Question

1. The sketch shows two 4 kg blocks on a horizontal surface, joined by a string S. They are attached to a 2 kg mass by another string which passes over a frictionless pulley, allowing the 2 kg mass to hang freely. Each of the blocks experiences 6 N of friction.

a) Show that the system accelerates to the right at 0.8 m/s². Calculate the tension in string S.
b) 4 kg S 4 kg 2 kg [4] [4]
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Answer 1

M g - T = M a acceleration of hanging block (M = 2)

2 g - T = 2 a where M = 2

T = 2 g - 2 a

T = 8 * a + 12 N acceleration of blocks on table

2 g - 2 a = 8 a + 12

10 a = 2 g - 12

a = .8 m/s^2 (assuming g = 10 m/s^2)

T = 2 g - 2 a = 2 * 10 - 2 * .8 = 20 - 1.6 = 18.4 N

Check: For blocks on table

a = (18.4 - 12) / 8 = 6.4 / 8 = .8 m/s^2