Weight question. Help please. (1 Viewer)

[d-alarmclock]

I'm not sure which formulas to use for the following question. Could someone please walk through the steps, and maybe for a few of them give a brief explanation of what they did?

Consider a man who weighs 675 N on Pluto (diameter of Pluto = 2274km, mass of Pluto = 1.3 c 10^22kg).
a) On another planet of diameter 13.4 x 10^9m he weighs 1658N. What is the mass of this second planet?
b) This same man the. Travels to Venus (mass = 4.86 x 10^24kg, equatorial radius = 6051km). What is the value of g for Venus?

Thanks in advance!

 

[d-alarmclock]

Bumpppppp

 

[strawberrye]

Ok, I will tell you the principles of each step of the necessary working out to get the answer and you will need to input the appropriate number in the calculator yourself to get the answer.

You need to calculate the mass of the man. Consider W=mg, and g=GM/r^2, so by remembering to divide the given diameter of Pluto by two and express it in m-since metres is Si units not km, you will get the value of r, G is just the value of the gravitational constant, and M is the mass of the planet in kg which is given, and so by substituting these values, you will get the value of g for Pluto.

since W=mg, so m=W/g, where W=675N, and you will get the g from the previous calculation, hence, you will get the mass of the man. -this is needed to calculate part a.

a)W=mg, W=1658N which is given, and you already know m-mass of the man is constant regardless of the planet the man is on, and so g=W/m, and hence you can calculate g for this second planet, once again, you know g=GM/r^2, divide the given diameter by two to get the radius-r, and G is the gravitational constant, and you already know g, so you can manipulate the equation to calculate the mass of the planet in kg, essentially, this is just g divide G/r^2.

b)The second part is a trick question, g=GM/r^2, so the mass of the man does not have any effect on the value of g on the planet, so convert the radius from km to m, and sub the values given-value of G can be found on formula sheet, M is given, r is found easily, and so you get the value of g for Venus.

Hope this helps

 

[d-alarmclock]

So when is F = GMm/d^2 used?

 

[Fizzy_Cyst]

So when is F = GMm/d^2 used?

Equate W=mg and F=GMm/d^2 to obtain g=GM/d^2