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 k = 0.20. Let the initial height of the block be h = 40 cm, its mass be m = 2.5 kg, and the spring constant k = 320 N/m.
While the block slides through the flat central part of length L find:
(a) The work done on the block by the gravitational force. Show your work
(b) The work done on the block by the normal force. Show your work
(c) The work done on the block by the frictional force. Show your work
(d) The speed of the block right before it reaches the beginning of the rough central part of length D. Show your work
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. Show your work
(f) The work done on the block by the normal force. Show your work
(g) The work done by the frictional force as it reaches the spring. Show your work
(h) The speed of the block just as it reaches the spring. Show your work
Assuming the block compresses the spring by x, find:
(i) The work done by the spring force. Show your work
(j) The compression distance, x, of the spring. Show your work
Homework Answers
A block slides from rest, along a track with an elevated left end, a flat central part, into a relaxed spring
(a) The work done on the block by the gravitational force.
=mgh
=2.5*9.8*40*10-2
=9.8J
(b) The work done on the block by the normal force.
normal force is perpendicular to displacement
work done=0
(c) The work done on the block by the frictional force.
workdone by the friction equals to zero
because
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