Need some physics help

[Finns14]

The mass of a robot is 6810 kg. This robot weighs 3150 N more on planet A than it does on planet B. Both planets have the same radius of 4.85 x 106 m. What is the difference MA -MB in the masses of these planets?


I would really love to know how you get to the answer. I can get the numerical value from the book but that doesn't help me solve similar problems.

 

[dullard]

weight = gravity * mass of robot

g = G*MP/r^2

g = gravity, G = gravitational constant, MR = robot mass, MP = planet mass, r = radius.

Thus FA - FB = 3150N = (gA*MR) - (gB*MR) = G*MR/r^2*(MA - MB)

You know everything there, so solve for MA - MB.

 

[Finns14]

hmm looks right I am still confused though

 

[dullard]

Originally posted by: Finns14
hmm looks right I am still confused though

Confused about what?

 

[Finns14]

so you set the difference (3150N) equal to the furthest right part of the equations the divided the weight by G*MR/r^2. Ok I hope I am right because I am starting to understand this more.

 

[dullard]

Originally posted by: Finns14
so you set the difference (3150N) equal to the furthest right part of the equations the divided the weight by G*MR/r^2. Ok I hope I am right because I am starting to understand this more.

Yes.

 

[Finns14]

awsome thanks alot your were super helpful

 

[Finns14]

Well if you could I have another problem I am stumped on its kinda similar

Three uniform spheres are located at the corners of an equilateral triangle. Each side of the triangle has a length of 0.837 m. Two of the spheres have a mass of 4.36 kg each. The third sphere (mass unknown) is released from rest. Considering only the gravitational forces that the spheres exert on each other, what is the magnitude of the initial acceleration of the third sphere?

 

[OdiN]

42

 

[Finns14]

Originally posted by: OdiN
42

Sigh

 

[dullard]

I won't do all the details, it is your homework to do.

Start by drawing a picture. For example, lets put the unknown sphere at the top center, and the two known ones on the bottom left and bottom right.

Ignore one sphere (lets just randomly choose the bottom right sphere to ignore) - it is there to confuse you for now.

Thus what does the bottom left sphere do to the unknown sphere? Answer: It pulls the sphere towards it. The acceleration, using the formula I gave above is: a = G*Mk/d^2.

a = acceleration, G = gravitational constant, Mk = mass of known sphere, d = distance

You know all of those, so you know acceleration. Acceleration is towards the bottom left. Thus, there is a component of acceleration down, and another component left. Use trigonometry to find the component down.

Now double that answer, since the bottom right sphere also pulls down the same amount. The left and right pulls cancel.

 

[Finns14]

Ok I think it was the other sphere that was confusing me