1. Two bodies of mass 3 kg and 4 kg are suspended at the ends of massless string passing over a
frictionless pulley. The acceleration of the system is (Take g = 9.8 m/s2)

2.A ball of mass 100 g and another ball of 120 g moves towards each other with speeds 6 m/s
and 5 m/s respectively. If they stick to each other colliding, what would be the velocity of the
combined mass after the collision?

1

Answers

2014-12-23T02:45:59+05:30

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The mass of 3 kg goes up  and  mass of 4 kg comes down with an acceleration a.  The tension in the string is uniform through out its length and is T.

     T - 3 * g = 3 * a
     4 * g - T = 4 * a
   solving these,  a = g/7 = 1.4 m/sec/sec   and    T = 24 * 1.4 Newtons

============================
       Inelastic collision. 
   momentum is conserved after collision.  There is a loss of energy in collision.

     100 * 6 - 120 * 5 = (100+120) * v
           v = 0          =>    the combined mass becomes stationary.

1 5 1
cant understand
1st question. tension - weight of 3kg = mass 3kg * acceleration.... weight of 4 kg - tension in string = mass 4 kg * acceleration .. since the string is tight, does not expand on pulling, the acceleration of 3 kg and 4 kg are same.. entire string moves at same speed at every instant.
sum of initial momentum of both = 100 gm * (+6 m/s) + 120 gms * (-5 m/s) = 0. we use -5 m/s as it is in - x direction when 6 m/s is in +x direction. Hence on adding the two vectors (momentum), net momentum is zero.
there is energy loss = 1/2 m1 v1^2 + 1/2 m2 v2^2. due to inelastic collision. this energy is dissipated as sound, heat and light. also the bodies get deformed in shape. the energy is used in changing the shape of bodies.