A 83-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.2 m/s in 0.76 s. The elevator travels with this constant speed for 5.0 s, undergoes a uniform negative acceleration for 1.8 s, and then comes to rest. What does the spring scale register in each of the following time intervals?
(a) before the elevator starts to move
(b) during the first 0.76 s of the elevator's ascent
(c) while the elevator is traveling at constant speed
(d) during the elevator's negative acceleration
To understand what the spring scale would register in each time interval, we need to consider the forces acting on the man standing on the scale in the elevator.
(a) Before the elevator starts to move:
When the elevator is at rest, the only force acting on the man is his weight, which can be calculated using the formula:
Weight = mass * gravity
Weight = 83 kg * 9.8 m/s² (acceleration due to gravity)
Weight = 813.4 N
So, the spring scale would register a force of 813.4 N.
(b) During the first 0.76 s of the elevator's ascent:
During this time interval, the elevator is accelerating, so there is an additional force acting on the man upwardly. This force can be calculated using the formula:
Force = mass * acceleration
Force = 83 kg * (1.2 m/s² / 0.76 s) (acceleration = change in speed / time)
Force = 130.26 N
Therefore, the spring scale would register a force of 813.4 N + 130.26 N = 943.66 N.
(c) While the elevator is traveling at a constant speed:
When the elevator is moving at a constant speed, it means there is no acceleration. Therefore, the net force on the man is zero. The only force acting on the man is his weight, as calculated in part (a). So, the spring scale would register a force of 813.4 N.
(d) During the elevator's negative acceleration:
During this time interval, the elevator experiences negative acceleration or deceleration. The additional force acting on the man, in the downward direction, can be calculated using the formula:
Force = mass * acceleration
Force = 83 kg * (-1.2 m/s² / 1.8 s) (negative acceleration = change in speed / time)
Force = -55.33 N
The scale would register a force of 813.4 N - 55.33 N = 758.07 N.
So, to summarize, the spring scale would register:
(a) 813.4 N
(b) 943.66 N
(c) 813.4 N
(d) 758.07 N
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