What is the force exerted by a catcher's glove on a 0.15-kg baseball moving at 35 m/s that is stopped in 0.02 s?
a = (V-Vo)/t = (0-35)/0.02 = -1750 m/s^2
F = m*a = 0.15 * -1750 = -262.5 N.
To find the force exerted by the catcher's glove on the baseball, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
First, let's calculate the initial momentum of the baseball:
Initial momentum (p1) = mass (m) × velocity (v)
= 0.15 kg × 35 m/s
= 5.25 kg·m/s
Next, let's calculate the final momentum of the baseball:
Final momentum (p2) = 0 (since the baseball is stopped, its final velocity is zero)
The change in momentum (Δp) can be calculated by subtracting the final momentum from the initial momentum:
Δp = p2 - p1
= 0 - 5.25 kg·m/s
= -5.25 kg·m/s
Since a change in momentum has a direction, the negative sign indicates that the momentum of the baseball is decreasing.
Now, we can find the force exerted by the glove using Newton's second law.
Newton's second law states that force (F) equals mass (m) multiplied by acceleration (a):
F = m × a
Acceleration (a) can be found using the formula:
a = Δv / Δt
Where Δv is the change in velocity and Δt is the time taken.
The change in velocity can be calculated by subtracting the final velocity from the initial velocity:
Δv = v2 - v1
= 0 - 35 m/s
= -35 m/s
Note: Since the ball is stopped, its final velocity is 0, and the negative sign indicates a decrease in velocity.
Now, let's calculate the acceleration:
a = Δv / Δt
= (-35 m/s) / (0.02 s)
= -1750 m/s^2
Again, the negative sign indicates a deceleration in the direction opposite to the original velocity.
Finally, we can calculate the force exerted by the glove on the baseball:
F = m × a
= 0.15 kg × (-1750 m/s^2)
= -262.5 N
Therefore, the force exerted by the glove on the 0.15 kg baseball moving at 35 m/s, which is stopped in 0.02 s, is approximately -262.5 N. Note that the negative sign indicates that the force is in the opposite direction of the initial motion.