The cart below including the cannon and the ball has a total

The cart below (including the cannon and the ball) has a total mass of 100 kg and a velocity of 3 m/sec to the right. The cannon ball (mass=10 kg) is fired at a speed of 30 m/sec to the left. What is the final velocity of the card (whose total mass is now 90 kg)? Assuming no heat loses, what is the initial PE stored in the gun powder?

Solution

Mass of the cart with cannon and ball M = 100 kg

Initial velocity of the cart u = 3 m/s

mass of ball m = 10 kg

velocity of ball v = -30 m/s

mass of cart m \' = M - m = 100 -10 = 90 kg

From law of conservationof momentum ,

   Mu = mv + m \' v \'

(100x3) = 10(-30) +90 v \'

   300 = -300 + 90 v \'

   90 v \' = 600

       v \' = 6.666 m/s

(b). Potential energy of the gun power, U= change in kinetic energy

           U =(1/2)Mu ²-[(1/2)mv ² +(1/2) m\'v\' ²]

              = [0.5 x100x 3 ² ]-[(0.5 x10x(-30) ² +(0.5x90x6.666 ²)]

             = 450 -[4500 +2000]

            = -6050 J

in magnitude U = 6050 j