# Friction and Inclined Planes

Hey guys thanks for the help on the last problem, I just had one more that I was trying to get finished studying for this big exam coming up:

A block with mass m = 13.0 kg slides down an inclined plane of slope angle 32.8 ° with a constant velocity. It is then projected up the same plane with an initial speed 3.85 m/s. How far up the incline will the block move before coming to rest?

Now I know its kind of like a normal inclined plane problem, but the whole pushing it back up part has got me confused. I actually cant even get my first values. So I probably need help with those too. Man im stupid Hope someone can help me! Thanks!

Well, O.K.

You have the mass, you have the initial speed. So calculate the kinetic energy.
After that, when you try to use the energy conservation law, you see that some amount of energy is being taken up by the friction on the plane and the rest by going against gravity.
Now, the question is, how much is being consumed by friction. Well, from the first part, you can calculate the co-effiecient ( say, k) of friction as follows.

For first case,
force of gravity = force of friction (because constant velocity )
so, mg*sin(32.8deg.)=kmg*cos(32.8deg.)
so, k = tan(32.8deg)

now, Second case (let the required distance be x )

Initial K.E. = work by friction + work by gravity

work by friction is kmg*cos(32.8deg.)*x
work by gravity is mg*sin(32.8deg)*x

You know the K.E
Simply solve and find x - the answer!

vibhav
www.geocities.com/physics_all/index.html

Thanks! 