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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 85 kg in newtons.
Answer to Problem 6SP
The true weight of the man of mass 85 kg in newtons is 833 N.
Explanation of Solution
Given info: The mass of the man is 85 kg.
Write the expression for the weight.
W=mg
Here,
W is the weight of the man
m is the mass of the man
g is the acceleration of the man
Substitute 85 kg for m and 9.8 m/s2 for g in the above equation to get W.
W=(85 kg)(9.8 m/s2)=833 N
Conclusion:
Thus, the true weight of the man of mass 85 kg in newtons is 833 N.
(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 110.5 N.
Explanation of Solution
Given info: The mass of the man is 85 kg and acceleration of the man is 1.3 m/s2.
Write the expression for the net force on the man.
Fnet=ma
Here,
Fnet is the net force acting on the man
a is the acceleration of the man
Substitute 85 kg for m and 1.3 m/s2 for a in the above equation to get Fnet.
Fnet=(85 kg)(1.3 m/s2)=110.5 N
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 110.5 N.
(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 722.5 N.
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
Fnet=Fg−FN
Here,
FN is the normal force acting on the mass by the floor of the elevator
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 110.5 N for Fnet and 833 N for Fg in the above equation to get FN
110.5 N=833 N−FNFN=722.5 N
Conclusion:
Thus, the force exerted on the man’s feet by the floor of the elevator is 722.5 N.
(d)
The apparent weight of the man in newtons.
Answer to Problem 6SP
The apparent weight of the man in newtons is 722.5 N.
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 722.5 N, Therefore apparent weight of the man is equal to 722.5 N.
Conclusion:
Thus, the apparent weight of the man in newtons is 722.5 N.
(e)
The apparent weight of the man if the elevator is accelerating upward with an acceleration of 1.3 m/s2.
Answer to Problem 6SP
The apparent weight of the man if the elevator is accelerating upward with an acceleration of 1.3 m/s2 is 943 .5 m/s2.
Explanation of Solution
Write the expression for the normal force acting on the man.
FN=Fg+Fnet
Substitute 110.5 N for Fnet and 833 N for Fg in the above equation to get FN.
FN=833 N+110.5 N=943.5 N
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 943.5 N, Therefore apparent weight of the man is equal to 943.5 N.
Conclusion:
Thus, the apparent weight of the man in newtons is 943.5 N.
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