Thinking Problem Down Here?

Question

Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that accelerated upward? Downward?
2.- THIS IS A SECOND PROBLEM
Would the springs inside a bathroom scale be more compressed or less compressed if you weighed yourself in an elevator that moved upward at a constant velocity? Downward at a Constant Velovcity?

Please answer them and specify which answer is for what problem.

Answer 1

PROBLEM 1
Newton's second law states that the total force exerted on a body equals the product of its mass times its acceleration, i.e. Ftotal=m*a.

If you are standing on a scale then the total force exerted on your body equals Fsc - B, where Fsc is the force from the scale, facing upwards and B the force from the planet earth (i.e. your weight), facing downwards.

If you are at rest (that is a=0) then

Fsc(rest) - B = m*0 = 0 i.e. Fsc(rest) = B

If you are accelerated upwards then the product m*a has a positive sign, so Fsc(up)=B+m*a which means that Fsc(up) > B. Taking the previous result into consideration we deduce that Fsc(up) > Fsc(rest) so the springs inside the scale are more compressed.

If your are accelerated downwards then the product m*a has a negative sign, so Fsc(down)=B-m*a which means that Fsc(down) < B. Taking the first result into consideration we deduce that Fsc(down) < Fsc(rest) so the springs inside the scale are less compressed.

PROBLEM 2
If you move at a constant velocity (either up or down) then a=0, so Fsc(constant)=B, that is Fsc(constant)=Fsc(rest). So the springs compress the same.

Answer 2

Problem 1: The springs would be more compressed if you weighted yourself in an elevator that accelerates upward, and less compressed if you weighted yourself in an elevator that accelerates downward.

Problem 2: The compression in the springs should not change if you weighted yourself in an elevator that is moving at a constant velocity (upward or downward).

It all has to do with Newton's second law, i.e. F=m*a.

I hope this helps.

Answer 3

The springs would be more compressed in an elevator accelerating upward, less compressed in an elevator accelerating downward and neither more nor less compressed in an elevator moving at constant velocity in either direction.