1) = W/[(m)(q)] = 330/[(49.8)(0.69)] = 8.94°F

t2 = t1 + (t2 - t1) = 70 + 8.94 = 78.94°F

For V = 300 ft/min:

Heat added (Q) = 600 cfm, Power input (W) = 660 watts, Heat per unit mass (q) = 0.69 Btu/lb.°F

Temperature difference (t2 - t1) = W/[(m)(q)] = 660/[(49.8)(0.69)] = 17.89°F

t2 = t1 + (t2 - t1) = 70 + 17.89 = 87.89°F

The graph of Temperature difference vs. Velocity at constant amperage of 3 is shown below:The increase in temperature difference is directly proportional to the increase in velocity.

As the airflow rate increases, so does the temperature difference across the heater. Since we're using a constant amperage of 3, the power input to the heater remains constant.

As a result, the rate of heat transfer remains constant. The temperature difference between the air and the heater will increase as the rate of airflow increases because more air is being heated over the same period. The accuracy of the system is affected by several factors such as the thermocouple's accuracy, heat losses, etc.

learn more about Heat on

https://brainly.com/question/30603212

#SPJ11

To calculate the base current (IB) required to switch a resistive load of 10mA, we can use the formula:

IB = (IL) / (Beta)

where IL is the load current and Beta is the DC current gain of the transistor.

Given that IL = 10mA and Beta = 100, we can substitute these values into the formula:

IB = (10mA) / (100)

IB = 0.1mA

So, the base current required to switch the load is 0.1mA.

To find the value of the base resistor (RB) required to switch the load fully "ON" when the input terminal voltage exceeds 5V, we can use Ohm's Law:

RB = (Vin - VBE) / IB

where Vin is the input terminal voltage and VBE is the base-emitter voltage of the transistor.

Given that Vin > 5V and assuming VBE = 0.7V for a silicon BJT, we can substitute these values into the formula:

RB = (Vin - 0.7V) / 0.1mA

Let's say Vin = 10V, then

RB = (10V - 0.7V) / 0.1mA

RB = 9.3V / 0.1mA

RB = 93kΩ

So, the value of the base resistor required to switch the load fully "ON" when the input terminal voltage exceeds 5V is 93kΩ.

(ii) To find the value of the base current into the transistor with a DC base bias voltage (VB) of 20V and an input base resistor (RB) of 50kΩ, we can use Ohm's Law:

IB = (VB - VBE) / RB

Given that VB = 20V and RB = 50kΩ, and assuming VBE = 0.7V for a silicon BJT, we can substitute these values into the formula:

IB = (20V - 0.7V) / 50kΩ

IB = 19.3V / 50kΩ

IB = 0.386mA

So, the value of the base current into the transistor is 0.386mA.

To find the minimum base current required to turn the transistor fully‐ON (saturated) for a load that requires 500mA of current when the input voltage is increased to 25.0V, we can use the formula:

IB = (IL) / (Beta)

Given that IL = 500mA and Beta = 100, we can substitute these values into the formula:

IB = (500mA) / (100)

IB = 5mA

So, the minimum base current required to turn the transistor fully‐ON (saturated) is 5mA.

Finally, to calculate the new value of RB, we can use Ohm's Law:

RB = (Vin - VBE) / IB

Given that Vin = 25V and assuming VBE = 0.7V for a silicon BJT, we can substitute these values into the formula:

RB = (25V - 0.7V) / 5mA

RB = 24.3V / 5mA

RB = 4.86kΩ

So, the new value of RB is 4.86kΩ.

To know more about current visit:

https://brainly.com/question/15141911

#SPJ11

The x value when the module of the force is max is [tex]a / \sqrt[3]{2}[/tex].

Given conditions:

Two punctual charges equal to Q are situated on the y-axis.

On y = a and -a. Let the distance between any point on the y-axis and the point of charge be x.

The electrical force exerted on a charge q situated at (x,0) is

[tex]F = k q Q / x^2[/tex]

The force vector for a charge q is directed along the x-axis.

If the force F is the greatest for a certain value of x, then the derivative of F with respect to x equals zero:

[tex]F' = -2 k q Q / x^3[/tex]

= 0

=> [tex]x =\sqrt[3]{2 k q Q} / F(x)[/tex]

Here, k is Coulomb's constant,

q and Q are charge values.

We have also stated that the force vector is directed along the x-axis. A possible method of solving the problem is to add the contribution of forces from two charges to determine the overall electrical force F acting on charge q.

Find the electrical force acting on charge q.

Let's calculate the electric force acting on a unit charge located at point P = (x, 0, 0) by the charge located at the point A = (0, a, 0).

F1 = (kqQ / (a² + x²))i

Let's calculate the electric force acting on a unit charge located at point P = (x, 0, 0) by the charge located at the point B = (0, -a, 0).

F2 = (kqQ / (a² + x²))i

We get the resultant force by adding F1 and F2:

F = F1 + F2

= 2(kqQ / (a² + x²))i

The expression of the electrical force on charge q becomes:

F = (2 k q Q / x^2)i

To find the maximum value of F, we'll differentiate the expression of F with respect to x and equate the derivative to zero:

(dF/dx) = (-4 k q Q / x^3)i

=0

=> [tex]x = \sqrt[3]{2 k q Q / F(x)}[/tex]

Therefore, [tex]x = \sqrt[3]{2 k q Q} ) / (2 k q Q / a^2)[/tex]

[tex]=a / \sqrt[3]{2}[/tex]

Thus, the x value when the module of the force is max is [tex]a / \sqrt[3]{2}[/tex].

