Physics help?

Question

The question is that there is a frictionless incline and the angle of inclination is 20 degrees, and the spring constant is 331N/m and the mass of the block is 7 kg. The block is released from rest with the spring initially unstretched and the acceleration of gravity is 9.80 m/s^2. I tried to draw a picture so it would look like an acute triangle and a rectangle put together and the block would be on the part of the acute triangle and there would have to be a pulley where the acute triangle and rectangle meet. So I think I have to find the distance between where the acute triangle and rectangle meet to the distance where the block traveled. How can I find how far it travels down the incline before coming to rest and is my diagram okay?

Answer 1

There are three interesting points in the motion of the block: First, where the spring and block pause momentarily before the block slides back up the incline to the point where the force in the spring balances the force of gravity trying to slide the block down the incline, and the block will return to the original position when the energy in the spring is again transferred to the PE of the block and the block starts to slide down again. Since there is no friction, the block will oscillate forever.

I will assume that you want to know how far down the slope the block will slide before it changes direction and slides back up.

Using energy
m*g*d*sin(20)=.5*k*d^2
solve for d
d=m*g*sin(20)*2/k
d=7*9.8*sin(20)*2/331
d=0.142 m

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