Mass on spring up a ramp over a chasm

[emam03]

Hey guys,

I'm having difficulty with this problem. Any help would be appreciated!

A block of mass m is placed against a compressed spring with spring constant k. When the
spring is released, the block is launched up a ramp and across a chasm of width D. The ramp has a coefficient of kinetic friction uk= 1/2 and angle of 45 degrees. Find the minimum compression distance of the spring, Δx that is needed in order for the block to reach the other size of the chasm at height h. You may assume that the distance, Δx, by which the spring is compressed is always very much less than D or h so that the mass always starts at rest at point O. You may neglect air resistance. Your answer may contain some or all of the following: k, D, h and m, and the acceleration due to gravity, g.

I know the initial potential energy is stored in the spring and know it's .5kx^2. I know the final potential energy is mgh. I know how to calculate the gravity and friction acting against the mass but I don't know how to relate all of these to find the compression needed. Thanks!

 

[rock.freak667]

Your energy balance would just be initial energy= final energy (this is at the top of the ramp)

so 1/2 kx²=1/2mv² + mgh -Work done against friction


At the top of the ramp, it will leave the final velocity 'v'. So you should be able to find the distance 'D' in terms of 'v' using the parabolic motion equations.

 

[emam03]

Thanks!