To know more about force visit

https://brainly.com/question/30507236

#SPJ11

Approximately 6.5312 meganewtons (MN) of thrust is needed to launch the 667,267 kg rocket, assuming the force of thrust is just enough to overcome the weight of the rocket.

To determine the amount of thrust needed to launch a rocket, we need to consider Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a. In this case, the force required is the upward thrust needed to overcome the weight of the rocket, which is equal to the gravitational force acting on it. The gravitational force is given by the formula: F_gravity = m * g, where g represents the acceleration due to gravity (approximately 9.8 m/s^2 on Earth). So, to launch the rocket, we need a thrust equal to its weight, which is F_thrust = m * g. Given that the mass of the rocket (m) is 667,267 kg, we can calculate the thrust required: F_thrust = 667,267 kg * 9.8 m/s^2 = 6,531,241.6 N.To convert this value to meganewtons (MN), we divide by 1 million: F_thrust = 6,531,241.6 N / 1,000,000 = 6.5312 MN. Therefore, approximately 6.5312 meganewtons (MN) of thrust is needed to launch the 667,267 kg rocket, assuming the force of thrust is just enough to overcome the weight of the rocket.

To learn more about force:

https://brainly.com/question/13191643

#SPJ11

To determine the y-position of a projectile launched, we can use the equations of projectile motion. we get y = (13.8 m/s × sin(34°)) × t - (1/2) × (9.8 m/s²) × t².

To find the y-position of the projectile when x = 7 meters, we need to analyze the projectile motion. The initial velocity can be split into its horizontal and vertical components using trigonometry.

The horizontal component of the initial velocity is given by v_x = v × cos(θ), where v is the initial speed and θ is the launch angle. Substituting the values, we get v_x = 13.8 m/s × cos(34°).

The vertical component of the initial velocity is given by v_y = v × sin(θ), which becomes v_y = 13.8 m/s × sin(34°).

Since there is no vertical acceleration, the time taken to reach x = 7 meters horizontally will be the same as the time taken to reach the corresponding y-position.

Using the equation x = v_x × t, we can solve for t. Thus, t = x / v_x.

Substituting the given values, we have t = 7 m / (13.8 m/s × cos(34°)).

Now that we have the time, we can find the vertical displacement using the equation y = v_y × t - (1/2) × g × t², where g is the acceleration due to gravity.

Plugging in the values, we get y = (13.8 m/s × sin(34°)) × t - (1/2) × (9.8 m/s²) × t²

Finally, by substituting the calculated value of t, we can find the y-position of the projectile when x = 7 meters. Rounding the answer to one decimal place will provide the final result.

To learn more about projectile, click here brainly.com/question/2818076

#SPJ11

For a parallel-plate capacitor with a capacitance of 7.50 pF and a plate separation of 1.90 mm, the maximum magnitude of charge that can be placed on each plate is 1.425 nC when the electric field is not to exceed 300×[tex]10^4[/tex] V/m.

The capacitance of a parallel-plate capacitor is given by the formula C = ε₀A/d, where C is the capacitance, ε₀ is the permittivity of free space (ε₀ ≈ 8.85 × [tex]10^{-12[/tex] F/m), A is the area of each plate, and d is the separation between the plates.

In this case, the given capacitance is 7.50 pF (picofarads) and the plate separation is 1.90 mm (millimeters). To find the maximum charge that can be placed on each plate, we can rearrange the capacitance formula as Q = C⋅V, where Q is the charge and V is the voltage across the plates.

For part A, when the electric field is not to exceed 100×[tex]10^4[/tex] V/m, we can calculate the maximum voltage by rearranging the formula for electric field as E = V/d. Substituting the given electric field limit, we have V = E⋅d = (100×[tex]10^4[/tex] V/m) × (1.90 mm) = 190×[tex]10^4[/tex] V.

Plugging this value into the charge formula, we find Q = C⋅V = (7.50×[tex]10^{-12[/tex] F) × (190×[tex]10^4[/tex] V) = 1.425 nC.

For part B, when the electric field is not to exceed 300×[tex]10^4[/tex] V/m, we repeat the process and find V = E⋅d = (300×[tex]10^4[/tex] V/m) × (1.90 mm) = 570×[tex]10^4[/tex] V. Plugging this value into the charge formula, we obtain Q = C⋅V = (7.50×[tex]10^{-12[/tex] F) × (570×[tex]10^4[/tex] V) = 4.275 nC.

Learn more about capacitance here:

https://brainly.com/question/31871398

#SPJ11

As per the given conditions of the problem, A child sprays her sister with water from a garden hose.

The water is supplied to the hose at a rate of 0.117 L/s, and the diameter of the nozzle is 5.95 mm.

We need to determine the speed at which the water exits the nozzle.

To determine the speed v at which the water exits the nozzle, we need to apply Bernoulli's principle.

