A block slides from rest, along a track with an elevated left end, a flat centra

Question

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

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 ½k = 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

Explanation / Answer

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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