A 0.145 kg baseball is pitched at 42 m/s. The batter hits it horizontally to the pitcher at 58 m/s.
GIVEN:
m = 0.145 kg
v = 42 m/s
batter v = 58 m/s
a. Find the change in momentum of the ball.
p = mv
p = (0.145)(42)
p = 6.09
--> What velocity would I use? Would i use the velocity of the baseball
b. If the ball and bat are in contact for 4.6 x 10^-4 s, what is the average force during contact?
a. Ah, the change in momentum! Well, since momentum is calculated by multiplying mass and velocity, we need to use the velocity of the baseball to find its momentum. So, the change in momentum would be:
Δp = (0.145 kg) × (42 m/s) = 6.09 kg·m/s
b. Now, to determine the average force during contact, we can use the formula:
F = Δp / Δt
Where Δt is the time interval the ball and bat are in contact. In this case, Δt is given as 4.6 × 10^-4 seconds. Plugging in the values, we get:
F = (6.09 kg·m/s) / (4.6 × 10^-4 s) = some gigantic force!
Remember, though, this value is only an average force, so it might not be representative of the exact dynamics at play. But hey, that's physics for you – always trying to keep you on your toes!
a. To find the change in momentum of the ball, you can calculate the change in momentum using the formula:
Change in momentum = final momentum - initial momentum
Since the given velocity of the ball is before it was hit, we can consider it as the initial momentum. Therefore, the initial momentum is:
Initial momentum = mass x initial velocity = (0.145 kg)(42 m/s) = 6.09 kg·m/s
The final momentum of the ball can be calculated using the mass and the velocity after it was hit. However, the question does not provide the velocity of the ball after it was hit. Therefore, we cannot determine the change in momentum without that information.
b. To calculate the average force during contact, you can use the formula:
Average force = change in momentum / time
Since we do not have the change in momentum, we cannot determine the average force during contact without that information.
a. The change in momentum of the ball can be calculated using the formula:
Change in momentum (Δp) = Final momentum (p final) - Initial momentum (p initial)
Since the baseball is pitched initially and then hit by the batter, we need to consider the change in momentum due to each action separately.
For the initial momentum (p initial), we use the velocity of the baseball when it is pitched, which is given as 42 m/s. The mass of the baseball is also given as 0.145 kg.
p initial = m * v
= 0.145 kg * 42 m/s
= 6.09 kg·m/s
For the final momentum (p final), we use the velocity of the baseball after it is hit by the batter. The velocity is given as 58 m/s.
p final = m * v
= 0.145 kg * 58 m/s
= 8.41 kg·m/s
Now we can calculate the change in momentum:
Δp = p final - p initial
= 8.41 kg·m/s - 6.09 kg·m/s
= 2.32 kg·m/s
Therefore, the change in momentum of the ball is 2.32 kg·m/s.
b. To find the average force during contact, we can use the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse exerted on it. The impulse can be calculated by multiplying the average force during contact (F) by the time of contact (Δt):
Impulse (J) = Δp = F * Δt
To find the average force during contact, we rearrange the formula:
F = Δp / Δt
Using the calculated value of Δp as 2.32 kg·m/s and the given time of contact as 4.6 x 10^-4 s, we can now calculate the average force during contact:
F = Δp / Δt
= 2.32 kg·m/s / (4.6 x 10^-4 s)
= 5.04 x 10^3 N
Therefore, the average force during contact is 5.04 x 10^3 Newtons.
a) The sign of the velocity changes after the ball is hit. That makes the CHANGE in momentum equal to
M[42 -(-58)] = 0.145 kg * 100 m/s
b) Impulse
= (average force) x (time of contact)
= (change in momentum) = 14.5 kg m/s
Solve for the average force