According to Bernoulli's principle, the pressure of a fluid decreases as its velocity increases, keeping the total energy constant.

The Bernoulli equation is written as:

P₁ + ρgh₁ + 1/2ρv₁² = P₂ + ρgh₂ + 1/2ρv₂²

where:

P₁ = Pressure at Point 1v₁ = Velocity at Point 1h₁ = Height at Point 1ρ = Density

g = Acceleration due to gravity

P₂ = Pressure at Point 2v₂ = Velocity at Point 2h₂ = Height at Point 2

Assuming that the hose is horizontal, the height at both points 1 and 2 are equal, so the terms ρgh₁ and ρgh₂ can be ignored.

Also, assuming that the fluid is incompressible, the term P₁ can be considered negligible in comparison to P₂.

Hence the Bernoulli equation can be written as:

1/2ρv₁² = 1/2ρv₂²

The mass flow rate is given by:

ṁ = ρAvwhere,

ṁ = mass flow rate

ρ = density of the fluid

A = cross-sectional area of the nozzle

v = velocity of the fluid

To know more about sprays visit:

https://brainly.com/question/28842403

#SPJ11

The net force on the point charge at x=8 cm is -15.88N to the left.

The force acting on a point charge by another point charge is given by Coulomb's law, which states that the force of attraction or repulsion between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

If two charges have the same sign, the force will be repulsive, and if they have opposite charges, the force will be attractive.

So, in the given charge configuration to the right, the net force (magnitude and direction) on the point charge at x=11 cm is given as follows:

At point x = 11 cm, there is a 6 μC charge 5 cm to the left and a 4 μC charge 3 cm to the right. So, the distance between the 2 charges will be 8 cm. Therefore, the net force (magnitude and direction) on the point charge at x=11 cm is given by:

[tex]����=��1�2�2=��(�1(�1−�)2+�2(�−�2)2)F net​[/tex]

[tex]= r 2 kq 1​ q 2​ ​ =kq( (x 1​ −x) 2 q 1​ ​ + (x−x 2​ ) 2 q 2​ ​ )����[/tex]

[tex]=9×109⋅2��⋅6��(0.05+0.11)2−9×109⋅2��⋅4��(0.11−0.08)2[/tex]

[tex]=15.88�,to the rightF net​ = (0.05+0.11) 2 9×10 9 ⋅2μC⋅6μC​ − (0.11−0.08) 2 9×10 9 ⋅2μC⋅4μC​ =15.88N,to the right[/tex]

Where k = 9 x 10^9 Nm^2/C^2 is Coulomb's constant; q1 = 6 μC; q2 = 4 μC; x1 = 0.05 m and x2 = 0.08 m.

Next, let's find the net force on the point charge at x=8 cm:

At point x = 8 cm, there is a 4 μC charge 3 cm to the left and a 6 μC charge 5 cm to the right. So, the distance between the 2 charges will be 8 cm. Therefore, the net force (magnitude and direction) on the point charge at x=8 cm is given by:

[tex]����=��1�2�2=��(�1(�1−�)2+�2(�−�2)2)F net​[/tex]

[tex]= r 2 kq 1​ q 2​ ​ =kq( (x 1​ −x) 2 q 1​ ​ + (x−x 2​ ) 2 q 2​ ​ )����[/tex]

[tex]=9×109⋅2��⋅4��(0.08−0.05)2−9×109⋅2��⋅6��(0.05+0.08)2[/tex]

[tex]=−15.88�,to the leftF net​ = (0.08−0.05) 2 9×10 9 ⋅2μC⋅4μC​ − (0.05+0.08) 2 9×10 9 ⋅2μC⋅6μC​ =−15.88N,to the left[/tex]

Where k = 9 x 10^9 Nm^2/C^2 is Coulomb's constant; q1 = 4 μC; q2 = 6 μC; x1 = 0.05 m and x2 = 0.08 m.

To learn more about force, refer below:

https://brainly.com/question/30507236

#SPJ11

The dielectric constant of the material is 2.

The dielectric constant (k) of a material can be determined by comparing the electric field (E) before and after inserting the dielectric between the plates of a capacitor.

The dielectric constant is given by the formula k = E₀ / E, where E₀ is the electric field without the dielectric and E is the electric field with the dielectric. In this case, the initial electric field (E₀) is 3000 V/m, and the electric field with the dielectric (E) is 1500 V/m.

Substituting these values into the formula, we find k = 3000 V/m / 1500 V/m = 2. Therefore, the dielectric constant of the material is 2.

To know more about dielectric constant refer here

brainly.com/question/13265076#

#SPJ11

Plug in the coordinates (1, 2, 3) into the expressions for E1, E2, and E3, and calculate the values of E1, E2, and E3. Then add them up to find E_net at P(1, 2, 3).

a. To find the electric field at an arbitrary point, we need to calculate the contribution from each point charge and then sum them up.

The electric field at a point due to a point charge is given by Coulomb's Law:

E = k * (q / r^2) * r_hat

where E is the electric field vector, k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2), q is the charge of the point charge, r is the distance from the point charge to the point of interest, and r_hat is the unit vector in the direction from the point charge to the point of interest.

