Question

A block with mass m= 10.0kg is at rest on a ramp inclined at angle 30 degrees. A hanging block with mass M is connected to the first block by a mass-less rope, strung over a friction-less pulley.
If the coefficient of static friction between the block and the ramp is 0.231, what range of masses, M, could hold the system at rest? Also, why is are a range of masses, M, reasonable?

Picture: http://oi57.tinypic.com/24v5qfc.jpg

Answer 1

math srry i suck

Answer 2

Haha, it's ok, I suck at it too >.<

Answer 3

;)

Answer 4

Have you tried solving for the mass of M that keeps the mass of m resting at equilibrium?

The force that keeps m at rest is calculated with the following equation:
\[F = mg \sin \theta + \mu mg \cos \theta\]

Plugging everything in gives:
\[F = 68.77 N\]

The weight of M must be equal to 68.77 N to keep it at rest.
Setting this equal where W=mg,
\[68.77 N = (9.81m/s^2)m\]
\[m = 7.01 kg\]
So this means that one of the possible masses of M to keep the other mass resting could be 7.01kg. Sorry if this doesn't help at all.

Answer 5

ya sounds right