Block, Ramp, Friction, and Spring?

Question

A physics student pulls a block of mass m = 22 kg up an incline at a slow constant velocity for a distance of d = 3 m. The incline makes an angle q = 30° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.2.

Picture: https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/fall/homework/Ch-08-Energy-Conservation/block_ramp_friction_spring/9.gif

a) What is the work Wm done by the student?

b) What is the speed v of the block when it first reaches the horizontal surface?

c) What is the spring constant k of the spring?

d) How far up the incline d1 does the block rebound?

For part b-d

At the top of the incline, the string by which she was pulling the block breaks. The block, which was at rest, slides down a distance d = 3 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 = 0.8 m, then rebounds back from the spring, retraces its path along the horizontal surface, and climbs up the incline.

Answer 1

a) The work is F*d, what is F?
It is sin(30)*22*9.8+cos(30)*22*9.8*0.2
or
22*9.8*(sin(30)+cos(30)*0.2)
and the distance is 3 m
so work is 435 J

b) again, with energy
3*22*9.8*(sin(30)-cos(30)*0.2)=
.5*22*v^2
solve for v
=4.38 m/s

c) since L=0.8 m
.5*22*4.38^2=.5*k*0.8^2
solve for k

k=660 N/m

d) Again with energy
.5*22*4.38^2=
d*22*9.8*(sin(30)+cos(30)*0.2)

solve for d
1.46 m

j