When a 0.15 kg baseball is hit, it approaches the bat with a speed of 20 m/s and undergoes an elastic collision. (a) What is the impulse delivered to the bat by the ball? (b) If the baseball is in contact with the bat for 1.3 ms, what is the average force exerted by the bat on the ball? Assume a 1-dimensional collision
3.195 N
To find the impulse delivered to the bat by the ball, we can use the impulse-momentum principle, which states that the impulse applied to an object is equal to the change in momentum of the object.
(a) The impulse delivered to the bat by the ball can be calculated using the equation:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Given that the mass of the baseball is 0.15 kg and the speed of the baseball is 20 m/s before the collision, the initial momentum of the baseball is:
Initial momentum = 0.15 kg × 20 m/s
To find the final momentum of the baseball after the collision, we need to know the speed of the baseball after the collision. Since the collision is elastic, the kinetic energy before the collision is equal to the kinetic energy after the collision. Therefore, we can use the equation for kinetic energy:
Kinetic energy = 0.5 × mass × velocity^2
Given that the mass of the baseball is 0.15 kg and the speed of the baseball before the collision is 20 m/s, the initial kinetic energy of the baseball is:
Initial kinetic energy = 0.5 × 0.15 kg × (20 m/s)^2
After the collision, since the ball is rebounding, the final kinetic energy of the baseball is also equal to:
Final kinetic energy = 0.5 × 0.15 kg × (velocity after collision)^2
Since the collision is elastic, the kinetic energy before the collision is equal to the kinetic energy after the collision:
0.5 × 0.15 kg × (20 m/s)^2 = 0.5 × 0.15 kg × (velocity after collision)^2
Simplifying the above equation gives:
(20 m/s)^2 = (velocity after collision)^2
Taking the square root of both sides, we find that the speed of the baseball after the collision is also 20 m/s.
Therefore, the final momentum of the baseball is:
Final momentum = 0.15 kg × 20 m/s
The change in momentum is the difference between the final momentum and the initial momentum:
Change in momentum = Final momentum - Initial momentum
Substituting the values we found earlier:
Change in momentum = 0.15 kg × 20 m/s - 0.15 kg × 20 m/s
Simplifying the equation gives:
Change in momentum = 0
Hence, the impulse delivered to the bat by the ball is zero.
(b) The average force exerted by the bat on the ball can be calculated using the equation:
Force = Impulse / Time
Given that the impulse is zero (as determined in part (a)), the average force exerted by the bat on the ball is also zero.