Understanding the Concepts
* Potential Energy: The energy an object possesses due to its position relative to a reference point (in this case, the ground). Potential energy (PE) is calculated as: PE = mgh, where:
* m = mass (kg)
* g = acceleration due to gravity (9.8 m/s²)
* h = height (m)
* Kinetic Energy: The energy an object possesses due to its motion. Kinetic energy (KE) is calculated as: KE = (1/2)mv², where:
* m = mass (kg)
* v = velocity (m/s)
* Conservation of Energy: In a closed system, the total energy remains constant. This means that energy can be transformed from one form to another (like potential energy to kinetic energy) but the total amount of energy stays the same.
Solution
1. Initial Energy: At the top, the ball has only potential energy. Calculate this:
PE = mgh = (0.3 kg)(9.8 m/s²)(8 m) = 23.52 J (Joules)
2. Final Energy: Just before hitting the ground, the ball has only kinetic energy. Since energy is conserved, the initial potential energy is now converted into kinetic energy:
KE = 23.52 J
3. Find the Velocity: Now, use the formula for kinetic energy to solve for the velocity:
KE = (1/2)mv²
23.52 J = (1/2)(0.3 kg)v²
v² = 156.8
v = √156.8 ≈ 12.52 m/s
Answer: The ball will be going approximately 12.52 m/s when it hits the ground.
