Sample Problem Force And Motion

Sample Problem Force And Motion

A passenger of mass m = 72.2 kg stands on a platform scale in an elevator cab. We are concerned with the scale readings when the cab is stationary, and when it is moving up or down.

SOLUTION: One Key Idea here is that the scale reading is equal to the magnitude of the normal force N on the passenger from the scale. The only other force acting on the passenger is the gravitational force , as shown in the free-body diagram of the passenger.

A second Key Idea is that we can relate the forces on the passenger to the acceleration of the passenger with Newton’s second law . However, recall that we can use this law only in an inertial frame. If the cab accelerates, then it is not an inertial frame. So, we choose the ground to be our inertial frame and make any measure of the passenger’s acceleration relative to it.

(a) A passenger stands on a platform scale that indicates his weight or apparent weight. (b) The free-body diagram for the passenger, showing the normal force N on him from the scale and the wavitational force~.
(a) A passenger stands
on a platform scale that
indicates his weight or apparent
weight. (b) The
free-body diagram for the
passenger, showing the
normal force N on him
from the scale and the
gravitational force

What does the scale read if the cab is stationary or moving upward at a constant.

SOLUTION: The Key Idea here is that for any constant velocity (zero or otherwise), the acceleration a of the passenger is zero. Substituting this and other known values into, we find

This is the weight of the passenger and is equal to the magnitude of the gravitational force on him

What does the scale read if the cab accelerates upward at 3.20 m/s2 and downward.

SOLUTION

1

1

During the upward acceleration in part (c), what is the magnitude  of the net force on the passenger, and what is the magnitude  of the passenger’s acceleration as measured in the frame of the cab? Does F net = map.

CHECKPOINT 8: In this sample problem what does the scale read if the elevator cable breaks, so that the cab falls freely that is, what is the apparent weight of the passenger in free fall?

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