A 0.140-kg baseball traveling 39.0 m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 13.0 cm.
What was the average force applied by the ball on the glove?
May someone please take me through this problem step by step? Very lost????
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 applied on an object is equal to the rate of change of its momentum.
Step 1: Find the initial momentum of the baseball.
The momentum (p) of an object is given by the product of its mass (m) and its velocity (v). In this case, the mass of the baseball is 0.140 kg and its velocity is 39.0 m/s. Therefore, the initial momentum of the baseball is:
p = m * v
= 0.140 kg * 39.0 m/s
Step 2: Find the final momentum of the baseball.
Since the baseball comes to rest after striking the glove, its final velocity is 0 m/s. Therefore, the final momentum of the baseball is:
p' = m * v'
= 0.140 kg * 0 m/s
= 0 kg m/s
Step 3: Calculate the change in momentum.
The change in momentum (Δp) is equal to the final momentum subtracted by the initial momentum. So,
Δp = p' - p
Step 4: Convert the displacement of the glove to meters.
The recoil of the glove is given as 13.0 cm. To use the SI unit system, we need to convert centimeters to meters. There are 100 centimeters in 1 meter, so the displacement of the glove is:
d = 13.0 cm * (1 m / 100 cm)
Step 5: Calculate the average force.
The average force (F) applied by the ball on the glove can be calculated using the impulse-momentum principle, which states that the change in momentum is equal to the product of the force and the time interval over which it acts. So,
Δp = F * Δt
Here, Δt represents the time interval over which the force acts. Since we do not have the exact value for the time interval, we can assume that it is very small compared to the actual time interval. Therefore, we can ignore it. The equation simplifies to:
F = Δp / Δt
= Δp
So, the average force applied by the ball on the glove is equal to the change in momentum, Δp.
To summarize:
1. Calculate the initial momentum of the baseball: p = m * v
2. Calculate the final momentum of the baseball: p' = m * v'
3. Calculate the change in momentum: Δp = p' - p
4. Convert the displacement of the glove to meters: d = 13.0 cm * (1 m / 100 cm)
5. Calculate the average force: F = Δp
Now you can substitute the appropriate values into the equations to find the average force applied by the ball on the glove.
a=v²/2•s
F=ma=m•v²/2•s