(a)
The work done by the applied force.
(a)
Explanation of Solution
Given:
The mass of sled is
The coefficient of friction between sled and road is
The distance traveled by sled is
The force applied to the sled is
Formula used:
Write the expression for work done by external force.
Here,
Calculation:
Substitute
Conclusion:
Thus, the work done by external force is
(b)
Theenergy dissipated by friction.
(b)
Explanation of Solution
Given:
The mass of sled is
The coefficient of friction between sled and road is
The distance traveled by sled is
The force applied to the sled is
Formula used:
Write the expression for friction force.
Here,
Write the expression for thermal energy.
Here,
Substitute
The free body diagram of sled is given below.
Write the expression for resultant force in vertical direction.
Here,
Substitute
Substitute
Calculation:
Substitute
Conclusion:
Thus, the energy dissipated by frictionis
(c)
The change in kinetic energy of the sled.
(c)
Explanation of Solution
Given:
The mass of sled is
The coefficient of friction between sled and road is
The distance traveled by sled is
The force applied to the sled is
Formula used:
Write the expression for work done by external force.
Here,
Write the expression for friction force.
Here,
Write the expression for thermal energy.
Here,
Substitute
The free body diagram of sled is given below.
Write the expression for resultant force in vertical direction.
Here,
Substitute
Substitute
Total energy of sled 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,
The height of sled is constant all the time; so, change in potential energy is zero.
Substitute
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the change in kinetic energy of the sled is
(d)
The speed of sled after it has traveled
(d)
Explanation of Solution
Given:
The mass of sled is
The coefficient of friction between sled and road is
The distance traveled by sled is
The force applied to the sled is
Formula used:
Write the expression for work done by external force.
Here,
Write the expression for friction force.
Here,
Write the expression for thermal energy.
Here,
Substitute
The free body diagram of sled is given below.
Write the expression for resultant force in vertical direction.
Here,
Substitute
Substitute
Total energy of sled 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,
The height of car is constant all the time; so, change in potential energy is zero.
Substitute
Write the expression for change in kinetic energy.
Rearrange the above expression in terms of
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the speed of sled after it has traveled
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Chapter 7 Solutions
Physics for Scientists and Engineers
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