A 0.140-kg baseball traveling 38.0m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 15.0cm .What was the average force applied by the ball on the glove?
To find the average force applied by the ball on the glove, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity: momentum = mass x velocity.
Let's calculate the initial momentum of the baseball before it strikes the glove.
Mass of the baseball, m = 0.140 kg
Velocity of the baseball, u = 38.0 m/s
Initial momentum, P₁ = mass x velocity
= m x u
Now, let's calculate the final momentum of the baseball and glove system after the collision. Since the baseball comes to rest, the final velocity of the system is zero.
Final momentum, P₂ = mass x velocity
= (m + m) x 0
According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:
P₁ = P₂
m x u = (2m) x 0
Next, let's calculate the change in momentum (∆P) of the system:
∆P = P₂ - P₁
The negative sign in front of P₁ indicates the change in direction of momentum.
∆P = 0 - (m x u)
= -m x u
Since force is the rate of change of momentum, the average force can be calculated using the formula:
Average force = ∆P / time
To calculate the time, we need to convert the displacement in cm to meters (since all other measurements are in SI units):
Displacement = 15.0 cm = 0.15 m
We need to find the time it takes for the glove to move 0.15 m during the collision.
Time, t = Displacement / Velocity of the glove
Let's calculate the time:
t = 0.15 m / u
Finally, we can calculate the average force:
Average force = ∆P / t
= (-m x u) / (0.15 m / u)
Simplifying the expression, we get:
Average force = (-m x u^2) / 0.15
Now we can substitute the given values:
m = 0.140 kg
u = 38.0 m/s
Average force = (-0.140 kg x (38.0 m/s)^2) / 0.15
Calculating this gives the average force applied by the ball on the glove.
To find the average force applied by the ball on the glove, you can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
First, let's find the initial momentum of the ball. Momentum is calculated by multiplying the mass of an object by its velocity. In this case, the mass of the baseball is 0.140 kg and its velocity is 38.0 m/s. So, the initial momentum of the ball is:
Initial momentum = mass × velocity = 0.140 kg × 38.0 m/s = 5.32 kg·m/s
Since the ball comes to rest, its final velocity is 0 m/s. Therefore, the change in momentum is equal to the initial momentum.
Now, let's find the change in momentum. The change in momentum can be calculated by subtracting the initial momentum from the final momentum (which is zero in this case):
Change in momentum = Final momentum - Initial momentum = 0 - 5.32 kg·m/s = -5.32 kg·m/s
The negative sign indicates that the momentum is in the opposite direction of the initial momentum.
To find the average force, we divide the change in momentum by the time it took to achieve this change. However, the time is not given in the question. Instead, we are given the displacement (15.0 cm) of the catcher's mitt as it recoils.
To relate the displacement and time, we need to use the equation for average velocity: velocity = displacement / time.
Since the final velocity is zero and the initial velocity is 38.0 m/s (the velocity of the ball), we can write:
0 = 15.0 cm / time
Solving for time, we convert the displacement to meters and rearrange the equation:
time = displacement / velocity = 0.150 m / 38.0 m/s = 0.00395 s
Now that we have the time, we can calculate the average force using Newton's second law:
Average force = Change in momentum / time = (-5.32 kg·m/s) / (0.00395 s) ≈ -1348 N
The negative sign indicates that the force is acting in the opposite direction of the initial momentum, which is expected because the ball decelerates and comes to rest in the opposite direction. So, the average force applied by the ball on the glove is approximately 1348 N.
change of momentum = .14 * 38
average speed during stop = 38/2 = 19
time to stop = t =.15/19 = .00789 seconds
F = change in momentum/time = .14*38/.00789
= 674 Newtons
(ouch)