What is the "apparent" weight of a 80kg person standing on a bathroom scale in an elevator accelerating upward at a rate of 2 m/s/s?

Question

The difference between "apparent" weight and your "gravitational" weight is simple. Gravitational weight is dependent on your mass and the strength of the gravitational field you are in. Apparent weight is how much you "feel" you weigh.

Example: Astronauts in the International Space Station feel as if they are weightless even though they still weigh up to 80% as much as they do on earth. They still have mass and they still are well within the Earth's gravitational field. However, their "apparent" weight is zero because if they tried to stand on a scale, the scale would be falling at the same rate as they are and would read zero force.

This elevator question is again another example of what you weigh vs. what it "feels" like you weigh. AKA .. Normal Force.

Answer 1

The trick to this question is realizing that your apparent weight is what you feel from the scale pushing up onto your feet. Because of Newton's 3rd Law, the scale will push upward onto your body with the same force you press down onto it.

Their are two forces acting on your body at this time. The Earth exerts a downward force and the scale provides and upward force. This upward force the scale provides to you (normal force) must be greater than your actual weight in order to accelerate you upward. If the force that the scale presses on you is more than your weight, then you press downward on the scale with a force more than your weight. This is why you feel heavier and why the scale will read a number greater than your weight.

If we draw a free body diagram and write the true statement that Fnet = Fn - Fw where Fnet is net force, Fn is normal force, and Fw is weight, then we can solve for Fn = Fnet + Fg. Fnet = ma and Fw = mg

Fn = ma + mg

Fn = (80kg)(2m/s^2) + (80kg)(10m/s^2) = 960N

For ease of calculations the value of g was rounded to 10m/s^2 rather than 9.8m/s^2.