1. Potential Energy at the Top:
* The box has potential energy (PE) due to its height. The formula for potential energy is:
PE = mgh
where:
* m = mass (20 kg)
* g = acceleration due to gravity (9.8 m/s²)
* h = height (4.0 m)
* Calculate the potential energy:
PE = (20 kg)(9.8 m/s²)(4.0 m) = 784 J (joules)
2. Conservation of Energy:
* As the box falls, its potential energy is converted into kinetic energy (KE). The total mechanical energy (PE + KE) remains constant.
* The formula for kinetic energy is:
KE = (1/2)mv²
where:
* m = mass (20 kg)
* v = velocity (what we want to find)
3. Setting up the Equation:
* At the top, all the energy is potential energy (PE = 784 J).
* At the bottom, all the energy is kinetic energy (KE = 784 J).
* Therefore:
KE = PE
(1/2)mv² = mgh
4. Solving for Velocity:
* Cancel out the mass (m) on both sides:
(1/2)v² = gh
* Multiply both sides by 2:
v² = 2gh
* Take the square root of both sides:
v = √(2gh)
* Substitute the values:
v = √(2 * 9.8 m/s² * 4.0 m)
v = √(78.4 m²/s²)
v ≈ 8.85 m/s
Therefore, the velocity of the box as it reaches the floor is approximately 8.85 m/s.
