Answer to Question #287775 in Physics for kocii

Question

A 20 kg block (m1) and a bucket with mass m2 are connected by a light string that passes over a frictionless pulley as shown in Figure 2. The block lies on an incline plane of angle, α = 53.1° and the coefficient of kinetic friction between the block and the plane is 0.40. Calculate the mass of the hanging bucket, m2 if it is moving downward with the acceleration of 2.67 m/s 2 

Answer 1

1) Write the equations for both body according to Newton's second law:

$$-\mu m_1g\cos\theta-m_1g\sin\theta+T=m_1a,\\ -m_2a=-m_2g+T.$$

2) From the first equation, for the tension T, we have

$$T=m_1(a+g(\mu \cos\theta+\sin\theta))=257.2\text{ N}.$$

3) From the second equation, express the mass of the bucket and find it:

$$m_2=\dfrac{T}{g-a}=36\text{ kg}.$$