A 3 kg block and a 5 kg block are connected by a thin string, which is hung over

Question

A 3 kg block and a 5 kg block are connected by a thin string, which is hung over a pulley as shown. Initially, the 5 kg block is resting on a table while the 3 kg block is hanging in the air. Assume the pulley's mass and friction are negligible. What are the magnitudes of the tension in the string (pulling on each of the blocks) and the normal force of the table (pushing up on the 5 kg block)? The table is suddenly removed, so that the 5 kg block falls downwards and pulls the 3 kg block upwards. What will the acceleration of each block be? What is the tension in the string after the table is removed?

Explanation / Answer

m = 3 kg

M = 5 kg

T = tension in the rope

Fn = normal force on 5 kg block by the surface

from the force diagram for block of 3 kg

T = mg

T = 3 x 9.8 = 29.4 N

from the force diagram for block of 5 kg

T + Fn = Mg

29.4 + Fn = 5 x 9.8

Fn = 19.6 N

b)

acceleration of atwood machine is given as

a = (M - m)g/(M+ m) = (5 - 3) (9.8)/(5 + 3) = 2.45 m/s2

c)

T' = tension force in atwood machine = 2 Mmg/(M+ m) = 2 (5) (3) (9.8)/(5 + 3) = 36.75 N

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