A baseball pitcher in good form can throw a baseball that attains a speed of 86 mi/h in a distance of 1.3 m. Assume that the ball starts from rest and its mass is 0.15 kg.
Determine the average force (in N) exerted on the ball.
To determine the average force exerted on the ball, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's convert the speed of the ball from miles per hour (mi/h) to meters per second (m/s). 1 mile is approximately equal to 1.60934 kilometers, and 1 kilometer is equal to 1000 meters. Therefore, 86 mi/h is equal to (86 * 1.60934 * 1000) / (60 * 60) ≈ 38.46 m/s.
Next, we need to calculate the acceleration of the ball. The ball starts from rest and reaches a speed of 38.46 m/s in a distance of 1.3 m. We can use the following equation to calculate the acceleration:
v^2 = u^2 + 2as,
where v is the final velocity, u is the initial velocity (0 in this case), a is the acceleration, and s is the distance traveled.
Rearranging the equation to solve for acceleration (a), we get:
a = (v^2 - u^2) / (2s) = (38.46^2 - 0^2) / (2 * 1.3) ≈ 758.46 m/s^2.
Now, we can calculate the force exerted on the ball using Newton's second law:
F = ma,
where F is the force, m is the mass of the ball (0.15 kg), and a is the acceleration (758.46 m/s^2).
Substituting the values, we get:
F = 0.15 kg * 758.46 m/s^2 ≈ 113.77 N.
Therefore, the average force exerted on the ball is approximately 113.77 Newtons.