(a)
The initial kinetic energy of rock.
(a)
Explanation of Solution
Given:
The mass of rock piece is
The initial speed of rock piece is
The maximum height attained by the rock piece is
Formula used:
Write the expression for initial kinetic energy.
Here,
Calculation:
Substitute
Conclusion:
Thus, the initial kinetic energy of rock pieceis
(b)
The increase in thermal energy due to air resistance.
(b)
Explanation of Solution
Given:
The mass of rock piece is
The initial speed of rock piece is
The maximum height attained by the rock piece is
Formula used:
Write the expression for change in potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Total energy of object 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,
There is no external force acting on the block; so, the work done by external force is zero.
Substitute
Substitute
Calculation:
Substitute
Conclusion:
Thus, the increase in thermal energy due to air resistance is
(c)
The final speed of the rock piece.
(c)
Explanation of Solution
Given:
The mass of rock piece is
The initial speed of rock piece is
The maximum height attained by the rock piece is
The increase in thermal energy during downward motion is
Formula used:
Write the expression for change in potential energy.
Here,
Write the expression for change in kinetic energy.
Here,
Total energy of object 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,
There is no external force acting on the block; so, the work done by external force is zero.
For rock-piece moving upward:
Substitute
Substitute
For rock-piece moving downward:
Substitute
Substitute
Calculation:
Substitute
Conclusion:
Thus, the final speed of the rock piece is
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Chapter 7 Solutions
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