To determine the kinetic energy (KE) of a baseball just before impact, you would indeed use the formula:
\[ KE = \frac{1}{2} m v^2 \]
Where:
- \( KE \) is the kinetic energy.
- \( m \) is the mass of the baseball (in kilograms).
- \( v \) is the velocity of the baseball just before impact (in meters per second).
Steps to Follow:
-
Measure the Mass of the Baseball:
- Use a digital scale to measure the mass of the baseball. For example, let’s say the measured mass \( m \) is approximately 0.145 kg (which is the standard mass for a baseball).
-
Determine the Speed Just Before Collision:
- If you have access to high-speed cameras or radar equipment, set it up to record the baseball as it travels just before impact.
- Calculate the velocity \( v \) based on the frame rate of the camera or the measurements provided by the radar system. For instance, if the camera records the ball travelling 10 meters in 0.1 seconds, you can calculate the speed: \[ v = \frac{\text{distance}}{\text{time}} = \frac{10 \ \text{m}}{0.1 \ \text{s}} = 100 \ \text{m/s} \]
-
Calculate the Kinetic Energy:
- Substitute the values of \( m \) and \( v \) into the kinetic energy formula: \[ KE = \frac{1}{2} (0.145 \ \text{kg}) (100 \ \text{m/s})^2 \] \[ KE = \frac{1}{2} (0.145) (10000) \] \[ KE = \frac{1}{2} (1450) = 725 \ \text{Joules} \]
Conclusion:
The kinetic energy of the baseball just before impact, given a mass of 0.145 kg and a velocity of 100 m/s, would be approximately 725 Joules. Remember to ensure that all measurements are taken accurately and that the correct values are used in your calculations.