Let's calculate the electric field due to each point charge and sum them up:

For q1 at P1(7, 3, 5):
r1 = sqrt((x - 7)^2 + (y - 3)^2 + (z - 5)^2)
r1_hat = ((x - 7) / r1, (y - 3) / r1, (z - 5) / r1)
E1 = k * (q1 / r1^2) * r1_hat

Similarly, for q2 at P2(12, 4, 3):
r2 = sqrt((x - 12)^2 + (y - 4)^2 + (z - 3)^2)
r2_hat = ((x - 12) / r2, (y - 4) / r2, (z - 3) / r2)
E2 = k * (q2 / r2^2) * r2_hat

And for q3 at P3(6, -3, 2):
r3 = sqrt((x - 6)^2 + (y + 3)^2 + (z - 2)^2)
r3_hat = ((x - 6) / r3, (y + 3) / r3, (z - 2) / r3)
E3 = k * (q3 / r3^2) * r3_hat

The net electric field, E_net, is the sum of E1, E2, and E3:
E_net = E1 + E2 + E3

b. To find the electric field at P(1, 2, 3), substitute the values of x, y, and z into the expressions for E_net that we derived in part a.:

E_net = E1 + E2 + E3

To know more about coordinates visit:

https://brainly.com/question/32836021

#SPJ11

The air resistance force will balance the force of gravity, resulting in zero net force and zero acceleration. At this point, the projectile reaches terminal , where its velocity remains constant.

Set up a projectile launcher with a fixed initial velocity.

Measure and record the range (horizontal distance traveled) of the projectile for different launch angles.

Keep the other factors, such as initial velocity and projectile mass, constant throughout the experiment.

Vary the launch angle systematically, covering a range of angles from 0° to 90°.

Repeat each launch angle multiple times to ensure consistency and accuracy of measurements.

Plot the range of the projectile as a function of the launch angle.

Prediction and Reasoning:

Changing the initial launch angle will affect the path of the projectile.

For a fixed initial velocity, increasing the launch angle (up to 45°) will result in an increased range because the vertical component of the initial velocity contributes more to the time of flight, allowing the projectile to stay in the air longer and cover a greater horizontal distance.

However, if the launch angle exceeds 45° and approaches 90°, the range will decrease because the vertical component of the initial velocity becomes dominant, causing the projectile to spend more time in the air but covering a shorter horizontal distance.

Factors affecting range with air resistance:

Air resistance has a significant effect on the range of a projectile.

Factors such as projectile shape, cross-sectional area, and mass will impact the range when air resistance is present.

Increased air resistance will cause the projectile to experience more drag, slowing it down and reducing its range.

Behavior of velocity and acceleration vectors with air resistance:

With air resistance, the velocity vector of the projectile will gradually decrease in magnitude over time.

The acceleration vector will include both the force due to gravity and the opposing force of air resistance.

As the projectile moves, the acceleration vector will be directed downward due to gravity and opposing the direction of motion due to air resistance.

Spacing of black dots on the projectile's path:

The closer spacing of black dots near the top of the projectile's path indicates a slower horizontal velocity at that point.

As the projectile descends, it accelerates due to gravity and its horizontal velocity increases, causing the dots to be further apart.

Terminal velocity situation:

To create a situation where the projectile reaches terminal velocity, consider a projectile with a large surface area, such as a flat sheet.

Initially, the projectile will experience acceleration due to gravity, and its velocity will increase.

As the projectile gains speed, the air resistance force acting on it will also increase.

Eventually, the air resistance force will balance the force of gravity, resulting in zero net force and zero acceleration. At this point, the projectile reaches terminal velocity, where its velocity remains constant.

Here you can learn more about force of gravity

https://brainly.com/question/7379745#

#SPJ11  

Newton's First Law of Motion states that an object will remain at rest or move at a constant speed in a straight line unless acted upon by an unbalanced force. This means that if there are no forces acting on an object,

it will stay in its current state of motion. In order for an object to satisfy this law, there must be a balance of forces acting upon it.

One example of an object satisfying Newton's First Law of Motion is a ball rolling on a flat surface with no external forces acting upon it. In this scenario, the force of gravity is acting upon the ball, pulling it towards the Earth. However, the normal force of the surface on the ball is equal and opposite to the force of gravity, resulting in a net force of zero. As a result, the ball remains at a constant speed in a straight line. The absence of any unbalanced forces acting on the ball satisfies Newton's First Law of Motion.

Another example of an object satisfying Newton's First Law of Motion is a satellite in orbit around the Earth. In this scenario, the gravitational force of the Earth is pulling the satellite towards it. However, the satellite is also moving at a constant speed in a straight line, which results in a balance of forces. The gravitational force acting on the satellite is exactly balanced by the satellite's centripetal force, which keeps it in orbit. Therefore, the satellite satisfies Newton's First Law of Motion, as there are no unbalanced forces acting upon it.

To know more about Newton's First Law visit:

https://brainly.com/question/1966860

#SPJ11

Minimum power of the motor is  16.67 W. A reducer must be attached to decrease the motor speed from 1400 rpm to approximately 3.183 rpm.

To calculate the minimum power of the motor for the crane, we need to consider the lifting speed and the load.

