Q. 225.0( 3 Votes )

# In a simple Atwood machine, two unequal masses m_{1} and m_{2} are connected by a string going over a clamped light smooth pulley. In a typical arrangement (figure 5-E7) m_{1} = 300 g and m_{2} = 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 :

Let acceleration of the blocks be

Let tension in the string be T

Given:

Mass m_{1}=300 g=0.3 kg

Mass m_{2}=600 g=0.6 kg

Let the mass 1 be moving upward and mass 2 moves downward

Equation for mass 1,

-----(1)

Equation for mass 2,

------(2)

Adding both the equation we get,

Now putting the values, we get,

i)

Using the equation of motion,

Where u=initial velocity = 0 m/s and tie t=2s

ii) From equation (1), we get,

iii) Force on the clamp is due to tension from both side of the pulley, i.e., twice of tension

∴ required force

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