a body of mass 50 kg is raised to a height of 20m above the ground a) what is the potential energy b) what is the Kinetic energy change of the the object as it is about to strike the ground at the height of 20m above down level. c) Calculate the maximum velocity developed by the body being in fall?

All_for_one

2 years ago

a) The potential energy of an object raised to a height above the ground can be calculated using the formula:

Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)

Where:
m = 50 kg (mass of the body)
g ≈ 9.81 m/s² (standard gravitational acceleration)
h = 20 m (height)

PE = 50 kg * 9.81 m/s² * 20 m = 9810 Joules

So, the potential energy of the body at a height of 20 meters is 9810 Joules.

b) When the object is about to strike the ground from a height of 20 meters, its potential energy is converted into kinetic energy. The change in kinetic energy can be calculated using the following formula:

Change in Kinetic Energy = Initial Potential Energy - Final Potential Energy

Initial Potential Energy = 9810 Joules (as calculated in part a)
Final Potential Energy = 0 Joules (at ground level)

Change in Kinetic Energy = 9810 Joules - 0 Joules = 9810 Joules

The change in kinetic energy is 9810 Joules.

c) To calculate the maximum velocity developed by the body as it falls, you can use the law of conservation of energy. At the highest point (20m above the ground), all potential energy is converted into kinetic energy. The formula for kinetic energy is:

Kinetic Energy (KE) = 0.5 * mass * velocity^2

Initially, all the potential energy is potential energy, which is equal to 9810 Joules (as calculated in part a). This potential energy is converted into kinetic energy when the object falls to the ground.

So, 9810 Joules = 0.5 * 50 kg * velocity^2

Now, solve for velocity:

velocity^2 = (2 * 9810 Joules) / 50 kg
velocity^2 = 392.4 m²/s²

velocity ≈ √392.4 ≈ 19.81 m/s

The maximum velocity developed by the body when it falls is approximately 19.81 meters per second.