Question

(Newton's Law of Motion) A mass of 8 kg and another of 12 kg are suspended by a string on either side of a frictionless pulley. Find the acceleration of each mass.

Answer 1

Each mass has gravity acting on it, where the force is mg, for m = 8kg and 12kg respectively.

That results in a tension in the rope from each mass. If the masses were equal, the tension on the rope would exactly cancel gravity and the masses wouldn't move.

But as it is, clearly the 12 kg mass accelerates down, meaning the net force acting on it must be not zero and pointing down.

Answer 2

The force acting on that mass is

(Force of gravity) + (Force of tension from the 8kg mass)
= -12g + 8g
= -4g

where the negative means down.

Therefore, as F = ma, it must be that this mass, acceleration satisfies the equation
F = ma
-4g = 12a
i.e.,
a = -g/3

Answer 3

Find now the acceleration on the 8kg mass. Intuitively it should be the exact opposite.

Answer 4

Make sense?

Answer 5

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