Question

1.Solve the following
A) A bus starts from the stop and takes 50sec to get the speed of 10m/s.If the mass of the bus along with the passengers is 10000kg, calculate the force applied by the engine of bus to push the bus at a speed of 10m/s.
b) A vehicle having mass equal to 1000kg is running with a speed of 10m/s.After applying the force of 1000N for 10sec. what will happen to the speed of the vehicle?
c)Find the recoil velocity of a gun having mass equal to 8kg, if a bullet of 25gm aquires the velocity of 400m/s after firing from the gun.
d)A girl of 30kg mass is running with a velocity of 2m/s.She jumps over a stationary cart of 3kg while running.Find the velocity of the cart after jumping of boy.

Answer 1

A)
v = u + a t
u = 0 ,  t = 50 sec.  v = 10 m/s
   => a = 10/50 = 0.20 m/s²
Force = F = m a = 10, 000 * 0.20 = 2, 000 Newtons = 2, 000 kN

Force can also be calculated as the rate of change of momentum of the bus:
     = [ 10, 000 * 10 - 10, 000 * 0 ]  / 50  = 2000 kN

B)

  F = 1, 000 N  and  m = 1,000 kg
   =>  a = F/m = 1 m/s²

  u = 10 m/s    t = 10 s        
       v = u + a t = 10 + 1 * 10 = 20 m/s

c)
We apply the conservation of momentum principle.
       m1 = 8 kg,  v1 = ?    m2 = 25 gm    and    v2 = 400 m/s
           m1 v1 + m2 v2 = 0 
           v1 = - 0.025 * 400 / 8 = -1.25 m/s
   the gun recoils with 1.25 m/s

d)
   we apply the principle of conservation of momentum. we ignore the friction between the cart and the ground as well as between the girl and the ground..

       m1 = 30 kg    m2 = 3 kg      v1 = 2 m/s    v2 = 0

         m1 v1 + m2 v2 = (m1 + m2) v
             30 kg * 2 m/s + 3 kg * 0 = (33) * v
           v =  20/11 m/sec
both the cart and the girl move together with this velocity after the girl jumps on to the cart.