Question

Two blocks, with masses 4.00 kg and 8.00 kg are connected by a string and slide down a

30 inclined plane (see figure). The coefficient of kinetic friction between the 4.00 kg block and the

plane is 0.25; that between the 8.00 kg block and the plane is 0.35. Calculate

a) the acceleration of each block

b) the tension in the string

Answer 1

Determine the acceleration. Begin with writing equations for both blocks using Newton's second law:

$4:-T+mg\sin\theta-\mu_4mg\cos\theta=ma,\\ 8:T+Mg\sin\theta-\mu_8Mg\cos\theta=Ma.$

The solution of this system is

$$a=g\frac{(m+M)\sin\theta-(\mu_4m+\mu_8M)\cos\theta}{m+M}=2.21\text{ m/s}^2.\\\space\\ T=M(a+g(\mu_8\cos\theta-\sin\theta))=2.24\text{ N}.$$