A baseball of a mass 0.15 kg is thrown by a pitcher with a speed 20m/s. The bat is in contact with the ball for 0.01 second and gives it a speed of 30m/s in a direction straight towards the picther.find the value of the force and the impluse?
change in velocity 20+30 = 50 m/s
change of momentum = .15 * 50 kg m/s
= impulse
F = change in momentum / time
= .15 * 50 / .01
Newtons
To find the value of force and impulse, we can use the principles of momentum.
1. First, we need to find the initial momentum of the ball before it is hit by the bat.
Initial momentum (P1) = mass x initial velocity
P1 = 0.15 kg x 20 m/s
P1 = 3 kg⋅m/s
2. Next, let's find the final momentum of the ball after it is hit by the bat.
Final momentum (P2) = mass x final velocity
P2 = 0.15 kg x 30 m/s
P2 = 4.5 kg⋅m/s
3. The change in momentum (impulse) can be calculated by subtracting the initial momentum from the final momentum.
Impulse = P2 - P1
Impulse = 4.5 kg⋅m/s - 3 kg⋅m/s
Impulse = 1.5 kg⋅m/s
4. Finally, the force can be determined using the formula:
Force = Impulse / time
As given, the time of contact between the bat and the ball is 0.01 seconds.
Force = 1.5 kg⋅m/s / 0.01 s
Force = 150 N
Therefore, the value of the force exerted on the ball by the bat is 150 Newtons, and the impulse is 1.5 kilogram meter per second.
To find the value of force and impulse, we can use the principles of momentum.
1. Calculate the initial momentum of the baseball before it is hit by the bat:
Initial momentum = mass × velocity
Initial momentum = 0.15 kg × 20 m/s
Initial momentum = 3 kg·m/s
2. Calculate the final momentum of the baseball after being hit by the bat:
Final momentum = mass × velocity
Final momentum = 0.15 kg × 30 m/s
Final momentum = 4.5 kg·m/s
3. Calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 4.5 kg·m/s - 3 kg·m/s
Change in momentum = 1.5 kg·m/s
4. Since impulse is the change in momentum, we can calculate impulse:
Impulse = Change in momentum
Impulse = 1.5 kg·m/s
5. The duration of contact between the bat and the ball is given as 0.01 seconds. To calculate the force, divide the impulse by the time of contact:
Force = Impulse / Time
Force = 1.5 kg·m/s / 0.01 s
Force = 150 N
Therefore, the value of the force exerted on the ball by the bat is 150 Newtons, and the impulse is 1.5 kilogram-meters per second.