# Gravitational Force on bathroom scales

• Celer

#### Celer

Hi all, I'm new here. So anyways, I have been studying for exams by going through my old tests, and I found a question from one of them that I can't solve...I hope someone can help me.

1. A person stands on a set of bathroom scales which have been calibrates in Newtons. The scales read 500N (assume 3 sig figs)
A)What would the reading be if the same person stood on the scales on a planet where the gravitational field strength, g is 14 N/kg?

B) If this planet had a mass of 7.0 x 10^24 kg, what would its radius be?

C) What mass would this person weigh at an altitude of 2.8 x 10^6 m above the planet's surface?

## Homework Equations

Well I used the equations for
A)
F=mg

B)
F = G (mass planet) (mass object) / d^2

C) I don't know what equation to use...

So what I did:

for A) I used Fg=mg
so:

Fg = mg
500 = m (9.8)
m = 51

then I substituted for the planet.

Fg = m(14)
Fg = (51)(14)
Fg = 714

For B) I used F = G (mass planet) (mass object) / d^2
so,

Fg = 6.67 x 10^-9 *7.0x10^24 / d^2
d^2 = 4.669
d = 2160789.4 km

For C) given height, I don't know what equation to use.

So really, I don't know whether I used my equations correctly, so I would appreciate someone to point out my errors.

C) What mass would this person weigh at an altitude of 2.8 x 10^6 m above the planet's surface?

Hi. The mass of a person should always be constant when he/she moves away from the surface of the planet. I believe the verb "weigh" here does not imply the weight of the person.

for A) I used Fg=mg
so:

Fg = mg
500 = m (9.8)
m = 51

then I substituted for the planet.

Fg = m(14)
Fg = (51)(14)
Fg = 714
Looks good.

For B) I used F = G (mass planet) (mass object) / d^2
so,

Fg = 6.67 x 10^-9 *7.0x10^24 / d^2
d^2 = 4.669
d = 2160789.4 km
Did you leave out the mass of the person?

For C) given height, I don't know what equation to use.
Use the same equation that you used for B. What would be the person's distance to the center of the earth?

Last edited:
C) What mass would this person weigh at an altitude of 2.8 x 10^6 m above the planet's surface?
I assume that the word mass was an error and that the question should read: What would this person weigh...

So, would the mass of the person be unchanged, at 51 kg? I am not sure on what you meant when you said use the same equation as "C".

Do you mean using Fg = mg? If so, how do I factor the given altitude into the equation?

So, would the mass of the person be unchanged, at 51 kg?
Yes.
I am not sure on what you meant when you said use the same equation as "C".
Oops... I meant: Use the same equation as used in "B".