Calculating Work, Speed & Power of a Car Climbing a Hill

[xupe33jrm]

1. A car of mass 1100 kg starts from rest at sea level and climbs a hill of altitude 50 m. At the top of the hill the car has a speed of 25 m/s. From the top of the hill the driver turns off the engine and coasts down to an altitude of 15 m. Assume the friction and the air resistance to be negligibly small.

a. work produced by the engine of the car?
b.Speed of the car when the altitude is 15m
c. After passing the altitude of 15m, the driver climbs up again, without turning the engine on. In this case, the speed of the car would be zero
at an altitude of?
d. In reality the friction and the air resistance are not zero. If the work needed to overcome thefriction and the air resistance is 5.2×105 Joules, the answer to part (a) would change. In thiscase, the work produced by the engine to climb to 50 m and have a speed of 25 m/s at the topwould be?
e. In part (d) the car reaches the top of the hill in 80 seconds. The power developed by the
engine is?

I have the answers, I am just confused where to start and what equations to use. Please help me get started on these!

 

[berkeman]

1. A car of mass 1100 kg starts from rest at sea level and climbs a hill of altitude 50 m. At the top of the hill the car has a speed of 25 m/s. From the top of the hill the driver turns off the engine and coasts down to an altitude of 15 m. Assume the friction and the air resistance to be negligibly small.

a. work produced by the engine of the car?
b.Speed of the car when the altitude is 15m
c. After passing the altitude of 15m, the driver climbs up again, without turning the engine on. In this case, the speed of the car would be zero
at an altitude of?
d. In reality the friction and the air resistance are not zero. If the work needed to overcome thefriction and the air resistance is 5.2×105 Joules, the answer to part (a) would change. In thiscase, the work produced by the engine to climb to 50 m and have a speed of 25 m/s at the topwould be?
e. In part (d) the car reaches the top of the hill in 80 seconds. The power developed by the
engine is?

I have the answers, I am just confused where to start and what equations to use. Please help me get started on these!

What can you tell us about Total Energy TE, Potential Energy PE, Kinetic Energy KE, and Work W? How are they related? What are the equations for each?

 

[xupe33jrm]

On A I tried to use the Work equation W=KE(final)-KE(initial), with KE(f) = .5mv^2(f) and initial being same but using initial velocity. How do I find V final?

 

[berkeman]

On A I tried to use the Work equation W=KE(final)-KE(initial), with KE(f) = .5mv^2(f) and initial being same but using initial velocity. How do I find V final?

The car starts from rest.

EDIT -- and there is also a change in PE.

 

[xupe33jrm]

I am spinning in circles. What am I missing?

 

[berkeman]

I am spinning in circles. What am I missing?

The work done by the engine climbing the hill is the sum of the change in PE and the change in KE. Write that equation and solve for the work done climbing the hill.

 

[willem2]

I am spinning in circles. What am I missing?

Part a) is only about the climb to 50m because the engine is turned off after that, so v_final is 25 m/s as given in the problem.

The car also gains potential energy, and the work to do this is also produced by the engine.