What is the force that a baseball pitcher must apply to a 145 g baseball over a distance of 2.2 m to give it a speed of 144 km/hr when the ball is released? Assume that the force is constant.

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Quizplus · Accepted Answer

To find the force, we first need to convert the given speed to meters per second (m/s) from kilometers per hour (km/hr). $144 \, \text{km/hr} = 144 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 40 \, \text{m/s}$. Then, we use the work-energy principle, where the work done by the force is equal to the change in kinetic energy of the baseball. The kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass in kilograms and $v$ is the velocity in m/s. The mass of the baseball is $145 \, \text{g} = 0.145 \, \text{kg}$, and the final velocity is $40 \, \text{m/s}$. So, $KE = \frac{1}{2} \times 0.145 \, \text{kg} \times (40 \, \text{m/s})^2 = 116 \, \text{J}$. Since work done (W) is also equal to force (F) times distance (d), and we know the work done is equal to the change in kinetic energy, we have $W = KE = Fd$. Therefore, $F = \frac{W}{d} = \frac{116 \, \text{J}}{2.2 \, \text{m}} = 52.7 \, \text{N}$.

What Is the Force That a Baseball Pitcher Must Apply