A softball having a mass of 0.29kg is pitched at 97km/h . By the time it reaches the plate, it may have slowed by 8.0%.
Neglecting gravity, estimate the magnitude of the average force of air resistance during a pitch, if the distance between the plate and the pitcher is about 13m .
.92 * 97 = 89.24
97* 1000/3600 = 26.94 m/s
89.24 *1000/3600 = 24.79 m/s
a = change in velocity/change in time
how long to reach plate
Vaverage = (26.94+24.79)/2 = 25.87 m/s
so time to plate = 13/25.87 = .503 s
so a = (24.79-26.94)/.503 = 4.27m/s^2
F = m a = .29(4.27) =1.24 N
Thanks for showing me the process step by step!
To estimate the magnitude of the average force of air resistance during a pitch, we can use the concept of work and energy.
1. We need to convert the speed of the softball from km/h to m/s:
- Velocity = 97 km/h = (97 * 1000 m) / (60 * 60 s) = 26.9 m/s
2. Next, we calculate the initial kinetic energy of the softball:
- Initial kinetic energy = (1/2) * mass * velocity^2
- Initial kinetic energy = (1/2) * 0.29 kg * (26.9 m/s)^2
3. The softball slows down by 8.0%, which means the kinetic energy decreases by 8.0%. We calculate the new kinetic energy after it slows down:
- Decrease in kinetic energy = 0.08 * Initial kinetic energy
- New kinetic energy = Initial kinetic energy - Decrease in kinetic energy
4. Next, we calculate the final velocity of the softball:
- Final kinetic energy = (1/2) * mass * final velocity^2
- Final kinetic energy = New kinetic energy
- (1/2) * 0.29 kg * final velocity^2 = New kinetic energy
- final velocity = sqrt((2 * New kinetic energy) / (0.29 kg))
5. The work done by air resistance is equal to the change in kinetic energy:
- Work done by air resistance = Initial kinetic energy - New kinetic energy
6. Finally, we calculate the magnitude of the average force of air resistance:
- Average force of air resistance = Work done by air resistance / distance
- Average force of air resistance = (Initial kinetic energy - New kinetic energy) / distance
Substituting the given values:
- Mass = 0.29 kg
- Velocity = 26.9 m/s
- Decrease in kinetic energy = 0.08 * [ (1/2) * 0.29 kg * (26.9 m/s)^2 ]
- Distance = 13 m
You can now calculate the magnitude of the average force of air resistance by following the steps above.