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What is the force of a pitching machine on a baseball?

Baseballs pitched by a machine have a horizontal velocity of 30 meters/second. The machine accelerates the baseball from 0 meters/second to 30 meters/second in 0.5 seconds. If a baseball has a mass of 0.15 kilograms, the force the machine exerts is [tex]\square[/tex] newtons. Use [tex]F = ma[/tex], where [tex]a = \frac{v-u}{t}[/tex].



Answer :

To find the force exerted by the pitching machine on the baseball, we can follow these steps:

1. Identify the given values:
- Mass of the baseball, [tex]\( m = 0.15 \, \text{kg} \)[/tex]
- Initial velocity, [tex]\( u = 0 \, \text{m/s} \)[/tex]
- Final velocity, [tex]\( v = 30 \, \text{m/s} \)[/tex]
- Time, [tex]\( t = 0.5 \, \text{s} \)[/tex]

2. Calculate the acceleration:
The formula to calculate acceleration is:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Plugging in the values, we get:
[tex]\[ a = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{0.5 \, \text{s}} = \frac{30}{0.5} = 60 \, \text{m/s}^2 \][/tex]

3. Calculate the force:
The formula for force is:
[tex]\[ F = m \cdot a \][/tex]
Using the calculated acceleration and the given mass, we obtain:
[tex]\[ F = 0.15 \, \text{kg} \cdot 60 \, \text{m/s}^2 = 9 \, \text{N} \][/tex]

Thus, the force that the machine exerts on the baseball is [tex]\(\boxed{9}\)[/tex] newtons.