At a baseball game a ball of mass m = 0.11 kg moving at a speed v = 22 m/s is caught by a fan. the ball is stopped in 0.014 s , find the average force of the ball on the catcher's hand?
Well, catching a baseball can be quite the hand-buster! But don't worry, I'm here to help you calculate the average force.
To find the average force, we can use Newton's second law, which states that force (F) equals mass (m) times acceleration (a).
We know the mass of the ball (m = 0.11 kg) and the time it takes to stop (t = 0.014 s). To find the acceleration, we can use the equation a = ∆v/∆t, where ∆v is the change in velocity, which is equal to the initial velocity (v = 22 m/s) since the ball is stopped.
So, the acceleration is given by a = v/t = 22/0.014 ≈ 1571.43 m/s².
Now we can plug in the values into Newton's second law to find the average force:
F = m * a = 0.11 kg * 1571.43 m/s² ≈ 172.86 N.
So, the average force of the ball on the catcher's hand is approximately 172.86 Newtons. That's quite a slap on the hand!
To find the average force exerted by the ball on the catcher's hand, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass of the object (m) multiplied by its acceleration (a). In this case, we need to determine the acceleration of the ball.
Acceleration is defined as the change in velocity (Δv) divided by the change in time (Δt). Since the ball is caught and stopped, its final velocity (vf) is 0 m/s, its initial velocity (vi) is 22 m/s, and the change in time (Δt) is 0.014 s.
Δv = vf - vi = 0 - 22 = -22 m/s
Now, we can calculate the acceleration (a) of the ball:
a = Δv / Δt = -22 m/s / 0.014 s = -1571.43 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
Now, we can find the average force (F) using the formula:
F = m * a
Plugging in the values:
F = 0.11 kg * (-1571.43 m/s^2) ≈ -172.86 N
Therefore, the average force exerted by the ball on the catcher's hand is approximately 172.86 N. The negative sign indicates that the force is in the opposite direction to the motion of the ball.