Question

42) When you weigh yourself on good old terra firma (solid ground), your weight is 142 lb. In an elevator your apparent weight is 121 lb. What are the direction and magnitude of the elevator’s acceleration?

Answer 1

We are given the following information

Actual weight = 142 lb.

Apparent weight = 121 lb.

Direction of the elevator's acceleration:

Notice that the apparent weight (121 lb.) is less than the actual weight (142 lb.)

This means that the direction of the elevator's acceleration must be downward since a downward acceleration

results in an apparent weight less than the actual weight.

Magnitude of the elevator’s acceleration:

There are two forces acting on you in the elevator.

The applied force of scale acts upward and the force due to gravity acts downward.

Let us apply Newton's 2nd law of motion to find the magnitude of the elevator’s acceleration.

`\begin{gathered} \sum F_y=m\cdot a \\ W_a-W=m\cdot a \\ a=(W_a-W)/(m) \\ a=(W_a-W)/((W)/(g)) \\ a=(W_a-W)/(W)\cdot g \\ a=(121-142)/(142)\cdot9.81 \\ a=-1.5\; \; (m)/(s^2) \end{gathered}`

Notice that the negative sign represents a downward acceleration as we discussed earlier.

When we are interested in the magnitude, we only consider the numerical value, not the direction.

Therefore, the magnitude of the elevator’s acceleration is 1.5 m/s²