A baseball of mass 0.145 kg approaches a bat at 40.0 m/s. After it is hit, the ball leaves the bat at 50.0 m/s directly back. Find the impulse of the bat on the ball.
13.1 kg * m/s
To find the impulse of the bat on the ball, we can use the principle of impulse-momentum.
Impulse is defined as the change in momentum of an object and is given by the equation:
Impulse = Δp = m * Δv
Where:
Δp = change in momentum
m = mass of the object (baseball)
Δv = change in velocity
In this case, the change in velocity is the final velocity minus the initial velocity.
Given:
Initial velocity (before the ball is hit), vi = 40.0 m/s
Final velocity (after the ball is hit), vf = -50.0 m/s (since the ball leaves the bat in the opposite direction)
Now calculate the change in velocity:
Δv = vf - vi
= -50.0 m/s - 40.0 m/s
= -90.0 m/s
Since impulse is equal to the change in momentum, and momentum is given by:
Momentum (p) = mass (m) * velocity (v)
The impulse of the bat on the ball can be calculated as:
Impulse = m * Δv
= 0.145 kg * -90.0 m/s
= -13.05 kg*m/s
Therefore, the impulse of the bat on the ball is -13.05 kg*m/s.
To find the impulse of the bat on the ball, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of that object.
The impulse can be calculated using the equation:
Impulse = Change in momentum
The momentum of an object can be calculated using the equation:
Momentum = Mass x Velocity
Given:
Mass of the ball, m = 0.145 kg
Initial velocity of the ball, u = 40.0 m/s
Final velocity of the ball, v = -50.0 m/s (since it is directly back)
To find the change in momentum, we need to calculate the initial momentum and final momentum, and then subtract the initial momentum from the final momentum.
Initial momentum = m x u
Final momentum = m x v
Substituting the given values:
Initial momentum = 0.145 kg x 40.0 m/s
Final momentum = 0.145 kg x (-50.0 m/s)
Calculating:
Initial momentum = 5.8 kg·m/s
Final momentum = -7.25 kg·m/s
Now, we can find the change in momentum by subtracting the initial momentum from the final momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = (-7.25 kg·m/s) - (5.8 kg·m/s)
Change in momentum = -13.05 kg·m/s
Therefore, the impulse of the bat on the ball is -13.05 kg·m/s. Note that the negative sign indicates that the ball experienced a change in momentum in the opposite direction (from positive to negative) due to the impact with the bat.