Answer to Question #269549 in Mechanics | Relativity for sadman2222

Question

2. Block 1 and block 2, with masses m1 = 5kg and m2 = 2kg, 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)

Let acceleration of m₁ will be a m/s² and acceleration of m₂ will be $\frac{a}{2}$ m/s²

$m_1g -2T =m_1a\\ 5 \times 10 -2T = 5a \\ 50 -2T = 5a \\ m_2g -T = m_2 \frac{a}{2} \\ 2 \times 10 -T = 2 \times \frac{a}{2} \\ 20 -T = a \\ T = 20 -a \\ 50 -2(20-a) = 5a \\ 50 -40 + 2a = 5a \\ 10 = 3a \\ a = \frac{10}{3} = 3.33 \;m/s^2$

(c)

$20 -T = 3.33$

$T = 20 -3.33 = 16.67 \;N$ (on m₂)

Tension of m₁ $= 2T = 2 \times 16.67 = 33.34 \;N$