Ramp question, not hard (10 pts to first correct answer!)?

Question

Can you please answer the following question in terms of changes in energy and work?

A 500g block is shot up the incline with angle 25 degrees at an initial speed of 200 cm/s. How far up the incline will it go if the coefficient of friction between it and the incline is 0.15?

I think my book might have made a mistake..

Answer 1

I hate physics professors.

The simple way to solve the problem is to look only at the acelerations. The mass terms divide out and all you need to know is the inital velocity, angle and friction factor. But your answer will be counted wrong if you work it that way. Rats!!

The hard way is to look at the total energy.

The Kinetic energy for the block is 0.5 Kg (1/2)(2 M/s)^2

Part of the work being done is the lifting of the block or increasing its potential energy. 0.5 Kg (g) (change in height) Since the ramp is angled at 25 degrees the change in height divided by the distance traveled is sin(25 degrees).

The rest of the work done overcoming friction of the ramp itself.
Friction depends on the force normal to the incline which is 0.5 Kg x 9.8 M/s^2 x cos(25 degrees). That force is multiplied by the unitless friction factor of 0.15 . The work being done is Force x distance. (distance is distance up the ramp).

Kinetic Energy = Work lifting block + Work overcoming friction

Since both the lifting work and friction work can be expressed as functions of the distance up the ramp the point where they equal the inital Kinetic energy of the block is the final distance the block travels.

Good luck. I almost flunked physics because of questions like this.