Question

Block 1 and block 2, with masses m1 = 5 kg and m2 = 2 kg, are connected by a system of

massless, inextensible ropes and massless pulleys as shown in Fig. 2.

(a) (Marks: 2) Draw the complete free body force diagram of

the system.

(b) (Marks: 4) Solve for the accelerations of block 2 and block

1. Assume that downward direction is positive.

(c) (Marks: 2) Calculate the tensions in each rope.

Answer 1

(a)

(b)

$T_1=2T_2 \\ m_1a_2 = T_1 -m_1g \\ \frac{m_2a_2}{2} = m_2g -T_2 \\ m_2a_2 = 2m_2g -2T_2 \\ a_2(m_1+m_2) = (2m_2-m_1)g \\ a_2 = \frac{(2m_2 -m_1)g}{m_1+m_2} \\ a_2 = \frac{(2 \times 2 -5)10}{5+2} = \frac{-10}{7} \; m/s^2$

(c)

$m_1a_2 = T_1 -m_1g \\ 5 \times \frac{-10}{7} = T_1 – 5 \times 10 \\ T_1 = 50- \frac{50}{7} = \frac{300}{7} \;N$