The power of the motor can be calculated using the formula: Power = Force x Velocity. In this case, the force is the weight being lifted, which is 1 ton or 1000 kg, and the velocity is given as 1 m/min. However, we need to convert the velocity to m/s for consistent units. Since 1 min = 60 s, the velocity is 1 m/60 s = 1/60 m/s.

Therefore, the minimum power of the motor can be calculated as:

Power = 1000 kg x (1/60 m/s) = 16.67 W

To determine the reducer required for a 1400 rpm electric motor, we need to consider the relationship between the motor speed and the cable reel diameter.

The cable reel's diameter is given as 100 mm, which is equivalent to 0.1 m. We know that the circumference of the reel is 2πr, where r is the radius of the reel. Since the diameter is 0.1 m, the radius is 0.05 m.

The linear speed of the cable reel can be calculated using the formula: Speed = 2πr x Motor Speed.

Rearranging the formula to solve for the required motor speed, we have:

Motor Speed = Speed / (2πr) = 1 m/min / (2π x 0.05 m) = 3.183 rpm

Therefore, a reducer must be attached to decrease the motor speed from 1400 rpm to approximately 3.183 rpm.

It's worth mentioning that the additional parameters provided, such as the coefficient of elongation, densities, and heat capacities, seem unrelated to the given information about the crane and are not necessary for calculating the minimum motor power or determining the required reducer

Learn more about Force here:

https://brainly.com/question/13191643

#SPJ11

The body mass index (BMI) is the measure of an individual's body weight relative to their height.

Body mass index:

Body mass index (BMI) is determined by dividing the body weight of the individual (in kilograms) by their height (in meters) squared.

The formula for calculating BMI is as follows:

BMI = body weight (kg) / height² (m²)

Where, BMI is the body mass index, the body weight is the weight of the individual in kilograms, and the height is the height of the individual in meters.

Body mass index is a numerical value that is used to classify individuals into different weight categories such as underweight, normal weight, overweight, and obese.

These weight categories are determined by the following BMI ranges:

Underweight: BMI less than 18.5

Normal weight: BMI between 18.5 and 24.9

Overweight: BMI between 25 and 29.9

Obese: BMI greater than or equal to 30BMI is a useful tool in determining the weight status of an individual and can be used to monitor their weight over time.

It is important to note, however, that BMI is not a perfect measure of body fatness and should be used in conjunction with other measures such as waist circumference and body composition to get a more accurate picture of an individual's overall health.

Therefore, the body mass index (BMI) calculates a person's weight in relation to their height.

To learn more about body mass index from the given link.

https://brainly.com/question/2064513

#SPJ11

Blythe's mass, mB = 46.0 kgGeoff's mass, mG = 80.0 kgGeoff's initial velocity, uG = 0 m/sGeoff's final velocity, vG = 4.00 m/sWe are to calculate Blythe's speed vB after she pushes GeoffThe solution to the problem involves the application of the law of conservation of momentum which states that the total momentum of a closed system remains constant if no external forces act on it.

Main answerThe law of conservation of momentum is given as;Σp before = Σp afterwhere Σp before is the total momentum before collision and Σp after is the total momentum after collisionThe momentum, p is given as;p = mvwhere p is momentum, m is mass, and v is velocity Let the velocity of Blythe be vBΣp before = Σp after(mBvB + mGuG) = (mBvB1 + mGvG1)where vB1 is the velocity of Blythe after collisionSolving for vB1;vB1 = (mBvB + mGuG - mGvG1)/mBNow,

vG1 is the velocity of Geoff after collision given as;vG1 = (mGuG + mBvB1)/mGWe can substitute the expression for vB1 into the expression for vG1 and simplify to obtain;vG1 = (mGuG + mB(mBvB + mGuG - mGvG1)/mB)/mGvG1 = [(mGuG) + (mB^2vB) + (mBuG) - (mBmGvG1)]/(mGmB)We can solve for vB as follows;(mBvB + mGuG) = (mBvB1 + mGvG1)46vB + (80 × 0) = (46 × vB1 + 80vG1)46vB = (46 × vB1 + 80vG1)vB = (46vB1 + 80vG1)/, the speed of Blythe vB after she pushes Geoff is given by;vB = (46vB1 + 80vG1)/46

TO know more about that mass visit:

https://brainly.com/question/14651380

#SPJ11

The density of iron is 7.86 g cm −3 and the density of sea water is 1.10 g cm −3. Can iron float in sea water? The answer is No because the density of iron is more than the density of sea water.

Since the density of iron is greater than the density of seawater, it will sink in seawater; therefore, it cannot float in seawater.

Therefore, iron can not float in seawater, because of the buoyancy force acting on iron is lower than its weight. So, the buoyancy force is not strong enough to keep the iron object on the surface of the seawater.

The buoyancy of an object is determined by the mass and the volume of the object. If the mass of the object is greater than the mass of the volume of water that it displaces, then the object will sink.

However, it depends on the shape and surface area of the iron object. If the shape of the iron object is designed in such a way that the weight is distributed over a large surface area, it may float on the surface of the seawater. For example, think of anchor and cruise ships.

