Minimum mass

Classical Mechanics Level 3

What can be the minimum value of mass M M of hanging block so that 2 k g 2~kg block slips over 4 k g 4~kg block?

Details and assumptions - μ \mu denotes the coefficient of frictional force, g = 10 m / s 2 g=10m/s^2 ,pulley is light and neglect the mass of the rope.

20 k g 20~kg 30 k g 30~kg will not slip for any mass 5 k g 5~kg 10 k g 10~kg

Vilakshan Gupta by Vilakshan Gupta , 19, India

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1 solution

Steven Chase
Oct 21, 2017

This is a deceptively simple problem. The key to solving it is to imagine the extreme case (M = infinity). That represents the biggest forward acceleration possible for the two blocks, which is 10 m/s^2. Now the question is whether or not the friction between the 2 kg block and the 4 kg permits the small block to accelerate this way. We can easily see that the friction permits 15 m/s^2 of acceleration, so the small block will not slip for any mass M.

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