Slopes - Energy

These questions involve an object moving up or down slopes. There may or may not be friction. The object may be free-wheeling, or may use an engine. There are many types of questions. There is a simple energy relationship between all the energies in all such questions.

Going uphill
These questions revolve around Ek. Note the blue arrow linking the 2 Ek values.
The red arrows represent the energy obstacles in the way, and are negative.

Block any one of the numbers in the diagram with a finger, and guess what it is supposed to be.

Energy relationship in an equation form:
100-20-50 = 30

Question 1
A 2kg trolley is free-wheeling towards a slope of height 3m at a constant speed of 9m.s-1. The length of the slope is 5m and the friction that would be experienced along the slope is 2N.
As you calculate the answers, put the energies back into the diagram, using positive only. This makes it easier to grasp the solution.

1.1 Calculate the kinetic energy of the trolley at the bottom.

1.2. Calculate the Ep of the trolley when it reaches the top.

1.3. Calculate the magnitude of work done to overcome friction along the slope.

1.4. Calculate the kinetic energy of the trolley at the top.

1.5. Calculate the velocity of the trolley at the top.

Summary of the energies:

Bonus Questions
Assume that the trolley had a motor, and could thus go up the slope at constant speed.

1.6. What ADDITIONAL energy would be needed from the motor to achieve a constant speed up the slope?
The trolley would have been DEPRIVED (friction + hill) of a total of:

Thus the motor would have to replace this amount of energy.
Additional energy required would be 68,8J

1.7. How long would it take the trolley to reach the top.

1.8. How much power would be required by the motor to achieve this constant speed up the slope?
This energy is the extra energy the motor itself introduces, and the time is how long it took to get to the top.

Going downhill - can you figure the diagram out?