A baseball has a mass of 145 g. A bat exerts a force of [tex]$18,400 N$[/tex] on the ball. What is the acceleration of the ball?
Answer (2)
Convert the mass of the baseball from grams to kilograms: m = 145 g = 0.145 kg .
Apply Newton's second law of motion: a = m F .
Substitute the given values: a = 0.145 kg 18400 N .
Calculate the acceleration: a = 1.27 × 1 0 5 m/s 2 . The final answer is 1.27 × 1 0 5 m/s 2 .
Explanation
Problem Introduction We are given the mass of a baseball and the force exerted on it by a bat. We need to find the acceleration of the ball.
Converting Units First, we need to convert the mass from grams (g) to kilograms (kg) since the standard unit for mass in physics calculations is kilograms. To convert grams to kilograms, we divide by 1000: m = 1000 145 g = 0.145 kg
Applying Newton's Second Law Next, we use Newton's second law of motion, which states that force equals mass times acceleration ( F = ma ). We can rearrange this formula to solve for acceleration: a = m F
Calculating Acceleration Now, we plug in the given values for force ( F = 18 , 400 N ) and the calculated mass ( m = 0.145 k g ) into the formula: a = 0.145 kg 18400 N = 126896.55 m/s 2
Final Answer Therefore, the acceleration of the baseball is approximately 126896.55 m / s 2 , which can be written in scientific notation as 1.27 × 1 0 5 m / s 2 .
Examples
Understanding the acceleration of a baseball when hit by a bat helps in designing better sports equipment and training techniques. For example, engineers can use this information to create bats that maximize the force imparted on the ball, or coaches can use it to optimize a player's swing for maximum acceleration. This principle extends to other sports and engineering applications where understanding the impact force and resulting acceleration is crucial.
The acceleration of the baseball is approximately 126896.55 m/s², calculated using the mass of the ball (0.145 kg) and the force applied (18,400 N). This is derived from Newton's second law of motion, which relates force, mass, and acceleration. Therefore, the final answer is approximately 1.27 x 10^5 m/s².
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