Concepts of work and kinetic energy

[pb23me]

Homework Statement

A car with a mass of 1000kg is at rest at the base of a hill. It accelerates up the incline reaching a speed of 20m/s at a height of 100m.The work done by the frictional force is 450,000N.
a)Calculate the change in kinetic energy of the car.
b)Calculate the work done by the motor of the car.

Homework Equations

$$\Delta$$K=1/2mv²_f-1/2mv²_i=10,000NM
W_f=450,000NM
W_g=-(mgy_f-mgy_i)=-980,000NM

The Attempt at a Solution

The change in kinetic energy is equal to the Wnet so i set 450,000-980,000+W_m=10,000 and solved for W_m and got 540,000NM. I think my instructor was doing something different in class so I am not sure if this is correct...

 

[Chi Meson]

Your calculation of the KE of the car is very, very low. What key on the calculator did you forget to press?

And then, does friction do positive work or negative work on the car?

 

[pb23me]

Well i have inital velocity at zero so the change in kinetic energy is equal to .5*1000*400... this is what i read in my lab book that the change in kinetic energy is equal to the Wnet. The problem states that the work done by frictional force is equal to 450,000N so i would assume it does positive because the work is positive.

 

[Chi Meson]

Yes, KE is .5*1000*400 which is a bit more than 10,000 J.

Two ways to see that the work done by friction here is negative:
1) does the friction serve to increase KE or decrease KE? Is friction adding energy to the car or taking away energy from the car?
2) Is the direction of the frictional force on the car the same direction as the motion of the car, or the opposite direction ? Whenever the force vector and displacement vector are in opposite directions, negative work is being done by the force.

 

[pb23me]

So is it safe to say that any force that reduces kinetic energy is doing negative work while any force that increases kinetic energy is doing positive work?

 

[pb23me]

And why in the problem does it say that work due to the force of friction is 450,000NM instead of -450,000NM. That is a little confusing.

 

[Chi Meson]

And why in the problem does it say that work due to the force of friction is 450,000NM instead of -450,000NM. That is a little confusing.

This is one of the things you will need to be able to recognize: when is work being done BY a system, or when work is being done ON a system. Work is the transfer of energy. Does friction transfer energy OUT of the system (here, the car is the system), or IN? The quantity of work is given, you need to be able to determine whether to add or subtract it.

And to your other question, if there are multiple forces at work, then you need to be careful. But it is true that if a force acts to reduce KE, then it is negative work. A more generally true statement is that "negative work will reduce the mechanical energy of a system" which is the total of PE + KE.