I got all but this problem.
A 0.145-kg baseball is pitched at 42.0 m/s. The batter hits it horizontally to the pitcher at 58 m/s.
A. Find change in momentum? Is it =.145*58-(-.145*42)=1.45-kg m/s?
B. If bat and ball are in contact for 4.6 x 10-4 s, what is average force during contact?
ah 100*.145 = 14.5 not 1.45
the change in momentum divided by the time in contact = average force.
A. To find the change in momentum, you need to calculate the initial momentum and final momentum separately. The initial momentum of the baseball is given by the product of its mass (0.145 kg) and its initial velocity (-42.0 m/s).
Initial momentum = (-0.145 kg)(-42.0 m/s) = 6.09 kg⋅m/s
The final momentum of the baseball is given by the product of its mass (0.145 kg) and its final velocity (58.0 m/s). Since the baseball is hit horizontally, the final velocity in the vertical direction is still -42.0 m/s.
Final momentum = (0.145 kg)(-42.0 m/s) = -6.09 kg⋅m/s
The change in momentum is the difference between the final momentum and initial momentum.
Change in momentum = Final momentum - Initial momentum
= (-6.09 kg⋅m/s) - (6.09 kg⋅m/s)
= -12.18 kg⋅m/s
So, the change in momentum is -12.18 kg⋅m/s.
B. To find the average force during contact, you can use the impulse-momentum theorem. This theorem states that the impulse experienced by an object is equal to the change in its momentum. The impulse can be calculated as the product of the average force during contact and the duration of the contact.
Impulse = Average force x Duration of contact
Since we already know the change in momentum (from part A) and the duration of contact (4.6 x 10^-4 s), we can rearrange the equation to solve for the average force.
Average force = Impulse / Duration of contact
Substituting the values, we get:
Average force = (-12.18 kg⋅m/s) / (4.6 x 10^-4 s)
= -26,565.2 N
Therefore, the average force during contact is approximately -26,565.2 N, where the negative sign indicates that the force is in the opposite direction of the motion.
To find the change in momentum, you can use the equation:
Change in momentum = Final momentum - Initial momentum
A. Let's calculate it step by step:
1. Calculate the initial momentum:
Initial momentum = mass x initial velocity = 0.145 kg x 42.0 m/s
2. Calculate the final momentum:
Final momentum = mass x final velocity = 0.145 kg x 58.0 m/s
3. Calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Plug in the values:
Change in momentum = (0.145 kg x 58.0 m/s) - (0.145 kg x 42.0 m/s)
Simplify the equation to get the answer.
B. To find the average force during contact, you can use the equation:
Average force = change in momentum / time of contact
1. Calculate the change in momentum using the value obtained from part A.
2. Calculate the average force by dividing the change in momentum by the time of contact (4.6 x 10^-4 s).
Plug in the values:
Average force = change in momentum / time of contact
Simplify the equation to get the answer.