A baseball catcher puts on an exhibition by catching a .150-kg ball dropped from a helicopter at a height of 100m above the catcher. If the catcher "gives" with the ball for a distance of .750m while catching it, what avg. force is exerted on the mitt by the ball? (g = 9.8 m/s^2)
is this correct?
KE = mgh
KE = (.150)(9.8)(100) = 147 J
Yes, your calculation for the initial potential energy (PE) of the ball is correct. The formula you used, PE = mgh, is the correct formula for calculating potential energy, where m is the mass (0.150 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (100 m).
PE = (0.150 kg)(9.8 m/s^2)(100 m) = 147 J
However, please note that you calculated the potential energy of the ball, not the kinetic energy (KE). The formula for kinetic energy is KE = (1/2)mv^2, where m is the mass of the ball and v is its velocity.
To find the kinetic energy, we need to consider the distance the ball "gives" during the catch. Let's assume that the ball comes to a stop in this distance. The formula to find the average force exerted on the mitt is:
Force = (Change in Momentum) / (Time)
To calculate the change in momentum, we first need to find the final velocity of the ball when it comes to a stop. We can use the formula:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration (acceleration due to gravity, -9.8 m/s^2 since the ball is decelerating), and s is the distance the ball gives (.750 m).
Plugging the values into the formula:
v^2 = 0^2 + 2(-9.8 m/s^2)(-0.750 m)
v^2 = 11.025 m^2/s^2
v ≈ 3.32 m/s
Now we can calculate the change in momentum:
Change in Momentum (Δp) = mass * (final velocity - initial velocity)
Δp = (0.150 kg) * (3.32 m/s - 0 m/s)
Δp = 0.498 kg·m/s
Finally, to find the average force exerted on the mitt, we need to divide the change in momentum by the time it takes for the ball to stop.
We can estimate the time by assuming that the deceleration of the ball is constant over the given distance:
Time = distance / velocity
Time = 0.750 m / 3.32 m/s
Time ≈ 0.226 sec
Average Force = Change in Momentum / Time
Average Force = 0.498 kg·m/s / 0.226 sec
Average Force ≈ 2.20 N
Therefore, the average force exerted on the mitt by the ball is approximately 2.20 N.
Yes, your calculation for the initial kinetic energy (KE) of the ball is correct. The formula KE = mgh is used to calculate the potential energy (PE) of an object at a certain height. In this case, the initial potential energy is converted to kinetic energy as the ball falls.
However, to calculate the average force exerted on the mitt by the ball, we need to consider the distance over which the force is applied. In this case, the ball "gives" with the mitt for a distance of 0.750 m. To calculate the average force (F_avg), we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:
Work = F_avg * d
Since the work done on the ball is equal to the change in its kinetic energy:
Work = KE - 0
Therefore:
F_avg * d = KE
Substituting the given values:
F_avg * 0.750 = 147 J
Now, we can solve for F_avg:
F_avg = 147 J / 0.750 m
F_avg ≈ 196 N
Therefore, the average force exerted on the mitt by the ball is approximately 196 N.