Two objects (46.0 and 18.0 kg) are connected by a massless string that passes ov
ID: 1772403 • Letter: T
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