Advertisements
Advertisements
Question
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
Advertisements
Solution
The given situation can be represented as shown in the following figure.
Where,
AO = Incident path of the ball
OB = Path followed by the ball after deflection
∠AOB = Angle between the incident and deflected paths of the ball = 45°
∠AOP = ∠BOP = 22.5° = θ
Initial and final velocities of the ball = v
Initial velocity's horizontal component = vcos θ along RO
Initial velocity's vertical component = vsin θ along PO
Final velocity's horizontal component = vcos θ along OS
Final velocity's vertical component = vsin θ along OP
The horizontal velocity components remain unchanged. The vertical velocity components are directed oppositely.
∴Impulse imparted to the ball = Change in the linear momentum of the ball
`= mvcostheta - (- mvcos theta)`
`= 2mvcos theta`
Mass of the ball, m = 0.15 kg
Velocity of the ball, v = 54 km/h = 15 m/s
∴ Impulse = 2 × 0.15 × 15 cos 22.5° = 4.16 kg m/s
APPEARS IN
RELATED QUESTIONS
The below figure shows the position-time graph of a particle of mass 4 kg.
- What is the force on the particle for t < 0, t > 4 s, 0 < t < 4 s?
- What is the impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only.)
A car accelerates on a horizontal road due to the force exerted by.
A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude.
Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.
A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg, respectively. Assuming that the magnitudes of acceleration and deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s2.
A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?
An aeroplane is moving uniformly at a constant height under the action of two forces (i) Upward force (lift) and (ii) Downward force (weight). What is the net force on the aeroplane?
Two bodies A and B of same mass are moving with velocities v and 2v, respectively. Compare their (i) inertia and (ii) momentum.
Write the mathematical form of Newton's second law of motion. State the conditions if any.
The unit of linear momentum is :
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate: The velocity acquired by the body.
A car is moving with a uniform velocity 30 ms-1. It is stopped in 2 s by applying a force of 1500 N through its brakes. Calculate the following values : The change in momentum of car.
State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s-2.
Which of the following has the largest inertia?
What do you mean by an impulsive force?
What do you mean by linear momentum of a body? A force causes an acceleration of 10 ms-2 in a body of mass 1 kg. What acceleration will be caused by the same force in a body of mass 4 kg?
A metre scale is moving with uniform velocity. This implies ______.
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
