A catcher “gives” with the ball when he catches .15 kg baseball moving at 25 m/s. (a) If he moves his glove a distance of 2.0 cm, what is the average force acting on his hand? (b) Repeat for the case in which his glove and hand more 10 cm.
The average velocity of the ball between first contact with the glove and when it stops is 25/2 = 12.5 m/s. The time that the ball is decelerated is T = D/12.5 m/s, where d is the distance that the glove moves backwards.
The average force is given by the momentum law
(avg. Force) * T = initial momentum
avg. Force = M V*(V/2)/D = K.E./D
This is another way of saying that the ball does work on the backwards-moving glove that equals the initial kinetic energy of the ball.
To calculate the average force acting on the catcher's hand, we can use Newton's second law formula: force (F) equals the change in momentum (Δp) divided by the change in time (Δt).
(a) Calculation for a glove movement of 2.0 cm:
1. Convert the glove movement to meters: 2.0 cm = 0.02 m.
2. Calculate the change in momentum:
Δp = mass (m) * change in velocity (Δv)
Δp = 0.15 kg * (-25 m/s) [since the ball's velocity changes from 25 m/s to 0 m/s when caught]
Δp = -3.75 kg·m/s
3. Calculate the change in time:
Δt = change in distance (Δd) / average velocity (v)
Δt = 0.02 m / (25 m/s / 2) [since the glove moves the given distance in half the time due to average velocity]
Δt = 0.02 m / 12.5 m/s
Δt = 0.0016 s
4. Calculate the average force:
F = Δp / Δt
F = -3.75 kg·m/s / 0.0016 s
F ≈ -2343.75 N
Therefore, the average force acting on the catcher's hand for a movement of 2.0 cm is approximately -2343.75 N.
(b) Calculation for a glove movement of 10 cm:
1. Convert the glove movement to meters: 10 cm = 0.1 m.
2. Calculate the change in momentum:
Δp = 0.15 kg * (-25 m/s) [same as before]
Δp = -3.75 kg·m/s
3. Calculate the change in time:
Δt = 0.1 m / (25 m/s / 2) [same as before]
Δt = 0.1 m / 12.5 m/s
Δt = 0.008 s
4. Calculate the average force:
F = Δp / Δt
F = -3.75 kg·m/s / 0.008 s
F ≈ -468.75 N
Therefore, the average force acting on the catcher's hand for a movement of 10 cm is approximately -468.75 N.
To find the average force acting on the catcher's hand, we can use the equation:
Force = (Change in momentum) / (Change in time)
(a) In this case, we have to find the change in momentum and use the given distance to calculate the change in time.
1. First, let's find the change in momentum:
The initial momentum of the baseball is given by:
Initial momentum = mass × initial velocity
Initial momentum = 0.15 kg × 25 m/s
The final momentum is zero because the ball comes to rest in the catcher's glove:
Final momentum = 0 kg × final velocity
Final momentum = 0
Therefore, the change in momentum can be calculated as:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 0 - (0.15 kg × 25 m/s)
2. Next, let's calculate the change in time:
We know that the distance traveled is 2.0 cm, which is equal to 0.02 m.
The average velocity can be calculated as:
Average velocity = Distance / Time
Rearranging the equation, we can find the change in time:
Time = Distance / Average velocity
Time = 0.02 m / 25 m/s
Now we have the change in momentum and the change in time, so we can calculate the average force:
Force = Change in momentum / Change in time
(b) We repeat the same steps as above, but this time using a distance of 10 cm, which is equal to 0.10 m.
With these values, the calculations can be performed to find the average force acting on the catcher's hand.
By following this method, you should be able to find the average force for both cases and get the answers you are looking for.