What Is the Elevator's Z Acceleration When Your Apparent Weight Is Half?

[gtaylor]

Imagine that you are standing on a scale in an elevator and you find that your apparent weight as read by the scale is half your real weight. What is the elevator's z acceleration az relative to the ground? Express you answer as a multiple of g, and make sure that your value for az has the correct sign.

 

[kuruman]

Draw a free body diagram and write down Newton's Second Law. Go for it.

 

[tomcue]

I would first like to clarify that z acceleration refers to the acceleration in the vertical direction, or along the z-axis. With that in mind, let's consider the situation described in the content.

When standing on a scale in an elevator, the scale measures the normal force exerted by the elevator on the person's feet, which is equal to the person's apparent weight. In this scenario, the scale reads half of the person's actual weight, indicating that the normal force exerted by the elevator is also half of the person's actual weight.

From Newton's second law, we know that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force acting on the person is the difference between their actual weight and their apparent weight, which is equal to half of their actual weight. Therefore, we can write the following equation:

Fnet = m * az

Where Fnet is the net force, m is the mass of the person, and az is the z acceleration of the elevator.

Now, we also know that the weight of an object is equal to its mass multiplied by the acceleration due to gravity, or g. Therefore, we can rewrite the equation as:

mg - (1/2)mg = m * az

Simplifying this equation, we get:

(1/2)mg = m * az

Dividing both sides by m, we get:

(1/2)g = az

This means that the z acceleration of the elevator, relative to the ground, is half of the acceleration due to gravity, or g. We can express this as a multiple of g by dividing both sides by g, which gives us:

az = (1/2)g/g = 1/2

Therefore, the z acceleration of the elevator is -1/2g, with a negative sign indicating that it is in the downward direction. In conclusion, the elevator's z acceleration relative to the ground is -1/2g, or half of the acceleration due to gravity in the downward direction.