A 10.8-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 3.10 m/s in 1.39 s. In the process, the spring is stretched by 0.227 m. The block is then pulled at a constant speed of 3.10 m/s, during which time the spring is stretched by only 0.0801 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.

Question
Asked Jul 17, 2019

A 10.8-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 3.10 m/s in 1.39 s. In the process, the spring is stretched by 0.227 m. The block is then pulled at a constant speed of 3.10 m/s, during which time the spring is stretched by only 0.0801 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.

check_circleExpert Solution
Step 1

Draw the free body diagrams for the two cases of application of forces on the block as:

Fret
Case I
Case II
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Fret Case I Case II

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Step 2

Consider Case I and write the kinematic equation of motion for block which starts from rest to solve for acceleration of the block as:

vuat
v-u
a =
t
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vuat v-u a = t

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Step 3

Substitute suitable values...

3.10 m/s 0 m/s
a =
1.39 s
2.23 m/s
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3.10 m/s 0 m/s a = 1.39 s 2.23 m/s

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