Calculate the force a mother must exert to hold her 12.0 kg child in an elevator

Question

Calculate the force a mother must exert to hold her 12.0 kg child in an elevator under the following conditions.

(a) The elevator accelerates upward at 0.850 m/s2.
_____N
Calculate the ratio of this force to the weight of the child._______


(b) The elevator moves upward at a constant speed.
______N
Calculate the ratio of this force to the weight of the child._____


(c) The upward bound elevator decelerates at 2.30 m/s2.
_______ N
Calculate the ratio of this force to the weight of the child._______

Explanation / Answer

Given,

m = 12 kg ;

weight of the child = W = mg = 12 x 9.8 = 117.6 N

(a) a = 0.85 m/s2

As elevator is accelerating upwards, the net force will be;

F = m (g + a) = 12 x (9.8 + 0.85) = 127.8 N

Hence, required force = F = 127.8 N (128 N aprox)

Ratio = F/W = 127.8/117.6 = 1.09

Hence, F/W = 1.09

(b)At constant speed the acceleration on the child is only acceleration due to gravity.

F = ma = 12 x 9.8 = 117.6 N

Hence, required force = F = 117.6 N (118 N aprox)

Ratio = F/W = 117.6/117.6 = 1

Hence, Ratio = F/W = 1

(c)When the elevator is decelerating with, a = 2.3 m/s2

F = m ( g - a ) = 12 x (9.8 - 2.3) = 90 N

Hence, Required force = F = 90 N

Ratio = F/W = 90/117.6 = 0.765

Hence,F/W = 0.765

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