A 0.145-kg baseball traveling 35.0 m/s strikes the catcher's mitt which, in bring the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove?
The kinetic energy of the baseball is converted to work pushing the catcher's glove. That work equals Fav*X
where Fav is the average force and X is the distance moved by the glove.
Thus
Fav = (M/2) V^2/X
807.4 N ?
Where could i find the answer?
To find the average force applied by the ball on the glove, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. The formula for force is:
Force = Change in momentum / Time
Since the ball comes to rest, the change in momentum is equal to the initial momentum of the ball. The momentum of an object is calculated by multiplying its mass and velocity:
Momentum = mass × velocity
First, let's calculate the initial momentum of the ball. The mass of the baseball is given as 0.145 kg, and its velocity is given as 35.0 m/s:
Initial momentum = 0.145 kg × 35.0 m/s
Now, we need to convert the distance the glove recoils into meters. The given distance is 11.0 cm, which is equal to 0.11 m.
Now, we can calculate the average force applied by the ball on the glove. Since the time duration is not given, we can assume it to be 1 second:
Average force = Change in momentum / Time
Average force = (Initial momentum - Final momentum) / Time
Since the ball comes to rest, the final momentum is 0. Therefore:
Average force = Initial momentum/ Time
Finally, plug in the values to calculate the average force:
Average force = (0.145 kg × 35.0 m/s) / 1 s
Simplifying, we find:
Average force = 5.075 N
Therefore, the average force applied by the ball on the glove is 5.075 Newtons.