Two objects (46.0 and 18.0 kg) are connected by a massless string that passes ov

Question

Two objects (46.0 and 18.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find (a) the acceleration of the objects and (b) the tension in the string.

Two blocks are sliding to the right across a horizontal surface, case A the mass of each block is 4.4 kg. In Case B the mass of block 1 (the block behind) is 8.8 kg, and the mass of block 2 is 4.4 kg. No frictional force acts on block 1 in either Case A or Case B. However, a kinetic frictional force of 8.6 N does act on block 2 in both cases and opposes the motion. For both Case A and Case B determine (a) the magnitude of the forces with which the blocks push against each other and (b) the magnitude of the acceleration of the blocks.

Explanation / Answer

1) a) Let tension be T and acceleration be a, applying force equation on the blocks,

T-mg = ma

Mg - T = Ma

Adding the two equations,

Mg - mg = Ma +ma

a = g*(M-m) /(M+m) = 9.8*(46-18)/(46+18)

= 4.2875 m/s^2 Answer

T = mg +ma = 18*(9.8+4.2875)

= 253.6 N answer

2 a) Let the force be F, Writing force equation on two blocks whose accelerations has to be same,

On B, F-8.6 =ma, and on A, - F= ma

F-8.6 = - F

F= 4.3 N

in second case, F-8.6 = 4.4a, and - F = 8.8a

F - 8.6 = - 0.5F

F =8.6/1.5 = 5.73 N answer

B) in first case, a =F/m = 4.3/4.4 = 0.977 m/s^2

In second case, a = F/M= 5.733/8.8 = 0.651 m/s^2

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