Concept explainers
A 85-kg man is in an elevator that is accelerating downward at the rate of 1.3 m/s2.
- a. What is the true weight of the man in newtons?
- b. What is the net force acting on the man required to produce the acceleration?
- c. What is the force exerted on theman’s feet by the floor of the elevator?
- d. What is the apparent weight of the man in newtons? (This is the weight that would be read on the scale dial if the man were standing on a bathroom scale in the accelerating elevator.)
- e. How would your answers to parts b through d change if the elevator were accelerating upward with an acceleration of 1.3 m/s2?
(a)
The true weight of the man of mass
Answer to Problem 6SP
The true weight of the man of mass
Explanation of Solution
Given info: The mass of the man is
Write the expression for the weight.
Here,
Substitute
Conclusion:
Thus, the true weight of the man of mass
(b)
The net force acting on the man required to produce the acceleration.
Answer to Problem 6SP
The net force acting on the man required to produce the acceleration is
Explanation of Solution
Given info: The mass of the man is
Write the expression for the net force on the man.
Here,
Substitute
Since the acceleration is in the downward direction , the net force will also in the downward direction.
Conclusion:
Thus, the net force acting on the man required to produce the acceleration is
(c)
The fore exerted on the man’s feet by the floor of the elevator.
Answer to Problem 6SP
The force exerted on the man’s feet by the floor of the elevator is
Explanation of Solution
Force exerted on the man’s feet by the floor is in the upward direction.
Write the expression for the net force acting on the man
Here,
The negative sign in the above equation indicate that the normal force is opposite to gravitational force. Since gravitational force is in downward direction normal force is in the upward direction.
Substitute
Conclusion:
Thus, the force exerted on the man’s feet by the floor of the elevator is
(d)
The apparent weight of the man in newtons.
Answer to Problem 6SP
The apparent weight of the man in newtons is
Explanation of Solution
The apparent weight is the weight is the weight experienced by the man in the elevator.
This is weight measured by a weighing apparatus in an elevator. According to newtons third law
This should be equal to normal force acting on the man by the floor.
The normal force on the man by the floor is equal to
Conclusion:
Thus, the apparent weight of the man in newtons is
(e)
The apparent weight of the man if the elevator is accelerating upward with an acceleration of
Answer to Problem 6SP
The apparent weight of the man if the elevator is accelerating upward with an acceleration of
Explanation of Solution
Write the expression for the normal force acting on the man.
Substitute
The apparent weight is the weight is the weight experienced by the man in the elevator.
This is weight measured by a weighing apparatus in an elevator. According to newtons third law This should be equal to normal force acting on the man by the floor.
The normal force on the man by the floor is equal to
Conclusion:
Thus, the apparent weight of the man in newtons is
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Chapter 4 Solutions
Physics of Everyday Phenomena
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