Answer to Question #131997 in Physics for Hannah

Question

A brick with the mass of 5kg is sitting on a table connected to another hanging bucket by a string over a pulley. The coefficient of kinetic friction between the brick and table top is 0.40. Believe that the pulley is massless and frictionless. If the system accelerates at 5.0m/s^2, what is the mass of the bucket?

Answer 1

To answer this question, first we need to obtain the equation for mass in terms of acceleration, the other mass, and other constants.

Consider the brick. The normal force, force of gravity, friction, and tension are acting together and result in certain acceleration. Assume that Y points up and X point to the right. Assume that the brick moves to the right, then

$$Ma=T-\mu Mg,\\ T=M(a+\mu g).$$

For the hanging and moving bucket, we have

$$-ma=T-mg,\\ m=\frac{T}{g-a}=\frac{M(a+\mu g)}{g-a}=9.29\text{ kg}.$$

This result was obtained with g=9.8 m/s².