A particle weighing 20 g freely falls from a certain height without an initial velocity. At what altitude is the potential

A particle weighing 20 g freely falls from a certain height without an initial velocity. At what altitude is the potential energy 1/3 of the kinetic energy? What is the speed of the particle at this height? If the total mechanical energy is 6 J.

1. Let’s designate: K – kinetic energy of a particle. This means that the potential energy is equal to K / 3.

2. Let’s make the equation:

K + K / 3 = 6;

4K / 3 = 6;

K / 3 = 6/4;

K / 3 = 1.5;

The potential energy is equal to 1.5 J at the moment when it is one third of the kinetic energy. The kinetic energy at this moment is 4.5 J.

1. Potential energy is found by the formula: m * g * h, where m is the mass of the particle, g is the acceleration of gravity, h is the height. Find the height:

h = 1.5 / (10 * 0.02) = 7.5 meters;

1. The kinetic energy is equal to m * U ^ 2/2, where U is the particle velocity. Let’s find the speed of the particle at a height of 7.5 meters:

U ^ 2 = 2 * 4.5 / 0.02 = 450;

If U ^ 2 = 450, then U = 21.21 m / s.

Answer: the height is 7.5 meters; the speed is 21.21 m / s.