1. An 80 kg person stands in an elevator which is ascending towards the top of a

Question

1. An 80 kg person stands in an elevator which is ascending towards the top of a building.

A) As the elevator begins its ascent, it accelerates at the rate of 1 m/s2. What is the force that the elevator must exert on the man in order to cause this acceleration in the upward direction?
B) As the elevator ascends at constant speed, what is the force that the elevator exerts on the person?
C) As the elevator reaches the desired floor it decelerates at the rate of 1 m/s2 before coming to a complete stop. What is the force that the elevator exerts on the person in this situation?

Explanation / Answer

Weight of person is acting Downwards = m*g
Let the Force exerted by Elevator on the man = F

(A)
Net Acceleration a is Upwards -
Fnet = m*a
Fnet = F - mg
m*a = F - mg
F = ma + mg
F = 80*( 1 +9.8)
F =  864 N
Force exerted by Elevator on the man, F =  864 N

B)
If the elevator is moving with constant Velocity, acceleration a = 0
Fnet = F - mg
m *a = F - mg
0 = F - mg
F = mg
F = 80 * 9.8 N
F = 784 N
Force exerted by Elevator on the man, F =  784 N

(C)
Now the elevator is decelerating, a = -1 m/s^2
Fnet = F - mg
m *a = F - mg
- 80 * 1 = F - 80 * 9.8
F = 80 (9.8 -1)
F = 704 N
Force exerted by Elevator on the man, F =  704 N

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