Question

In a simple Atwood machine, two unequal masses m₁ and m₂ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the following figure), m₁ = 300 g and m₂ = 600 g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds; (b) find the tension in the string; (c) find the force exerted by the clamp on the pulley.

Answer 1

The masses of the blocks are m₁ = 0.3 kg and m₂ = 0.6 kg
The free-body diagrams of both the masses are shown below:

For mass m₁,
 T − m₁g = m₁a    ...(i)
For mass m₂,
m₂g − T= m₂a    ...(ii)

Adding equations (i) and (ii), we get:
g(m₂ − m₁) = a(m₁ + m₂)
\[\Rightarrow a = g{\left( \frac{m_2 - m_1}{m_1 + m_2} \right)}$\]
\[ = 9 . 8 \times \frac{0 . 6 - 0 . 3}{0 . 6 + 0 . 3}\]
\[ = 3 . 266 m/ s^2\]

(a) t = 2 s, a = 3.266 ms⁻², u = 0
So, the distance travelled by the body,
\[S = ut + \frac{1}{2}a t^2 \]
\[ = 0 + \frac{1}{2}\left( 3 . 266 \right) 2^2 = 6 . 5 m\]

(b) From equation (i),
T = m₁ (g + a)
   = 0.3 (9.8 + 3.26) = 3.9 N

(c)The force exerted by the clamp on the pulley,
F = 2T = 2 × 3.9 = 7.8 N