Consider a 71.0-kg man standing on a spring scale in an elevator. Starting from

Question

Consider a 71.0-kg man standing on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.34 m/s in 0.650 s. It travels with this constant speed for the next 5.00 s. The elevator then undergoes a uniform acceleration in the negative y direction for 2.00 s and comes to rest. (a) What does the spring scale register before the elevator starts to move? N (b) What does the spring scale register during the first 0.650 s? N (c) What does the spring scale register while the elevator is traveling at constant speed? N (d) What does the spring scale register during the time it is slowing down?

Explanation / Answer

(a) Spring Scale Register Before Elevator starts to move :

Given , mass of man = 71.0 kg

According to newtons second law , F = ma

   where F = force

m = mass

a = acceleration

Before Elevator starts to move , The acceleration felt by the man will be due to gravity of earth i.e.

g = 9.8 m/s2

therefore , F = ma = mg = 71.0 * 9.8 = 695.8 kg.m/s2 = 695.8 N

[N = newton , unit of force ]

Hence F = 695.8 N

(b) Spring scale register during first 0.650 s :

During first 0.650 second , the elevator attains its maximum speed of 1.34 m/s

We know acceleration is rate of change of speed i.e.

a = dv / dt = 1.34 / 0.650 = 2.061 m/s2

Therefore , force due to elevator = F = ma = 71.0 * 2.061 = 146.331 N

Since , elevator is moving ,The total force is sum of Force due to elevator and Force due to Gravity

F = ma + mg = 146.331 + 695.8 = 842.131 N

Hence , F = 842.131 N

(c) Spring scale register while elevator travelling at constant speed:

Since speed is constant , there is no additional acceleration

Therefore the force is only due to gravity { as calculated in (a) }

F = mg = 71.0 * 9.8 = 695.8 N

Hence , F = 695.8 N

(d) Spring scale register during the time it is slowing down :

The elevator undergoes uniform acceleration in negative y - direction for 2.00 s

Acceleration , a = - dv/dt = - 1.34 / 2.00 = - 0.67 m/s2

Therefore , Force due to Elevator = F = ma = 71.0 * (-0.67) = - 47.57 N

Total force will be sum of force due to elevator and force due to gravity

F = mg + ma = 695.8 + ( - 47.57 ) = 648.23 N

Hence , F = 648.23 N

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