I have no clue about this PROBLEM!!!?

[Jack]

Can anyone give me detailed description of how to this and what formula to use?
Thank you so much for the help!


A block with mass m = 15.6 kg slides down an inclined plane of slope angle 14.7o with a constant velocity. It is then projected up the same plane with an initial speed 2.80 m/s. How far up the incline will the block move before coming to rest?

[gp4rts]

The missing piece is the frictional force of the block against the plane. The first part of the problem lets you find that value:

If the block moves at constant velocity, the friction force Fr is equal to the force (gravity) pulling the block down. The gravity force on the block is m*g*sin?; therefore Fr = m*g*sin?.

You can solve the second part in two ways: energy conservation or mechanics. I prefer energy conservation:

Initial energy of the block = KE = 0.5*m*v0². The block will rise on the plane until that energy is used by friction and gravitation potential energy.

Friction energy used is Fr*L, where L is the distance along the plane
Gravity potential = m*g*h, where h is the altitude at the end of travel. If L is the distance traveled, h = L*sin?. So the total energy used going up the plane is

Fr*L + m*g*L*sin? and this is equal to 0.5*m*v0². Then using Fr from the first part,

m*g*L*sin? + m*g*L*sin? = 0.5*m*v0²

g*L*sin? + g*L*sin? = 0.5*v0²

L*2*g*sin? = 0.5*v0²

L = 0.25*v0²/(g*sin?)