To know more about density visit:

https://brainly.com/question/29775886

#SPJ11

a) The required expression for the magnitude of the force between the plates is ∣F∣ = 1/2 q²/ε₀A².

b) The magnitude of the force between the plates is 4.83 × 10⁻⁵ N.

c)  The required expression for the stress on either plate is ∣F∣/A = q²/ε₀A³.

d) The stress is 3.05 × 10⁸ N/m² or 305 MPa.

Given relationship is, ∣F∣=dU/dx

Where, F is the force between the plates,

U is the potential energy of the system,

x is the separation of the plates of a parallel plate capacitor.

(a) The potential energy of a parallel-plate capacitor can be written as

U=1/2 q²/ε₀A

Where, q is the charge of the capacitor,

ε₀ is the permittivity of the free space

A is the area of the plates.

Substituting the value of U in the given relationship, we get:

∣F∣ = dU/dx∣F∣ = d/dx [1/2 q²/ε₀A]

∣F∣ = 1/2 q²/ε₀A² ...[1]

This is the required expression for the magnitude of the force between the plates.

(b) Substituting the given values in equation [1],

q = 6.00μ

C = 6.00 × 10⁻⁶ A s

A = 2.50 cm² = 2.50 × 10⁻⁴ m²ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²

Thus, ∣F∣ = 1/2 × (6.00 × 10⁻⁶)²/8.85 × 10⁻¹² × (2.50 × 10⁻⁴)²

∣F∣ = 4.83 × 10⁻⁵ N

Therefore, the magnitude of the force between the plates is 4.83 × 10⁻⁵ N.

(c) The electric field between the plates can be expressed as,

E = σ/ε₀

Where,σ is the surface charge density of the plates.

Substituting σ = q/A, we get,

E = q/ε₀A

We know, force per unit area is electrostatic stress and is expressed as,∣F∣/A = ε₀E²

Thus, ∣F∣/A = ε₀(q/ε₀A)²

∣F∣/A = q²/ε₀A³

This is the required expression for the stress on either plate.

(d) Substituting the given values in the above equation, we get,

q = 110 Vx = 2.00 mm = 2.00 × 10⁻³ m

Thus, ∣F∣/A = (110)²/8.85 × 10⁻¹² × (2.50 × 10⁻⁴)³

∣F∣/A = 3.05 × 10⁸ N m⁻²

Therefore, the stress is 3.05 × 10⁸ N/m² or 305 MPa.

To know more about potential energy visit:

https://brainly.com/question/13905657

#SPJ11

To solve this problem, we'll use the kinematic equations of motion.

We'll assume that the acceleration due to gravity is approximately 9.8 m/s².

(a) To calculate the speed of the rock at launch, we can use the equation:

v = u + at,

where:

v = final velocity (speed)

u = initial velocity (speed)

a = acceleration

t = time

Since the rock is launched vertically, the final velocity at the peak of its trajectory is 0 m/s. Therefore, the equation becomes:

0 = u - 9.8 * 2.2.

Solving for u:

u = 9.8 * 2.2

u ≈ 21.56 m/s.

Therefore, the speed of the rock at launch is approximately 21.56 m/s.

(b) To calculate the speed of the rock 5.45 s after launch, we can again use the equation:

v = u + at.

Given that t = 5.45 s and a = -9.8 m/s² (negative because it opposes the direction of motion), we substitute these values into the equation:

v = 21.56 - 9.8 * 5.45.

Calculating:

v ≈ 21.56 - 53.51

v ≈ -31.95 m/s.

Therefore, the speed of the rock 5.45 seconds after launch is approximately 31.95 m/s in the downward direction.

Note: The negative sign indicates that the rock is moving downward after reaching its peak and starting to descend.

To know more about kinematic equations of motion visit:

https://brainly.com/question/14355103

#SPJ11

Schematic diagram of a heat engine:A heat engine is a device that uses thermal energy to produce mechanical work. Heat engines operate on the principle of the Carnot cycle, which involves four thermodynamic processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. The working principle of the heat engine is described as follows:

A gas that is initially at the temperature T1 and volume V1 is isothermally expanded to volume V2 by supplying heat from a high-temperature heat source, resulting in a decrease in pressure from P1 to P2. The gas is then adiabatically expanded from pressure P2 to pressure P3 while also losing heat to the low-temperature sink, resulting in a decrease in temperature from T1 to T2 and a decrease in volume from V2 to V3. The gas is then isothermally compressed to volume V4, releasing heat to the low-temperature sink, causing the pressure to rise from P3 to P4. Finally, the gas is adiabatically compressed back to volume V1,

raising the temperature from T2 to T1 and restoring the pressure from P4 to P1.The schematic diagram of a heat engine is given below:Schematic diagram of a refrigerator:A refrigerator is a device that uses work to transfer heat from a low-temperature environment to a high-temperature environment. A refrigeration cycle consists of four thermodynamic processes: isentropic compression, isobaric heat rejection, isentropic expansion, and isobaric heat absorption. The working principle of a refrigerator is as follows:

TO know more about that engine visit:

https://brainly.com/question/31140236

#SPJ11

Therefore, the cost of electricity to watch the 5.25-hour-long coverage of the Super Bowl on a 220 Watt television set is 8.66 cents or $0.0866.

