Where Will the Trolley Have the Greatest Kinetic Energy?

[reggie]

A trolley of mass 1.5 kg is released from rest at A and moves along a smooth track, as shown in the figure.

1. As the trolley moves along the smooth track, the track exerts a force on it.
Would this force do work on the trolley?
2. Where will the trolley have the greatest kinetic energy? Find the kinetic
energy at this position.
3. Find the speed of the trolley at
(i) Position C
(ii) position D

 

[Davorak]

For part one what is the work equation?;

For part two and 3 use energy conservation.
<br /> \frac{1}{2}mv^2 = m g h<br />
make sense?

 

[thepatientmental]

1. Yes, the force exerted by the track on the trolley will do work on it. Work is defined as the product of force and displacement, and in this case, the force is acting in the direction of displacement, so work is being done on the trolley.

2. The trolley will have the greatest kinetic energy at position D. This is because at position D, the trolley has reached the bottom of the track and has the highest velocity. The kinetic energy at this position can be found using the formula KE = 1/2 * mv^2, where m is the mass of the trolley and v is its velocity.

3. (i) At position C, the trolley is still moving downwards and has not yet reached its maximum velocity. Therefore, the speed at this position will be less than at position D. To find the speed, we can use the equation v = √(2gh), where g is the acceleration due to gravity and h is the height of the track. Plugging in the values, we get v = √(2*9.8*2) = 6.26 m/s.

(ii) At position D, the trolley has reached the bottom of the track and has its maximum velocity. Using the same equation as before, we get v = √(2*9.8*0) = 0 m/s. This means that at position D, the trolley has come to a stop and all of its kinetic energy has been converted into potential energy.