If the child has a mass of 15.1 kg, calculate the magnitude of the force the mot

Question

If the child has a mass of 15.1 kg, calculate the magnitude of the force the mother exerts on the child under the following conditions. (b) The elevator accelerates upward at 0.942 m/s2. 1.097 Refer to your answer to part (a). N Calculate the ratio of this force to the weight of the child. child's weight (c) The elevator moves upward at a constant speed Refer to your answer to part (a). N Calculate the ratio of this force to the weight of the child child's weight (d) The upward bound elevator decelerates at 2.25 m/s2 force force Calculate the ratio of this force to the weight of the child. force child's weight

Explanation / Answer

( b)

As elevator accelerate upwards, they feel more weight. Because, the support must supply

excess over the gravity to accelerate upwards. In this case, the acceleration is

a = (g + 0.942 ) = 9.8 m/s^2 + 0.942 m/s^2 = 10.742 m/s^2

Force, F = ma = (15.1 kg ) ( 10.742 m/s^2 ) = 162 N

And the force on child F = mg = ( 15.1 kg ) (9.8 m/s^2)

Force / child weight = ( 15.1 kg ) (9.8 m/s^2) / 162 N = 0.912

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(c) When it move at constant speed:

F = mg = (15.1 kg ) ( 9.8 m/s^2 ) = 147.98 N

In three significant digits , F = 148 N

And

Force / child weight = ( 15.1 kg ) (9.8 m/s^2) / 148 N = 1

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d)

When decelerates, the acceleration is

a = (g - 2.25) = 9.8 m/s^2 - 2.25 m/s^2 = 7.55 m/s^2

Thus, the force is

F = ma = (15.1 x 7.55 m/s^2) = 114 N.

And

Force / child weight = ( 15.1 kg ) (9.8 m/s^2) / 114 N = 1.298

In three significant digits, ratio = 1.30

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