A baseball player pops a pitch straight up. The ball (mass 160 g) was traveling horizontally at 32.0 m/s just before contact with the bat, and 24.0 m/s just after contact. Determine the magnitude of the impulse delivered to the ball by the bat.
The impulse equals the change in momentum. It will be the be the hypotenuse of a 3:4:5 right triangle of momentum.
That would make it 40 m/s *0.16 kg
= 6.4 kg m/s
To find the impulse delivered to the ball by the bat, you need to calculate the change in momentum of the ball.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v).
p = m * v
The impulse (I) is defined as the change in momentum and is calculated by subtracting the initial momentum (p_initial) from the final momentum (p_final).
I = p_final - p_initial
Given:
Mass of the ball (m) = 160 g = 0.16 kg
Initial velocity (v_initial) = 32.0 m/s
Final velocity (v_final) = 24.0 m/s
Let's calculate the initial momentum of the ball (p_initial):
p_initial = m * v_initial
p_initial = 0.16 kg * 32.0 m/s
Now, calculate the final momentum of the ball (p_final):
p_final = m * v_final
p_final = 0.16 kg * 24.0 m/s
Next, calculate the impulse delivered to the ball (I):
I = p_final - p_initial
Substitute the known values into the equation to find the answer.
To determine the magnitude of the impulse delivered to the ball by the bat, we need to calculate the change in momentum of the ball.
Momentum is given by the formula p = m * v, where p is momentum, m is mass, and v is velocity.
Given that the ball's mass (m) is 160 g, we need to convert it to kg first by dividing it by 1000.
m = 160 g / 1000 = 0.160 kg
The velocity (v) just before contact with the bat is 32.0 m/s, and just after contact, it is 24.0 m/s.
Using the formula for momentum, the initial momentum (p1) of the ball is:
p1 = m * v1 = 0.160 kg * 32.0 m/s = 5.12 kg*m/s
And the final momentum (p2) is:
p2 = m * v2 = 0.160 kg * 24.0 m/s = 3.84 kg*m/s
The change in momentum (Δp) is the difference between the initial momentum and the final momentum:
Δp = p2 - p1 = 3.84 kg*m/s - 5.12 kg*m/s = -1.28 kg*m/s
The negative sign indicates that there is a decrease in momentum.
The magnitude of the impulse delivered to the ball by the bat is equal to the magnitude of the change in momentum:
|Δp| = |-1.28 kg*m/s| = 1.28 kg*m/s
Therefore, the magnitude of the impulse delivered to the ball by the bat is 1.28 kg*m/s.