A baseball has a mass of about 0.15 kg, and it is pitched towards home plate at a speed of about 60 m/s. If the bat exerts an average force of 8600 N for 2.4 ms, what is the final speed of the ball in m/s?
To find the final speed of the ball, we can use Newton's second law of motion, which states that the force applied to an object is equal to the rate of change of its momentum. The momentum of an object is given by the product of its mass and velocity.
First, we need to calculate the initial momentum of the ball. The initial velocity is given as 60 m/s, and the mass of the ball is 0.15 kg. Therefore, the initial momentum is:
Initial momentum = mass × velocity
Initial momentum = 0.15 kg × 60 m/s
Next, we need to calculate the change in momentum of the ball due to the force applied by the bat. The change in momentum is given by the product of the force and the duration of the force application. The average force applied by the bat is 8600 N, and the duration is 2.4 ms (converted to seconds):
Change in momentum = force × duration
Change in momentum = 8600 N × 2.4 ms (converted to seconds)
Finally, we can calculate the final momentum of the ball by adding the initial momentum and the change in momentum. The final momentum is equal to the mass of the ball multiplied by its final velocity:
Final momentum = initial momentum + change in momentum
Final momentum = (0.15 kg × 60 m/s) + (8600 N × 2.4 ms converted to kg⋅m/s)
To find the final velocity of the ball, we can rearrange the equation for momentum and solve for velocity:
Final velocity = final momentum / mass
Final velocity = (final momentum) / 0.15 kg
By substituting the values we calculated, we can find the final velocity of the ball in m/s.
Note: Please note that the calculation provided is a simplified representation and does not take into account various factors such as air resistance, coefficient of restitution, and other factors that may affect the actual ball trajectory and final speed.