To calculate the potential energy at a height and the kinetic energy halfway through the fall, we can make use of the principles of potential energy and conservation of energy.
- Potential Energy at a Height: The potential energy (PE) of an object at a certain height is given by the formula:
PE = mgh
Where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity
- h is the height above the reference point (in this case, the ground)
Given:
- Mass of the body, m = 30 kg
- Height above the ground, h = 2 cm = 0.02 m
- Acceleration due to gravity, g ≈ 9.8 m/s^2 (approximate value on Earth)
Calculating the potential energy:
PE = mgh = 30 kg × 9.8 m/s^2 × 0.02 m = 5.88 Joules
Therefore, the potential energy of the body at a height of 2 cm above the ground is approximately 5.88 Joules.
- Kinetic Energy Halfway through the Fall: According to the principle of conservation of energy, the total mechanical energy (sum of potential energy and kinetic energy) remains constant in the absence of external forces like friction. Therefore, the potential energy at the starting height will be converted entirely into kinetic energy halfway through the fall.
At the midpoint of the fall, all potential energy is converted into kinetic energy, so:
Kinetic Energy = Potential Energy at starting point
Therefore, the kinetic energy halfway through the fall is approximately 5.88 Joules.