Weight on a Hypothetical Planet

[raptik]

Homework Statement

The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weight 600 N on Earth, what would he weigh on this planet

Homework Equations

F = (G x M x m)/(R²)

The Attempt at a Solution

Well I know the mass of the person is the same so I rearrange this equation in terms of m and make it equal to the two equations based on their different conditions:
m = (F_e x R_e²)/(M_e x G) = (F_p x R_p²)/(M_p x G)

Working out for F_p I get F_p = (M_p/M_e) x (G/G) x (R_e²/R_p²) x F_e = 100 x 1 x (1/16) x 600N = 3750 N.

This is wrong. Somebody please help me understand what I'm doing wrong. What's the error in my method?

 

[guitarguy1]

You have the equation for force exerted by the planet.

F = (G x M x m)/(R2)

You know G (a constant), M (1/100 the mass of the earth), and R (1/4 the radius of the earth).

All you need is the mass of the person. If the Earth exerts 600N on this person, then his mass is equal to 600N/(9.8N/Kg). Just plug in all your values and it should be correct. I think you are just overcomplicating the process of finding the mass of the person. And also make sure that all of your units are correct.

If you think about it, the answer you have doesn't make sense. The force should me much smaller since the mass of the planet is much smaller while the radius doesn't change that much.

 

[raptik]

Just plug in all your values and it should be correct. I think you are just overcomplicating the process of finding the mass of the person. And also make sure that all of your units are correct.

If you think about it, the answer you have doesn't make sense. The force should me much smaller since the mass of the planet is much smaller while the radius doesn't change that much.

So the only way to solve this is to know the actual values of Earth's mass and Radius and adjust to their respective ratios and plug in the m? I was hoping there would be a way to simply utilize the ratios without having to know the Earth's mass or Radius. Also, I understand that my answer is wrong, but could you tell me where exactly I'm going off course. In theory, I think my idea works but clearly it doesn't. Could somebody explain why?

 

[Doc Al]

Working out for F_p I get F_p = (M_p/M_e) x (G/G) x (R_e²/R_p²) x F_e = 100 x 1 x (1/16) x 600N = 3750 N.

Your method is fine. You just got the ratios M_p/M_e and R_e²/R_p² backwards when you plugged in the numbers.

 

[guitarguy1]

So the only way to solve this is to know the actual values of Earth's mass and Radius and adjust to their respective ratios and plug in the m? I was hoping there would be a way to simply utilize the ratios without having to know the Earth's mass or Radius. Also, I understand that my answer is wrong, but could you tell me where exactly I'm going off course. In theory, I think my idea works but clearly it doesn't. Could somebody explain why?

Like I said before, to find the mass you don't need to use the mass and radius of the earth. The gravitational force on the surface of the Earth is 9.8 N/Kg. So take 600N/(9.8N/Kg) and it will give the mass of the person.

 

[raptik]

Your method is fine. You just got the ratios M_p/M_e and R_e²/R_p² backwards when you plugged in the numbers.

Oh! Clearly. I can't afford to have those kinds of stupid mistakes on an exam. Thnx for pointing that out, I would have totally overlooked that.