In a simple Atwood machine, two unequal masses `m_1 and m_2` are connected by string going over a clamped light smooth pulley . In a typical arrangement `m_1=300g` and `m_2=600g`. The system is released from rest. (a). Find the distance traveled 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.

Explanation

Given that ` m_1 = 0.3 kg
` m_2 = 0.6 kg`
` T-(m_1g+m_1a)=0` …….i.
` rarr t=m-1g+m_1a`
` Again, T+m_2a-m_2g=0`…………
`rarr T=m_2g-m_2a`
` From equations. i. and ii, we have
` m_1 g+m_1a+m_2a-m_2g=0`
`rarr a(m_1+m_2)=g(m_2-m_1)`

a. t=2 sec, acceleration a=3.266 ms^-2
Initial velocity u=0
So, distance traveled by the body
`S=ut+1/2 at^2 `
`= 0+1/2 (3.266)2^2=6.5m`
From equation i.
` T=m_1(g+a0`
=0.3(3.8+3.26)=3.9N`
The force exerted by the clap on the pulley is given by,
` F-2T=0`
`rarr F=2T=2xx3.9=7.8N`.