A catcher “gives” with the ball when he
catches a 0.179 kg baseball moving at
16.5 m/s.
If he moves his glove a distance of 2.25 cm,
what is the average force acting on his hand?
Answer in units of kN.
Force x distance = work done by ball = kinetic energy reduction
F = (1/2) M V^2/0.0225 m
The force will be in Newtons. Convert to kN
Well, catching a baseball can be quite the "glovely" experience! Let's calculate the average force acting on the catcher's hand.
First, we need to convert the distance from centimeters to meters. So, 2.25 cm is equal to 0.0225 m.
Now, to calculate the average force, we can use the equation:
Force = (change in momentum) / (time)
The momentum of the baseball can be found by multiplying its mass (0.179 kg) by its velocity (16.5 m/s). This gives us a momentum of 2.9535 kg⋅m/s.
Since the catcher "gives" with the ball, we can assume that the time taken to stop it is very short. Let's say it takes 0.001 seconds.
Now, plugging the values into our equation, we get:
Force = (2.9535 kg⋅m/s) / (0.001 s)
Calculating this gives us a force of 2953.5 N.
To convert this into kN (kilonewtons), we divide by 1000:
Force = 2953.5 N / 1000 = 2.9535 kN.
So, the average force acting on the catcher's hand is approximately 2.9535 kilonewtons. Keep in mind, this calculation assumes an instantaneous stop and a very short amount of time. However, catching a baseball is no joke, and it requires some serious hand-eye coordination!
To find the average force acting on the catcher's hand, we can use the impulse-momentum principle.
The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. Mathematically, it can be written as:
Impulse = Change in momentum
Impulse = (mass) x (change in velocity)
In this case, the mass of the baseball is 0.179 kg and the initial velocity is 16.5 m/s. We need to find the change in velocity.
The change in velocity can be calculated using the formula:
(change in velocity) = (final velocity) - (initial velocity)
In this case, the final velocity is 0 m/s since the catcher "gives" with the ball and makes it come to rest. Therefore, the change in velocity is:
(change in velocity) = 0 m/s - 16.5 m/s
(change in velocity) = -16.5 m/s
Now, we can calculate the impulse:
Impulse = (0.179 kg) x (-16.5 m/s)
Impulse = -2.9535 kg*m/s
The average force acting on the catcher's hand can be found by dividing the impulse by the time of contact (Δt) or the distance over which the force is exerted (Δx). In this case, we are given that the catcher moves his glove a distance of 2.25 cm (0.0225 m).
Average force = Impulse / Change in distance
Average force = (-2.9535 kg*m/s) / (0.0225 m)
Average force ≈ -130.8444 N
The average force is negative because it opposes the direction of motion. To convert it to kilonewtons (kN), we divide by 1000:
Average force ≈ -130.8444 N / 1000
Average force ≈ -0.1308 kN (approximately)
Therefore, the average force acting on the catcher's hand is approximately -0.1308 kN (negative because it opposes the direction of motion).
To find the average force acting on the catcher's hand, we can use the equation:
Force = (Change in momentum) / (Time)
First, let's calculate the change in momentum:
Momentum = (mass) x (velocity)
Given:
Mass of the baseball = 0.179 kg
Initial velocity of the baseball = 16.5 m/s
Initial momentum = (0.179 kg) x (16.5 m/s)
Now, when the catcher catches the baseball, it comes to rest. So, the final velocity is 0 m/s.
Final momentum = (0.179 kg) x (0 m/s)
Change in momentum = (Final momentum) - (Initial momentum)
Next, let's calculate the time taken for the ball to stop.
During the "give" with the ball, the catcher moves his glove a distance of 2.25 cm.
To calculate the time, we need to know the average speed of the glove.
Average speed = (Distance traveled) / (Time taken)
Given:
Distance traveled = 2.25 cm = 0.0225 m
Initial velocity of the baseball = 16.5 m/s
Final velocity of the baseball = 0 m/s
Average speed = (Initial velocity + Final velocity) / 2
Now, we can calculate the time taken:
Time = (Distance traveled) / (Average speed)
Finally, we can substitute the values we have calculated into the equation for force to find the average force acting on the catcher's hand.
Force = (Change in momentum) / (Time)
Make sure to convert the force into kilonewtons (kN) as specified.
That's how you can find the average force acting on the catcher's hand.