Gravitational Force on bathroom scales

In summary: So you would have to factor in the altitude into the equation. In summary, the conversation was about a person asking for help with a question involving bathroom scales and gravitational forces. The question asked for the reading on the scales on a different planet with a given gravitational field strength, the radius of the planet, and the person's weight at a certain altitude above the planet's surface. The person used the equations F=mg and F = G (mass planet) (mass object) / d^2 to solve the questions, but wasn't sure if they were correct and asked for clarification.
  • #1
Celer
13
0
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.
 
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  • #2
Celer said:
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
Celer said:
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:
  • #4
Celer said:
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
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
Celer said:
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".
 

1. What is the gravitational force on a bathroom scale?

The gravitational force on a bathroom scale is the force that the Earth's gravity exerts on an object placed on the scale. This force is what causes the scale to display a weight measurement.

2. How is the gravitational force on a bathroom scale calculated?

The gravitational force on a bathroom scale is calculated using the formula F = mg, where F is the force, m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s² on Earth). The scale measures the force and then calculates the mass using this formula.

3. Does the gravitational force on a bathroom scale change in different locations?

Yes, the gravitational force on a bathroom scale can vary slightly depending on the location. This is because the acceleration due to gravity is affected by factors such as altitude and the density of the Earth's core.

4. Why does the gravitational force on a bathroom scale change when I move around on it?

The gravitational force on a bathroom scale can change when you move around on it because the scale is measuring the force being exerted on it by your body. As you shift your weight, the scale's sensors detect a change in force and adjust the displayed weight accordingly.

5. Can the gravitational force on a bathroom scale be affected by objects placed near it?

Yes, the gravitational force on a bathroom scale can be affected by nearby objects. This is because all objects with mass have a gravitational pull, and if an object with a larger mass is placed near the scale, it can slightly alter the scale's measurements.

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