Question

A 5 kg mass is resting on a table, the coefficient of friction between the block and the table is 0.25, that block is connected to a 10 kg hanging mass over a string by a pulley as shown in the picture. What is the acceleration of the 5 kg mass?

Answer 1

Write forces acting on the mass on the table according to Newton's second law:

$$ma=T-\mu mg,\\ Ma=Mg-T.\\\space\\ T=ma+\mu mg,\\\space\\ Ma=Mg-ma-\mu mg,\\\space\\ a=g\frac{M-\mu m}{m+M}=5.72\text{ m/s}^2.$$