Physics question "Force"

[dorjiako]

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1.At what height above the earth's surface is the acceleration due to gravity 10% of that at sea level?
2.The moon has 1/6 the acceleration of gravity of the earth. What would the mass of the earth have to be to have this acceleration at its surface?

 

[costales]

1. M is Earth's mass, R radius. At sea level, g = GM/R^2. At unknown h above sea level, 0.1g = GM/(h+R)^2. Divide the two equations and solve for h .
2. g/6 = GM'/R^2. Solve for new mass M'.

 

[dorjiako]

Thanks a lot. Got the answer. However, I am presently stuck with this question:
1. Two masses are tied together by a string over a massless pulley so that they can both move vertically. One mass is 5kg and the other is 1kg. The masses are released from rest. How far does the mas fall to reach a velocity of 10m/s?

 

[costales]

On the 5kg side you have 5g - T = 5a. On the 1kg side you have T - 1g = 1a. Solve for a, then use t = v/a and y = .5at^2.

 

[dorjiako]

Thanks a million times. Yep, I got the answer. Thanks again.

 

[dorjiako]

I need help solving this problem:1, What is the minimum radius that a cyclist can ride around without slipping at 10 kilometers per second if the coefficient of friction between his tires and the road is 0.5?