Calculation of diameter of a 3.31 cm long tungsten filament in a light bulb if its resistance is 0.5899:

Given data:

Length of the tungsten filament, l = 3.31 cm

Resistance of the tungsten filament, R = 0.5899 Ω

Resistivity of tungsten, ρ = 5.60 × 10⁻⁸ Ωm

We know that resistance of a wire is given by:

R = (ρl)/A

Solving for A:

A = (ρl)/R

Putting the given values in the above equation:

A = (5.60 × 10⁻⁸ Ωm × 3.31 cm)/0.5899 Ω

A = 3.15 × 10⁻⁶ cm²

We know that the area of a circle is given by:

A = πd²/4

Putting the value of A in this equation:

πd²/4 = 3.15 × 10⁻⁶ cm²

Solving for d (diameter):

d² = (4 × 3.15 × 10⁻⁶ cm²)/π

d² = 1.26 × 10⁻⁵ cm²

d = √(1.26 × 10⁻⁵) cm = 0.00355 cm

Therefore, the diameter of the tungsten filament is 0.00355 cm or 35.5 µm.

To know more about tungsten filament visit:

https://brainly.com/question/30226571

#SPJ11  

1. The number of moles of 1,4 grams of Zinc is : 0.0214 moles,

2.The mass in grams of [tex]ZnCl_2[/tex]  2.91 grams.

To calculate the number of moles of zinc (Zn) in 1.4 grams, we need to use the molar mass of zinc.

1. Molar mass of zinc (Zn):

The molar mass of Zn is determined by adding up the atomic masses of its constituents. The atomic mass of Zn is 65.38 grams per mole (g/mol).

2. Number of moles of zinc (Zn):

We can use the formula:

Number of moles = Mass / Molar mass

Number of moles = 1.4 g / 65.38 g/mol

Number of moles ≈ 0.0214 mol

Therefore, the number of moles of 1.4 grams of zinc is approximately 0.0214 moles.

2. Mass in grams of[tex]ZnCl_2[/tex]:

To calculate the mass of [tex]ZnCl_2[/tex], we need to consider the balanced equation:

Zn(s) + 2HCl(aq) → [tex]ZnCl_2[/tex](aq) + H2(g)

From the balanced equation, we can see that one mole of Zn reacts with one mole of [tex]ZnCl_2[/tex]. Therefore, the molar ratio between Zn and [tex]ZnCl_2[/tex] is 1:1.

Using the number of moles of zinc calculated earlier (0.0214 moles), we can determine the number of moles of [tex]ZnCl_2[/tex] formed, which is also 0.0214 moles.

Now, we can calculate the mass of [tex]ZnCl_2[/tex]:

Mass = Number of moles × Molar mass

Molar mass of [tex]ZnCl_2[/tex] = molar mass of Zn + 2 × molar mass of Cl

Molar mass of [tex]ZnCl_2[/tex] = 65.38 g/mol + 2 × 35.45 g/mol (the molar mass of chlorine is 35.45 g/mol)

Molar mass of [tex]ZnCl_2[/tex] ≈ 136.28 g/mol

Mass of[tex]ZnCl_2[/tex] = 0.0214 mol × 136.28 g/mol

Mass of [tex]ZnCl_2[/tex] ≈ 2.91 grams

Therefore, the mass in grams of [tex]ZnCl_2[/tex] formed is approximately 2.91 grams.

For more such information on: moles

https://brainly.com/question/29367909

#SPJ8

As given, the power radiated by the cell phone is 1.12 W. The distance between the phone and point where the intensity is to be calculated is 3 cm.

Now, the average intensity of the waves can be calculated as:

Average Intensity = Power radiated per unit area= Power radiated / (4πr²)

Where, r is the distance between the phone and point where the intensity is to be calculated.

Thus, the average intensity of the radio waves is 0.83 W/m² (approximately).The peak intensity of the wave is four times the average intensity. Thus, the peak intensity of the wave is 3.32 W/m².The peak electric field strength can be calculated as:

E₀ = √(2I/μ₀c)

Where, I is the average intensity, c is the speed of light and μ₀ is the permeability of free space.

Thus, substituting the values of I, c and μ₀, we get:

E₀ = 9.4×10⁻⁴ N/C (approximately).The peak magnetic field strength can be calculated as:

B₀ = √(2I/ε₀c)Where, ε₀ is the permittivity of free space.

Thus, substituting the values of I, c and ε₀, we get:

B₀ = 2.4×10⁻⁵ T (approximately).

Therefore, the average intensity of these waves is 0.83 W/m², the peak intensity of the wave at this distance is 3.32 W/m², the peak electric field strength E₀ in these waves is 9.4×10⁻⁴ N/C and the peak magnetic field strength B₀ in these waves is 2.4×10⁻⁵ T.

To know more about power visit:

https://brainly.com/question/29575208

#SPJ11

(a) The acceleration of the car is 6.67 mi/hr/s.

To find the acceleration, we can use the equation:

acceleration = (change in velocity) / time

The change in velocity is the final velocity minus the initial velocity, which is 70 mi/hr - 30 mi/hr = 40 mi/hr. The time is given as 6 seconds. Converting the velocities to the consistent unit of miles per hour per second, we have:

acceleration = (40 mi/hr) / (6 s) = 6.67 mi/hr/s.

Therefore, the acceleration of the car is 6.67 mi/hr/s.

