59.0k views
21 votes
Consider two blocks that are attached bv a string. Block 1 (mass of 2 ko) lavs on a flat dlane. Block ? (mass of 3 kg) hangs freely off the edge of the plane. In the absence of friction, Block 2 would fall and the string would pull Block 1 towards the edge. Find the static coefficient of friction needed to keep Block at its starting position.

User Blaf
by
3.7k points

1 Answer

14 votes

With no friction, block 1 would be pulled to the edge of the table as block 2 falls. By Newton's second law, the net horizontal force on block 1 is

∑ F[1, h] = T = (2 kg) a

where T = magnitude of tension and a = acceleration of the blocks, while the net force on block 2 is

∑ F[2] = (3 kg) g - T = (3 kg) a

where (3 kg) g = weight of block 2 and g = 9.8 m/s². Notice that we take the downward fall of block 2 to be the positive direction.

Eliminate T and solve for a :

T + ((3 kg) g - T) = (2 kg) a + (3 kg) a

(3 kg) g = (5 kg) a

a = 3g/5

Solve for T :

T = (2 kg) (3g/5) = 6g/5 kg = 11.76 N

Now, taking friction into account, block 1 would have net force

∑ F[1, h] = T - sf = 0

so that the maximum magnitude of static friction is sf = 11.76 N. The net vertical force on block 1 is

∑ F[1, v] = n - (2 kg) g = 0

where n = magnitude of the normal force. Let µ be the coefficient of static friction. It follows that

n = (2 kg) g = 19.6 N

sf = µ n ⇒ µ = (11.76 N) / (19.6 N) = 0.6

User George Cscnt
by
3.2k points