A 0.15 kg baseball is pitched with a speed of 35 m/s (77 mph). When the ball hits the catcher's glove, the glove moves back by 2.7 cm (1.08 in.) as it stops the ball. Assuming a constant acceleration of the ball, what was the average force applied by the catcher's glove?
What is the speed of a 0.15 kg baseball whose kinectic energy is 77J? *
To find the average force applied by the catcher's glove, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a). In this case, the mass of the baseball is 0.15 kg.
First, let's find the acceleration of the baseball. We can use the equation of motion, which relates displacement, initial velocity, final velocity, and acceleration: Δx = (v_f^2 - v_i^2) / (2 * a). Here, the initial velocity (v_i) is 35 m/s, the final velocity (v_f) is 0 m/s since the glove stops the ball, and the displacement (Δx) is -2.7 cm, or -0.027 m (negative because the displacement is in the opposite direction of the initial velocity).
Plugging in the values, we get:
-0.027 = (0 - 35^2) / (2 * a)
Simplifying the equation, we have:
-0.027 = -1225 / (2 * a)
To isolate the acceleration (a), we can multiply both sides of the equation by (2 * a):
-0.054 * a = -1225
Dividing both sides by -0.054:
a = 1225 / 0.054
a ≈ 22685.19 m/s^2
Now that we have the acceleration, we can find the average force using Newton's second law of motion:
F = m * a
F = 0.15 kg * 22685.19 m/s^2
F ≈ 3402.77 N
Therefore, the average force applied by the catcher's glove is approximately 3402.77 Newtons.