Work, Kinetic Energy, Spring, Friction Problem

[Tristin_noel]

A block slides from rest, along a track with an elevated left end, a flat central part, into a relaxed spring, as shown in the figure. The curved portion of the track is frictionless, as well as the first portion of the flat part of L = 10 cm. The coefficient of kinetic friction between the block and the only rough part, D = 10 cm, is given by uk = 0.20. Let the initial height of the block be h = 40cm, its mass be m = 2.5 kg, and the spring constant k = 320 N/m. (Picture should be posted below.)

1. While the block slides through the flat central part of length L find:

a) The work done on the block by the gravitational force. = would you use W=mgh ?
b) The work done on the block by the normal force. = 0 bc the normal force is perpendicular to the displacement.
c) The work done on the block by the frictional force. = 0 bc no frictional force present
d) The speed of the block right before it reaches the beginning of the rough central part of length D. =2.8m/s used the eqautopn PE=KE , mgh=1/2m(vf^2-vi^2)

2) The block has now made it to the rough region of length D and will eventually slide head on into the spring at the end of the path. Over this region of length D, calculate:

e) The work done on the block by the gravitational force. = 0 bc perpendicular
f) The work done on the block by the normal force. = 0 bc perpendicular
g) The work done on the block by the frictional force. =-0.49J bc Wfriction=uk(mg)d
h) The speed of the block just as it reaches the spring. =2.73m/s using Vf^2-Vi^2=2(-ukg)d

3) Assuming the block compresses the spring by x, find:

i) The work done by the spring force. would you use W=1/2mVf^2 ?
j) The compression distance, x, of the spring. would you use W=kx and just solve for x?

https://s.yimg.com/hd/answers/i/6ae6d9b8385d4d3eb364c25c31aeb7d5_A.png?a=answers&mr=0&x=1425534324&s=478f148cd3470b7f93d03b19b2553c0b

 

[Simon Bridge]

The point of the exercise is to test/improve your understanding of conservation of energy and work.
Your questions are about what equations to use - you should use your understanding, which seems OK, to figure out the equations.
How would you go about answering your own questions? i.e. for (a) you want to know if the work due to falling a distance h under gravity is given by mgh.
How could you check? Perhaps by using the definition of work in terms of forces or in terms of the work-energy theorem?
Same for the work done by the spring.