A 0.149-kg baseball is pitched a 40 m/s. The batter hits it horizontally to the pitcher at 56 m/s. Find the change in momentum of the ball. If the ball and bat were in contact 4.2 multiplied by 10-4 s, what would be the average force while they touched?
Well, well, well, we've got ourselves a real physics problem here! Let's dive right into it.
To find the change in momentum of the ball, we need to calculate the difference between the initial and final momenta. The initial momentum is given by the product of the mass (0.149 kg) and the initial velocity (40 m/s), while the final momentum is given by the product of the mass (0.149 kg) and the final velocity (56 m/s).
So, the change in momentum is:
Change in momentum = (0.149 kg * 56 m/s) - (0.149 kg * 40 m/s)
Now, let's get those calculators out and crunch the numbers. *drumroll* The change in momentum is approximately 0.053 kg*m/s.
Now, as for the average force, we can use the equation:
Force = Change in momentum / Time
Since the contact time is given as 4.2 * 10^-4 s, we just plug in the numbers and get:
Force = 0.053 kg*m/s / (4.2 * 10^-4 s)
Oh boy, this math stuff is fun! After some calculations, we find that the average force is approximately 126,190 N.
But remember, this is all just an average. The actual force will vary during the contact time. So, don't forget to take this with a pinch of clownish humor!
To find the change in momentum of the ball, we need to calculate the final momentum and the initial momentum, and then subtract the initial momentum from the final momentum.
First, let's find the initial momentum of the ball. We can use the formula:
Initial momentum = mass * initial velocity
Given:
Mass of baseball (m) = 0.149 kg
Initial velocity of baseball (u) = 40 m/s
Initial momentum = 0.149 kg * 40 m/s = 5.96 kg·m/s
Now, let's find the final momentum of the ball. We can use the same formula, but this time we use the final velocity:
Final velocity of baseball (v) = 56 m/s
Final momentum = 0.149 kg * 56 m/s = 8.344 kg·m/s
The change in momentum is the difference between the final and initial momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 8.344 kg·m/s - 5.96 kg·m/s
Change in momentum = 2.384 kg·m/s
Now, let's calculate the average force exerted during the contact between the ball and bat. We can use the impulse-momentum principle, which states that the change in momentum is equal to the average force multiplied by the time of contact:
Change in momentum = Average force * Time of contact
Given:
Change in momentum = 2.384 kg·m/s
Time of contact (t) = 4.2 * 10^-4 s
Average force = Change in momentum / Time of contact
Average force = 2.384 kg·m/s / 4.2 * 10^-4 s
Average force ≈ 5,676 N
Therefore, the average force exerted while the ball and bat were in contact is approximately 5,676 Newtons.
To find the change in momentum of the ball, we can use the equation:
Change in momentum = Final momentum - Initial momentum
The momentum of an object can be calculated using the equation:
Momentum = mass of the object x velocity of the object
Given:
- Mass of the baseball (m) = 0.149 kg
- Initial velocity of the baseball (u) = 40 m/s
- Final velocity of the baseball (v) = 56 m/s
Now, let's calculate the initial and final momentum of the baseball:
Initial momentum = mass x initial velocity
Initial momentum = 0.149 kg x 40 m/s
Final momentum = mass x final velocity
Final momentum = 0.149 kg x 56 m/s
Change in momentum = Final momentum - Initial momentum
Now, let's calculate the change in momentum:
Change in momentum = (0.149 kg x 56 m/s) - (0.149 kg x 40 m/s)
The change in momentum can be positive or negative depending on the direction. In this case, since the ball is hit horizontally back towards the pitcher, the change in momentum would be:
Change in momentum = (0.149 kg x 56 m/s) - (0.149 kg x 40 m/s)
Now, to calculate the average force exerted by the ball and bat during their contact, we can use Newton's second law of motion:
Force = Change in momentum / Time
Given:
- Change in momentum = calculated above
- Time of contact (t) = 4.2 x 10^(-4) s
Now, let's calculate the average force:
Average force = Change in momentum / Time
Average force = (Change in momentum) / (4.2 x 10^(-4) s)
With this, you can find both the change in momentum of the ball and the average force exerted during their contact.