A 0.140- baseball traveling 34.0 strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 12.0. What was the magnitude of the average force applied by the ball on the glove?
To find the magnitude of the average force applied by the ball on the glove, we need to use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum.
The momentum of an object is the product of its mass (m) and velocity (v): p = mv.
In this case, the ball is traveling at a speed of 34.0 m/s. The mass of the ball is given as 0.140 kg.
Therefore, the momentum of the ball before it hits the glove is p = (0.140 kg) * (34.0 m/s).
When the ball comes to rest, its final momentum is zero because it has no velocity.
The change in momentum (Δp) is the final momentum minus the initial momentum: Δp = 0 - (0.140 kg * 34.0 m/s).
Since the force is equal to the rate of change of momentum, we can calculate the average force (F) using Newton's second law: F = Δp / Δt.
In this case, we are given that the glove recoils backward by a distance of 12.0 m. To calculate the time it takes for the ball to come to rest, we need to know the deceleration of the ball as it stops.
To find the deceleration, we can use the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s), u is the initial velocity (34.0 m/s), a is the acceleration, and s is the distance traveled.
Rearranging the equation, we have a = (v^2 - u^2) / (2s), which gives us a = (0 - (34.0 m/s)^2) / (2 * 12.0 m).
Once we have the deceleration, we can find the time (Δt) using the equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (34.0 m/s), a is the acceleration, and t is the time.
Rearranging the equation, we have t = (v - u) / a, which gives us t = (0 m/s - 34.0 m/s) / (-dec).
Finally, we can substitute the calculated values for Δp and Δt into the equation F = Δp / Δt to find the magnitude of the average force applied by the ball on the glove.