Concept explainers
(a)
The speed of block if the horizontal surface is frictionless.
(a)
Answer to Problem 15P
The speed of block if the horizontal surface is frictionless is
Explanation of Solution
Draw the figure fir the system as shown below.
In this system block is pulled to some distance and then released from rest, so string comes back to its normal position.
Write the expression for elastic energy stored in the spring as.
Here,
Write the expression for work done by the spring on the block.
Here,
Write the expression for kinetic energy of the system.
Here,
Write the expression for change in kinetic energy of the system.
Here,
As energy of the system is conserved, therefore work done by the string is equal to change in kinetic energy.
Write the expression for change conservation of energy for the system.
Substitute
Value of stretch at final position is zero as string comes to normal state and initial velocity is also zero.
Substitute
Rearrange the above equation for
Conclusion:
Substitute
Thus, the speed of block if the horizontal surface is frictionless is
(b)
The speed of block if there is some friction between block and surface.
(b)
Answer to Problem 15P
The speed of block if there is some friction between block and surface is
Explanation of Solution
Draw the figure for the system considering some friction as shown below.
Friction force results in an increase in internal energy of the block-surface system.
Write the expression for the normal reaction force experience by the block.
Here,
Write the expression for friction force.
Here,
Substitute
Here,
Write the expression for total internal energy.
Here,
Substitute
Work done by string is total of change in kinetic energy and internal energy.
Write the expression for change conservation of energy for the system.
Rearrange the above equation.
Substitute
Value of stretch at final position is zero as string comes to normal state and initial velocity is also zero.
Substitute
Rearrange above equation for
Conclusion:
Substitute
Thus, the speed of block if there is some friction between block and surface is
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Chapter 8 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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