# Inclined Planes

1. Apr 27, 2010

### cheerspens

1. The problem statement, all variables and given/known data
In an ideal case of pulling a cart up a ramp where there is no friction should the efficiency be less than that of pulling a cart up a ramp with friction?

2. Relevant equations
W=F$$\Delta$$Xcos$$\theta$$
Efficiency=(work output/work input)*100

3. The attempt at a solution
I was trying to calculate this for a lab and my efficiency came out to be much less for a friction-less ramp than one with friction. Is this possibly right?
What I believe one of my problems was, was determining the effort force. How do you determine the effort force if you only know that there is no acceleration, no friction, the length of the ramp is 1.22 m and the mass of the cart is 0.783 kg?

2. Apr 27, 2010

### kuruman

Let's say you pull a cart up an incline at constant speed.

If there is no friction, then all the work your muscles do matches the negative work done by gravity and nothing else.

If there is friction, then the work that your muscles do matches the negative work done by gravity and the negative work done by friction.

The effort force is the sum of all the other forces when the object is moving at constant speed. This is a consequence of the work energy energy theorem.

3. Apr 27, 2010

### cheerspens

So if there is no friction and the force of gravity is say 8 N, then the effort force is 8 N?

4. Apr 27, 2010

### kuruman

I didn't say the forces are equal. If there is no friction, the work done by gravity is equal to the work done by the pulling force. The forces will be equal only if the cart is pulled vertically up. Use the definition for work to see why this is so.