Softball mass of 0,29 kg is pitched of 86.4 km/h. Whin it reaches the plate, it may haved slowed. by 19. Neglecting gravity, estimate amage force of resistance during a pitch, if the distance is air about 15 m.
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![**Estimating the Average Force of Air Resistance on a Pitched Softball**
A softball with a mass of 0.29 kg is pitched at a velocity of 86.4 km/h. Upon reaching the plate, its speed is reduced by 19%. Neglecting the effects of gravity, estimate the average force of air resistance acting on the softball over a distance of approximately 15 meters.
**Detailed Explanation:**
1. **Initial Conditions:**
- Mass of the softball \( m = 0.29 \, \text{kg} \)
- Initial velocity \( v_i = 86.4 \, \text{km/h} \)
- Distance traveled \( d = 15 \, \text{m} \)
2. **Velocity Conversion:**
To convert the initial velocity from km/h to m/s:
\[
v_i = 86.4 \, \text{km/h} \times \left( \frac{1000 \, \text{m}}{1 \, \text{km}} \right) \times \left( \frac{1 \, \text{h}}{3600 \, \text{s}} \right) = 24 \, \text{m/s}
\]
3. **Final Velocity:**
The final velocity \( v_f \) is 19% less than the initial velocity. Thus,
\[
v_f = v_i \times (1 - 0.19) = 24 \, \text{m/s} \times 0.81 = 19.44 \, \text{m/s}
\]
4. **Force Calculation:**
The average force can be found using the work-energy principle, which states that the work done by the air resistance force is equal to the change in kinetic energy.
\[
W = \Delta KE = \frac{1}{2} m (v_f^2 - v_i^2)
\]
\[
W = \frac{1}{2} \times 0.29 \, \text{kg} \times (19.44^2 \, \text{m}^2/\text{s}^2 - 24^2 \, \text{m}^2/\text{s}^2)
\]
\[
W = \frac{1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4211b25e-5640-4e59-912c-e01e8955356b%2F3e7fa642-e343-473f-a484-64b25cc187e5%2Fqunnczo_processed.jpeg&w=3840&q=75)
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