Question

Two blocks with masses 4.00 kg and 8.00 kg are connected by a string and slide down a 30.0° inclined plane as shown in Figure 1. 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.

Draw the free body diagram of the blocks.

Calculate the acceleration of the blocks.

Calculate the tension in the string.

Answer 1

a)

$$n_1=m_1g\cos{30}\\f_{k1}=\mu_{k1}m_1g\cos{30}\\m_1a_1=m_1g\sin{30}-\mu_{k1}m_1g\cos{30}\\a_1=9.8(\sin{30}-0.2\cos{30})=3.20\frac{m}{s^2}$$

$$n_2=m_2g\cos{30}\\f_{k2}=\mu_{k2}m_2g\cos{30}\\m_2a_2=m_2g\sin{30}-\mu_{k2}m_2g\cos{30}\\a_2=9.8(\sin{30}-0.4\cos{30})=1.51\frac{m}{s^2}$$

b)

$$m_1a_1=m_1g\sin{30}-\mu_{k1}m_1g\cos{30}-T\\m_2a_2=m_2g\sin{30}-\mu_{k2}m_2g\cos{30}+T$$

$$T=\frac{4\cdot8(3.2-1.51)}{4+8}=4.51\ N$$