An inexperienced catcher catches a 128 km/h fastball of mass 134 g within 1.01 ms, whereas an experienced catcher slightly retracts his hand during the catch, extending the stopping time to 10.1 ms. What is the average force imparted to the two gloved hands during the catches of the inexperienced catcher?
What is the average force imparted to the two gloved hands during the catches of the experienced catcher?
(Avg Force) = (momentum change)/(time)
= (mass)(velocity change)/(time)
Apply that equation to both situations.
V must be in m/s and mass in kg to get force in Newtons.
To calculate the average force imparted to the gloved hands during the catches, we can use the concept of impulse. Impulse is defined as the change in momentum of an object, and it can be calculated by multiplying the force acting on the object by the time over which the force is applied.
First, let's calculate the impulse for the inexperienced catcher:
1. Convert the fastball velocity from km/h to m/s:
128 km/h = 128 * (1000/3600) m/s = 35.6 m/s
2. Convert the mass of the fastball from grams to kilograms:
134 g = 134/1000 kg = 0.134 kg
3. Calculate the initial momentum of the fastball:
momentum = mass * velocity
momentum = 0.134 kg * 35.6 m/s = 4.77 kg⋅m/s
4. Calculate the change in momentum during the catch:
Since the fastball comes to rest, the change in momentum is simply the negative of the initial momentum:
Δmomentum = -4.77 kg⋅m/s
5. Calculate the time interval over which the force acts:
The catch takes place in 1.01 ms, which can be expressed as 1.01 × 10^(-3) s.
6. Now, let's determine the average force:
average force = Δmomentum / time
average force = (-4.77 kg⋅m/s) / (1.01 × 10^(-3) s)
Follow the same steps to calculate the average force for the experienced catcher:
1. Convert the extended stopping time from ms to s:
10.1 ms = 10.1 × 10^(-3) s
2. Calculate the change in momentum:
The initial momentum is the same as before (4.77 kg⋅m/s), but now the stopping time is longer:
Δmomentum = (-4.77 kg⋅m/s)
3. Calculate the time interval:
The catch now takes place in 10.1 ms, which can be expressed as 10.1 × 10^(-3) s.
4. Calculate the average force:
average force = Δmomentum / time
average force = (-4.77 kg⋅m/s) / (10.1 × 10^(-3) s)
Now you have all the necessary steps to calculate the average forces for both catchers. Plug in the values into the equations and perform the calculations to find the answers.