A bat strikes a 0.145-kg baseball. Just before impact, the ball is traveling horizontally to the right at 47.0 m/s ; when it leaves the bat, the ball is traveling to the left at an angle of 31.0 ∘ above horizontal with a speed of 58.0 m/s . The ball and bat are in contact for 1.75 ms . Find the horizontal and vertical components of the average force on the ball. Let +x be to the right and +y be upward
To find the horizontal and vertical components of the average force on the ball, we can use the concept of impulse. Impulse is the change in momentum of an object and is equal to the average force applied to the object multiplied by the time over which it is applied.
To calculate the change in horizontal momentum, we need to find the initial and final horizontal velocities of the ball. Initially, the ball is moving horizontally to the right at 47.0 m/s. After impact, the ball is moving horizontally to the left at an angle of 31.0° above the horizontal with a speed of 58.0 m/s.
The horizontal component of the initial velocity is given by:
Vix = 47.0 m/s
The horizontal component of the final velocity can be found using the angle and the overall speed:
Vfx = 58.0 m/s * cos(31.0°)
To calculate the change in horizontal momentum, we subtract the initial momentum from the final momentum:
ΔPx = mvfx - mvix
Where m is the mass of the ball.
Since the ball is struck by the bat and changes direction, the change in horizontal momentum can be found by:
ΔPx = 0.145 kg * Vfx - 0.145 kg * Vix
Next, we need to find the vertical component of the change in momentum.
The vertical component of the initial velocity is zero since the ball is moving horizontally.
The vertical component of the final velocity can be found using the angle and the overall speed:
Vfy = 58.0 m/s * sin(31.0°)
The change in vertical momentum is given by:
ΔPy = m * Vfy
Now, we can find the average force in the horizontal and vertical directions.
Average force in the horizontal direction:
F_avg_x = ΔPx / Δt
where Δt is the time over which the force is applied.
Average force in the vertical direction:
F_avg_y = ΔPy / Δt
Substituting the values of the change in momentum and the time of contact, we can calculate the horizontal and vertical components of the average force on the ball.