A baseball (m = 145 g) traveling 45 m/s moves a fielder's glove backward 15 cm when the ball is caught. What was the average force exerted by the ball on the glove?
find Magnitude
a=6750
To find the average force exerted by the ball on the glove, you can use Newton's second law of motion, which states that the force (F) exerted on an object is equal to the mass (m) multiplied by the acceleration (a) of the object.
First, let's convert the distance moved by the glove from centimeters to meters:
15 cm = 0.15 m
Next, we need to find the acceleration of the baseball. We can use the equation of motion:
v^2 = u^2 + 2aS
where v is the final velocity (0 m/s), u is the initial velocity (45 m/s), a is the acceleration, and S is the distance traveled (0.15 m).
Rearranging the equation, we have:
0 = (45 m/s)^2 + 2a(0.15 m)
2025 m^2/s^2 = 0.30a
a = 6750 m^2/s^2
Now that we have the acceleration, we can find the force using Newton's second law:
F = m × a
F = 0.145 kg × 6750 m^2/s^2
Calculating the product, we find:
F ≈ 983.25 N
Therefore, the average force exerted by the ball on the glove is approximately 983.25 Newtons.
To find the average force exerted by the ball on the glove, we can use the formula:
Force = Change in momentum / Time
First, let's find the change in momentum:
Change in momentum = Final momentum - Initial momentum
To calculate the initial momentum, we use the formula:
Initial momentum = mass * initial velocity
Substituting the given values:
Mass = 145 g = 0.145 kg (since 1 kg = 1000 g)
Initial velocity = 45 m/s
Initial momentum = 0.145 kg * 45 m/s = 6.525 kg*m/s
Now, let's calculate the final momentum:
Final momentum = mass * final velocity
Since the ball is caught and its final velocity is zero:
Final momentum = 0 kg * 0 m/s = 0 kg*m/s
Next, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 0 kg*m/s - 6.525 kg*m/s
= -6.525 kg*m/s
Note: The negative sign in the change in momentum indicates that the direction of the momentum has changed.
Now we need to convert the distance the glove moved into meters:
Distance = 15 cm = 0.15 m (since 1 m = 100 cm)
Lastly, we need to find the time taken for the ball to come to rest:
Using the formula: Distance = (Initial velocity * Time) + (0.5 * Acceleration * Time^2)
Where initial velocity = 45 m/s,
Acceleration = unknown,
and Distance = 0.15 m
Using the formula: (Initial velocity * Time) + (0.5 * Acceleration * Time^2) - Distance = 0
We can solve this quadratic equation to find the time taken.
Once we have the time, we can use the formula:
Force = Change in momentum / Time
Substituting the known values:
Force = -6.525 kg*m/s / Time
Now, you can plug in the calculated values to find the magnitude of the average force exerted by the ball on the glove.