(b) It takes approximately 500 seconds for light to reach the Earth from the Sun.

To calculate the time it takes for light to reach the Earth, we need to consider the distance between the two and the speed of light. The distance from the Earth to the Sun is given as 1.5 * 10^8 km, which can be converted to meters as 1.5 * 10^11 m. The speed of light is 3.0 * 10^8 m/s.

Using the equation:

time = distance / speed

Plugging in the values, we have:

time = (1.5 * 10^11 m) / (3.0 * 10^8 m/s) = 5.0 * 10^2 s.

Therefore, it takes approximately 500 seconds for light to reach the Earth from the Sun.

To know more about acceleration: https://brainly.com/question/460763

#SPJ11

A person who weighs 120 pounds on earth would weigh approximately 20 pounds on the moon. This is because the force of gravity is weaker on the moon due to its lower mass and smaller size. The radius of the moon is about 1,737 km (1,080 miles) while its mass is approximately 7.342 × 10²² kg (81 billion tons).

Using this data, we can calculate the acceleration of gravity on the moon's surface which is about 1.62 m/s².A person who weighs 120 pounds on earth would weigh approximately 20 pounds on the moon.

Here's how to calculate the acceleration of gravity on the moon's surface:G = GM / R² where G is the acceleration of gravity, M is the mass of the moon, and R is the radius of the moon.

We know that M = 7.342 × 10²² kg and R = 1,737 km = 1,737,000 meters so we can plug in these values to find G.G = (6.67 × 10⁻¹¹ N(m/kg)²) (7.342 × 10²² kg) / (1,737,000 m)²G = 1.62 m/s²

Therefore, the acceleration of gravity on the moon's surface is 1.62 m/s².

A person who weighs 120 pounds on earth would weigh approximately 20 pounds on the moon. This is because the force of gravity is weaker on the moon due to its lower mass and smaller size.

Learn more about acceleration here ;

https://brainly.com/question/2303856

#SPJ11

The speed of the river current is approximately 0.805 m/s, the swimmer's speed relative to the shore is approximately 1.62 m/s, and the swimmer should aim at an angle of approximately 30.18 degrees relative to a direct line across the river to arrive directly opposite her starting point.

To solve this problem, we can use the concept of vector addition and trigonometry.

Swimmer's maximum speed relative to the water (v_swimmer) = 1.40 m/s

Displacement downstream (d_downstream) = 46.0 m

Width of the river (d_river) = 80.0 m

To find the speed of the river current (v_current), we can use the equation:

v_current = d_downstream / t

where t is the time taken by the swimmer to cross the river.

To find the time taken by the swimmer, we can use the equation:

t = d_river / v_swimmer

Substituting the given values, we can calculate the time:

t = 80.0 m / 1.40 m/s ≈ 57.14 s

Now, we can calculate the speed of the river current:

v_current = 46.0 m / 57.14 s ≈ 0.805 m/s

The speed of the river current is approximately 0.805 m/s.

To find the swimmer's speed relative to the shore, we can use the Pythagorean theorem. The swimmer's speed relative to the shore (v_shore) can be calculated as:

v_shore = √(v_swimmer² + v_current²)

Substituting the given values, we can calculate the speed relative to the shore:

v_shore = √(1.40² + 0.805²) ≈ 1.62 m/s

The swimmer's speed relative to the shore is approximately 1.62 m/s.

To determine the direction the swimmer should aim to arrive directly opposite her starting point, we can use trigonometry. The angle (θ) can be calculated as:

θ = tan^(-1)(v_current / v_swimmer)

Substituting the given values, we can calculate the angle:

θ = tan^(-1)(0.805 / 1.40) ≈ 30.18 degrees

Therefore, the swimmer should aim at an angle of approximately 30.18 degrees relative to a direct line across the river to arrive at the point directly opposite her starting point.

To know more about trigonometry refer here

brainly.com/question/12068045#

#SPJ11

The horsepower transmitted by the belt is 0.187 HP.

To calculate the horsepower transmitted by the belt when a pulley on a shaft of an electric motor has a pulley with a diameter of 8" attached and is rotating at 1800rpm and when the belt drive is connected, the tension on the slack side is 20lb and that in the tight side is 110lb, we can use the following formula:

Horsepower (HP) = (T₁ - T₂) x V / 33000

Where T₁ is tension in tight side (lb),T₂ is tension in slack side (lb),V is the belt velocity (ft/s).

Given data:

Diameter of the pulley = 8 "Radius of the pulley = diameter / 2 = 4 " = 1/3 ft

Speed of rotation = 1800 rpm

Belt tension on slack side = 20 lb

Belt tension on tight side = 110 lb

From the speed of rotation, we can calculate the velocity of the pulley as follows:

Velocity (V) = 2 π N R / 60

where N is the speed of rotation and R is the radius of the pulley.

Substituting the given values, we get:V = 2 π x 1800 x 1/3 / 60 = 56.55 ft/s

Now, substituting the given values in the formula for horsepower, we get:

Horsepower (HP) = (110 - 20) x 56.55 / 33000 = 0.187 HP

Therefore, the horsepower transmitted by the belt is 0.187 HP.

To know more about horsepower, visit:

https://brainly.com/question/13259300

#SPJ11