# Mass vs. weight with a falling rock and a spring scale

## Homework Statement

1. You stand on a spring-loaded bathroom scale in a bathroom. The scale "reads" your mass. What is the scale actually measuring?

2. Similarly, you stand on a spring-loaded bathroom scale in an elevator that is accelerating upward at 2.0 m/s^2. The scale "reads" your mass. What is the scale measuring?

A) Your mass B) Your weight C) The force of the scale pushing up on your feet D) The force of your feet pushing down on the scale

1. A large rock falls on your toe. Which concept is most important in determining how much it hurts?

2. Similarly, if the large rock merely sits on your toe, which concept is most important in determining how much it hurts?

A) The mass of the rock B) The weight of the rock C) Both the mass and the weight are important. D) Either the mass or the weight, as they are related by a single multiplicative constant, g.

## Homework Equations

Weight = mg = dp/dt

Impulse = Δp = mΔv

## The Attempt at a Solution

For 1,2: To me, C seems correct for both of them, but B also seems correct for the first part, as weight is equal to the force of the scale on your feet for that part.

For 3,4: For a falling rock, to me it seems that mass would be most important as the pain level would be proportional to the change in momentum, or the impulse, on your foot. For a stagnant rock, it seems either weight or mass would be the same.

Last edited:

You would be correct in reasoning that C is right for the first two questions. While you might be tempted to say that a scale reads your weight, and it is true under normal circumstances that the force of your weight is equal to the upward force of the scale, the scale is calibrated to read the upward force it gives due to your weight. This is why you would appear heavier on a scale accelerating upward in an elevator; the acceleration adds to the "g" term in the equation, which causes a greater upward force to act on the scale.

I believe you may have copied questions 3 and 4 incorrectly; they appear the same as 1 and 2.

Here are the intended questions for 3 and 4:

A large rock falls on your toe. Which concept is most important in determining how much it hurts?

Similarly, if the large rock merely sits on your toe, which concept is most important in determining how much it hurts?

A) The mass of the rock B) The weight of the rock C) Both the mass and the weight are important. D) Either the mass or the weight, as they are related by a single multiplicative constant, g.

My attempt is above.

CWatters
Homework Helper
Gold Member
For question 1...

C) The force of the scale pushing up on your feet
D) The force of your feet pushing down on the scale

Rivercats... Is there a way to show that it's C) and not D) ?

CWatters
Homework Helper
Gold Member
For 3&4 I would have thought the amount of energy your toe had to absorb would be important. That's mgh. I reckon answer D.

For question 1...

Rivercats... Is there a way to show that it's C) and not D) ?

I should think so. Even though the force of your weight pushing down on the scale is what's being measured, the scale is calibrated to read the upward force that results from that. In other words, the scale attempts to balance the force of your weight by exerting an equal force (normal force) upward, and this normal force is what the scale reads.

Here are the intended questions for 3 and 4:

A large rock falls on your toe. Which concept is most important in determining how much it hurts?

Similarly, if the large rock merely sits on your toe, which concept is most important in determining how much it hurts?

A) The mass of the rock B) The weight of the rock C) Both the mass and the weight are important. D) Either the mass or the weight, as they are related by a single multiplicative constant, g.

My attempt is above.

I would say that D is correct. The amount of pain your foot feels is equivalent to the energy it absorbs, which is mgh. Since mg = weight, using either mg or simply weight means the equation remains the same. So, considering pain, mass and weight are pretty interchangeable.

Consider this also. On the moon, g changes, which means weight changes, not mass. This affects the amount of pain that is felt. This may lead you to answer B, but since D says "either" mass or weight, not both, I would still say D is correct.

Fnet=ma
1a. Fs-mg=0
1b. Fs-mg=ma

Thus the scale shows force acting on the body to produce static or accelerating.
So i think the answer is (C)

2a. All Potential energy to be absorbed by the toe before it stops
ΔPE=mgh
2b. The force acting on the toe equal to mg

So mass is the only constant factor in both 2a and 2b thus the answer is (A)