Concept explainers
(a)
The distance
(a)
Answer to Problem 39AP
The distance
Explanation of Solution
Given information: The mass of car is
From the law of energy conservation,
Here,
Formula to calculate the total initial energy of the system is,
Here,
Write the expression for the initial translational kinetic energy of the elevator is,
Here,
Write the expression for the initial translational kinetic energy of the counterweight is,
Here,
Write the expression for the initial rotational kinetic energy of the sheave is,
Here,
Write the expression for the moment of inertia of the pulley is,
Here,
Write the expression for the initial angular speed of the pulley is,
Here,
Substitute
Substitute
Since at the end the system comes to rest hence all the kinetic energies will be zero only potential energy remains in the system.
Formula to calculate the total final energy of the system is,
Here,
Write the expression for the final potential energy of the elevator is,
Here,
Write the expression for the final potential energy of the counterweight is,
Here,
Since the sheave pulley remains at its position so its final potential energy is zero.
Substitute
Substitute
Formula to calculate the mass of the elevator is,
Here,
Substitute
Substitute
Conclusion:
Therefore, the distance
(b)
The distance
(b)
Answer to Problem 39AP
The distance
Explanation of Solution
Given information: The mass of car is
The expression for the distance
Substitute
Conclusion:
Therefore, the distance
(c)
The distance
(c)
Answer to Problem 39AP
The distance
Explanation of Solution
Given information: The mass of car is
The expression for the distance
Substitute
Conclusion:
Therefore, the distance
(d)
The distance
(d)
Answer to Problem 39AP
The distance
Explanation of Solution
Given information: The mass of car is
The expression for the distance
Substitute
Conclusion:
Therefore, the distance
(e)
The integral values of
(e)
Answer to Problem 39AP
The expression in part (a) is valid only when
Explanation of Solution
Given information: The mass of car is
The expression for the distance
From the above expression, the distance
Conclusion:
Therefore, the expression in part (a) is valid only when
(f)
The explanation for the answer in part (e).
(f)
Answer to Problem 39AP
The mass of the elevator is less than the mass of the counterweight for the value of
Explanation of Solution
Given information: The mass of car is
The expression for the distance
Substitute
Since the value of distance
Conclusion:
Therefore, the mass of the elevator is less than the mass of the counterweight for the value of
(g)
The value of
(g)
Answer to Problem 39AP
The value of
Explanation of Solution
Given information: The mass of car is
The expression for the distance
Rearrange the above equation.
Substitute
Since the value of distance
Conclusion:
Therefore, the value of
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Physics for Scientists and Engineers with Modern Physics