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Gravitational Force on bathroom scales

  • Thread starter Celer
  • Start date
  • #1
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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 cant 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 dont 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.
 

Answers and Replies

  • #2
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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.
 
  • #3
Doc Al
Mentor
44,877
1,129
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 dont 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:
  • #4
Doc Al
Mentor
44,877
1,129
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...
 
  • #5
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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?
 
  • #6
Doc Al
Mentor
44,877
1,129
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".
 

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