A ball of mass \(200g\) is travelling in a straight line with speed of \(15ms^{-1}\) along negative X-axis is deflected by a bat at an angle of \(30^{o}\). If the speed of the ball after deflection is \(10ms^{-1}\). Find: the impulse on the ball.
Ans: \(J=4.8Ns\).
A rubber ball of mass \(50g\) falls from a height of \(1m\) and rebounds to a height of \(0.5m\). Find: the impulse and the average force acting between the ball and the ground if the time for which they are in contact was \(0.1s\).
Ans: \(J=0.378Ns\) and \(F_{avg}=3.78N\).
A ball is moving with a momentum of \(15 kg.ms^{-1}\) strikes against a vertical wall at an angle \(30^{o}\) with the wall and its reflected back with the same momentum at same angle. Calculate: impulse.
Ans: \(J=15\sqrt{3}kg\frac{m}{s}\).
A cricket ball of mass \(150g\) is moving with a velocity of \(12ms^{-1}\) and is hit by a bat so that the ball is turned back with a velocity of \(20ms^{-1}\). The force of the blow acts for \(0.01Sec\) on the ball. Find: the average force exerted by the bat on the ball?
Ans: \(F=-400N\).
A ball is moving with momentum of \(5 kg.ms^{-1}\) strikes against a wall at an angle \(45^{o}\) and reflected back to same angle. Calculate: change in momentum.
Ans: \(\Delta p=-7.07kg\frac{m}{s}\).
A batsman deflects a ball by an angle of \(45^{o}\) without changing its initial velocity which is equal to \(54 km.h^{-1}\). What is the impulse imparted on the ball if the mass of the ball is \(0.15kg\)?
Ans: \(J=4.16Ns\).
Below figure shows an estimated force-time graph for a base ball struck by a bat. From this graph determine: (I) Impulse delivered o the ball. (II) Force exerted on the ball. (III) Maximum force on the ball.
Ans:(I) \(J=\left(1.35\times10^{4}\right)kg\frac{m}{s}\), (II) \(F=\left(9\times10^{3}\right)N\) and (III) \(F_{max}=\left(18\times10^{3}\right)N\).
A force acting on a body of mass \(2kg\) varies with time as shown in below diagram; Find: (i) Impulse of the force? and (ii) Velocity of the body?
Ans:(i) \(J=12kg\frac{m}{s}\) and (ii) \(V_{final}=6\frac{m}{s}\).
A ball of mass \(0.1kg\) is thrown against a wall. It strikes the wall with a velocity of \(30ms^{-1}\) and rebounds with a velocity of \(20ms^{-1}\). Calculate: the impulse of the force exerted by ball on the wall.
Ans: \(|\vec{J}|=5Ns\).
A machine gun fires a bullet of mass \(40g\) with a speed of \(1200 ms^{-1}\). The person holding the machine gun can exeret a maximum force of \(144N\) on it. What is the number of bullet that can be fired from the machine gun per second?
Ans: \(n=3Nos\).
A hammer weighing \(1kg\) moving with a speed of \(10ms^{-1}\) strikes a head of a nail driving it \(10cm\) into a wall. Neglecting the mass of the nail. Calculate: (i)The acceleration during the impact? (ii) Time interval of the impact? and (iii) The impulse?
Ans:(i) \(a=-500\frac{m}{s^{2]}\), (ii) \(\Delta t=0.02Sec\) and (iii) \(J=-10Ns\).
The initial speed of a body of mass \(2Kg\) is \(0.5ms^{-1}\). A force acts for \(4s\) in the direction of the motion of the body. The forc-time graph is shown below. Calculate: the impulse of the force and final speed of body.
Ans: \(J=8.50Ns\) and \(V_{final}=9.25\frac{m}{s}\).
A body of mass \(10kg\) is acted upon by a force given by \(F=\left(3t^{2}-30\right)N\). The initial velocity of the body is \(10ms^{-1}\). Calculate: velocity of the body after \(5Sec\)?
Ans: \(V=7.5\frac{m}{s}\).
A golf ball of mass \(60g\) at rest is hit by striker. Find: the impulse of the hit if the ball stops after travelling a horizontal distance of \(50m\) with uniform retardation of \(4ms^{-2}\).
