(a)
The speed of the block at the bottom of the ramp.
(a)
Explanation of Solution
Given:
The mass of block is
The initial height of block is
The final height of block is
The distance traveled by block on horizontal surface is
Formula used:
Write the expression for change in potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Total energy of block is conserved at all points. Work done by external force is equal to the sum of change in gravitational potential energy, kinetic energy and thermal energy.
Write the expression of work done by external force.
Here,
Substitute
Rearrange the above expression in terms of
Calculation:
Substitute
Conclusion:
Thus, the speed of the block at the bottom of the ramp is
(b)
The energy dissipated by the friction force.
(b)
Explanation of Solution
Given:
The mass of block is
The initial height of block is
The final height of block is
The distance traveled by block on horizontal surface is
Formula used:
Write the expression for change in potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Total energy of block is conserved at all points. Work done by external force is equal to the sum of change in gravitational potential energy, kinetic energy and frictional energy.
Write the expression of work done by external force.
Rearrange the above expression in terms of
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, the energy dissipated by the friction force is
(c)
The coefficient of kinetic friction between the block and the horizontal surface.
(c)
Explanation of Solution
Given:
The mass of block is
The initial height of block is
The final height of block is
The distance traveled by block on horizontal surface is
Formula used:
Write the expression for change in potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Total energy of block is conserved at all points. Work done by external force is equal to the sum of change in gravitational potential energy, kinetic energy and frictional energy.
Write the expression of work done by external force.
Rearrange the above expression in terms of
Here,
Substitute
Write the expression for friction force.
Here,
Rearrange the above expression in terms of
Write the expression for frictional energy.
Here,
Rearrange the above expression in terms of
Substitute
Calculation:
Substitute
Substitute
Conclusion:
Thus, the coefficient of kinetic friction between the block and the horizontal surface is
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Chapter 7 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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