A 0.20 kg baseball is pitched horizontally with a speed of + 40 m/s. When it hits the bat a force of 1.7x10^4 N acts on the ball to send it soaring in the opposite direction. If the bat and ball are in contact for 8.0x10^-3 s, what is the impulse delivered to the ball by the bat?
Force * time = change of momentum = impulse
1.4*10^7 * 8 * 10^-3 = impulse
Is there no part b where they ask you the resulting speed ?
To find the impulse delivered to the ball by the bat, you need to use the impulse-momentum principle. The impulse is defined as the change in momentum of an object and can be calculated using the formula:
Impulse = Change in Momentum
The momentum of an object is defined as the product of its mass and velocity. In this case, the baseball's initial momentum is given by:
Initial momentum = mass × initial velocity
Final momentum is given by:
Final momentum = mass × final velocity
Since the ball changes direction and momentum when it is hit by the bat, the change in momentum can be calculated by subtracting the final momentum from the initial momentum:
Change in momentum = Final momentum - Initial momentum
Now, let's calculate the impulse delivered to the ball by the bat step by step:
Step 1: Calculate the initial momentum of the ball
Using the formula for momentum:
Initial momentum = mass × initial velocity
= 0.20 kg × 40 m/s
Step 2: Calculate the final momentum of the ball
Using the formula for momentum:
Final momentum = mass × final velocity
Since the ball's direction is reversed, the final velocity will be in the opposite direction and have a magnitude of 40 m/s:
Final momentum = 0.20 kg × (-40 m/s)
Step 3: Calculate the change in momentum
Using the formula:
Change in momentum = Final momentum - Initial momentum
Step 4: Calculate the impulse
The impulse delivered to the ball by the bat is equal to the change in momentum:
Impulse = Change in momentum
Now you can plug in the values and calculate the impulse delivered to the ball.