Work Done Car Uphill PE and KE

In summary, the work done by the car of mass 980kg as it accelerates up an incline of 10° and increases its speed from 8.3m/s to 13.8m/s in 60m is 161KJ, assuming constant air resistance of 50N and rolling resistance of 200N. However, it is possible that the actual answer is 175KJ when considering the units of Nm for the forces.
  • #1
MMCS
151
0
if a car of mass 980kg accelerates up an incline (10°to the horizontal) and increases its speed from 8.3m/s to 13.8m/s in 60m, both the air resistance and rolling resistance are taken as constant at 50N and 200N respectivelyfor the acceleration period described, determine work done

work done = Δkinetic energy + Potential energy

kinetic energy = 1/2 * mass * (v22-v12)
PE = mgh

work done = 1/2 * 980 * (13.82-8.32) + 980 * 9.81 * 60sin(10) + 50N + 200N = 161KJ

but I have the answer to be 175KJ
 
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  • #2
Hi MMCS! :smile:
MMCS said:
… + 50N + 200N = 161KJ

Anything strike you as odd about those units? :wink:
 
  • #3
Ah of course, multiply these forces by the the distance to get units of Nm. Thanks tiny-tim!
 

1. What is "work done" in relation to a car driving uphill?

Work done is a measure of the force applied to an object multiplied by the distance the object moves in the direction of the force. When a car drives uphill, work is done against the force of gravity to lift the car's mass to a higher position.

2. How does the potential energy of a car change when driving uphill?

The potential energy of a car increases when driving uphill because the car's mass is being lifted to a higher position against the force of gravity. This potential energy is stored in the car's position and can be converted into other forms of energy, such as kinetic energy, when the car moves downhill.

3. Is the work done by a car driving uphill only dependent on its mass and height?

No, the work done by a car driving uphill also depends on the distance the car travels and the angle of the incline. The steeper the incline, the more work is required to overcome the force of gravity and move the car uphill. The work done is also affected by external factors such as air resistance and friction.

4. How does the kinetic energy of a car change when driving uphill?

The kinetic energy of a car decreases when driving uphill as some of the car's energy is used to do work against the force of gravity. This means that the car's speed will decrease while driving uphill, and the kinetic energy will increase again when the car moves downhill.

5. Can a car's kinetic energy be converted into potential energy when driving uphill?

Yes, a car's kinetic energy can be converted into potential energy when driving uphill. As the car moves up the incline, its kinetic energy decreases and is converted into potential energy stored in the car's position. This potential energy can then be converted back into kinetic energy when the car moves downhill.

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