Block, Ramp, Friction, and Spring

[r34racer01]

A man pulls a block of mass m = 20 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 29° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.3.

a) What is the work Wm done by the man? Wm = 513.1

At the top of the incline, the string breaks and the block, assumed to be at rest when the string breaks, slides down a distance d = 3.5 m before it reaches a frictionless horizontal surface. A spring is mounted horizontally on the frictionless surface with one end attached to a wall. The block hits the spring, compresses it a distance L = 0.6 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.

b) What is the speed v of the block when it first reaches the horizontal surface? v = 3.91
c) What is the spring constant k of the spring? k = 849.3
d) How far up the incline d1 does the block rebound? d1 = ?

For picture: https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-08-GPE-ME/block_ramp_friction_spring/9.gif W = ΔKE, W = F*d, U = m*g*h

So I'm stuck on part d.). I thought I could do U = KE - W(friction) = (((1/2)m*v^2) - μmgh*cos(29)) / mg = 0.517 but that didn't work. Any help please?

 

[rl.bhat]

There is no mention of spring in the problem. How is that?

 

[r34racer01]

There is no mention of spring in the problem. How is that?

Sorry my bad, I've added the rest of the info after part a.), I've also added a link to the picture included.

 

[rl.bhat]

Angle of the inclined plane is not given. Whether d is the displacement along the inclined plane?

 

[r34racer01]

Angle of the inclined plane is not given. Whether d is the displacement along the inclined plane?

Yes it is.

The incline makes an angle q = 29° with the horizontal.

 

[rl.bhat]

While going up the kinetic energy of the block = work done against (frictional force + component of weight in the downward direction) + PE.