A sphere of radius R and mass M is held on a ramp that makes an angle with the h

Question

A sphere of radius R and mass M is held on a ramp that makes an angle with the horizontal by a string that pulls with force F directed up the ramp and running over the top of the sphere. If the magnitude of this force is as small as it can be and still hold the sphere at rest on the ramp, what must be the value of (s), the coefficient of static friction between sphere and ramp?

http://cl.ly/1r2A2V1D2r1o362s1S2L

1) tan/2

2) sin/tan

3) tan

4) 1/2tan

5) 2/tan

6) zero; no static friction is needed in this case

7) 1/2

8) tan2

9) 1.0

10) cos/tan

Explanation / Answer

net force along the ramp = F + f - Mgsin = 0, so f = Mgsin - F (1)
net torque about the touching point of the sphere and the ramp = MgRsin - F(2R) = 0, so F = Mgsin/2
put it into (1), f = Mgsin/2

net force perpendicular to the ramp = n - Mgcos = 0, so n = Mgcos

so = f/n = tan/2

answer: 1)

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