• nickclarson
In summary, the problem involves a box of mass 7.68 kg on a frictionless inclined plane, attached to a string with a constant tension of 113 N. The question is to find the work done by the tension, the speed of the box as a function of x and the angle of the plane, and the power delivered by the tension for a specific distance and angle. The solution involves using the kinetic energy work theorem to find the velocity, and then using that to calculate the power delivered by the tension. The final equation is P = T*sqrt((2x(T-mgsin(theta))/m)) and for x = 6.38 m and an angle of 30.5°, the power delivered is
nickclarson

## Homework Statement

A box of mass M = 7.68 kg is at rest at the bottom of a frictionless inclined plane.

The box is attached to a string that pulls with a constant tension T = 113 N. Write the general equation that gives the work done by the tension when the box has moved a distance x along the plane. Now, find the speed of the box as a function of x and the angle of the plane. Finally, for a distance of x = 6.38 m and an angle of 30.5°, determine the power delivered by the tension in the string as a function of x.

## Homework Equations

$$K=\frac{1}{2}mv^{2}$$
$$P=FV$$

## The Attempt at a Solution

I know I am supposed to multiply the net force by velocity for the last part, but I need to find the velocity.

I figured I could use kinetic energy to find the velocity using the ke work theorem. So...

$$KE_{f}-KE_{i}=W$$

And since the initial energy is 0

$$KE_{f}=W$$

Am I on the right track?

----------------------
Edit: Solved

Here's the final equation I derived:

$$P=T\sqrt{\frac{2x(T-mgsin\theta)}{m}}$$

Last edited:
For x = 6.38 m and an angle of 30.5°, the power delivered by the tension in the string is P = 544.2 W.

sin\theta

I would first commend the student for their attempt at solving the problem and for seeking help when they were unsure. I would also clarify that the work done by the tension is not equal to the kinetic energy, but rather the change in kinetic energy. So the equation should be KE_f - KE_i = W, as the student correctly stated later in their attempt.

To find the velocity, I would suggest using the formula for work done by a constant force, W = Fd = mad, where d is the distance moved and a is the acceleration. Since the box is on a frictionless plane, the only force acting on it is the tension force, so we can rewrite this as W = Td = mad. Solving for a, we get a = T/m. We can then use the formula for constant acceleration, v^2 = v_0^2 + 2ad, where v_0 is the initial velocity (0 in this case) and d is the distance moved. Rearranging for v, we get v = sqrt(2ad). Plugging in the values for T and m, we get v = sqrt(2Tx/m).

To find the power, we can use the formula P = W/t, where W is the work done and t is the time taken. Since we are given a distance and an angle, we can use trigonometry to find the displacement in the x-direction, which is equal to the distance the box has moved. So we can rewrite the formula as P = (W/d)(d/t), where d is the distance moved and t is the time taken. We can then substitute in the formula for work done by the tension, W = Td, and the formula for velocity we found earlier, v = sqrt(2Tx/m). This gives us P = (Td/d)(d/v) = Tsqrt(2Tx/m). Finally, we can substitute in the values for T, x, and m to get the final equation for power, which the student correctly derived in their attempt.

## 1. What is a frictionless plane?

A frictionless plane is a theoretical concept in physics where there is no resistance or friction present. This means that objects can move without any force opposing their motion, allowing for simplified calculations and analysis.

## 2. How do you calculate work on a frictionless plane?

The formula for calculating work on a frictionless plane is W = F x d, where W is work, F is force, and d is the distance the object moves. Since there is no friction, the force applied is the only force acting on the object, and the distance is measured in the direction of the force.

## 3. What is power in relation to a frictionless plane?

Power is the rate at which work is done or energy is transferred. On a frictionless plane, power is calculated by dividing the work done by the time it takes to do that work. This means that power is a measure of how quickly an object can move on a frictionless plane.

## 4. How do you find the power based on work and time on a frictionless plane?

To find the power, you would divide the work done by the time it took to do that work. The formula for this is P = W/t, where P is power, W is work, and t is time. On a frictionless plane, the work is equal to the force multiplied by the distance, so the formula can also be written as P = (F x d)/t.

## 5. Can you give an example of calculating power on a frictionless plane?

An example of calculating power on a frictionless plane would be a block being pushed with a force of 10 Newtons for a distance of 5 meters in 2 seconds. The work done would be 10 x 5 = 50 Joules. To find the power, we would divide the work by the time, so P = 50/2 = 25 Watts. This means that the power of the block on the frictionless plane is 25 Watts.

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