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When you weigh yourself on solid ground, your weight is 155 lb. In an elevator, your apparent weight is 135 lb.

What are the direction and magnitude of the elevator's acceleration?

Answer :

Final answer:

The magnitude of the elevator's acceleration is 1.29 m/s^2, and the direction is downward. This is determined by the change in normal and apparent weight using the conversion of pounds to newtons and Newton's second law.

Explanation:

When you weigh yourself on solid ground, your weight is the gravitational force acting on your body. If your apparent weight is less, such as when it's 135 lb instead of the normal 155 lb, that indicates the elevator is accelerating downward. To find the magnitude and direction of the elevator's acceleration, we can use Newton's second law (F=ma).

First, we need to convert your weight in pounds (lb) to the force in newtons (N). The conversion factor is approximately 4.44822 N per pound.

So, your normal weight is 155 lb times 4.44822 N/lb = 689.474 N. Your apparent weight in the elevator is 135 lb times 4.44822 N/lb = 600.509 N.

The difference in normal and apparent weight is the net force, which is due to the elevator's acceleration. Using Newton's second law, net force = mass imes acceleration. You can rearrange this to solve for acceleration: acceleration = net force / mass. Since your mass is your weight divided by the acceleration due to gravity (9.8 m/s2), we have: acceleration =

(689.474 N - 600.509 N) / (689.474 N / 9.8 m/s2)

= 1.29 m/s2 (downward).

Therefore, the magnitude of the elevator's acceleration is 1.29 m/s2, and the direction is downward.

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