A ball of mass 8kg falls from rest from a height of 100m. Calculate its total energy after falling a distance of 40m

1 answer

To calculate the total energy of the ball after falling a distance of 40m, we need to consider the potential energy and the kinetic energy.

The potential energy at a height of 100m is given by the equation:

PE = mgh

where m is the mass of the ball (8kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (100m). Substituting the values into the equation:

PE = 8kg x 9.8 m/s^2 x 100m = 7840 Joules

The kinetic energy at a height of 40m can be found using the equation:

KE = 1/2 mv^2

where m is the mass of the ball (8kg) and v is the velocity. To find the velocity, we can use the equation:

v^2 = u^2 + 2as

where u is the initial velocity (0 m/s), a is the acceleration due to gravity (9.8 m/s^2), and s is the distance (40m). Substituting the values into the equation:

v^2 = (0 m/s)^2 + 2 x 9.8 m/s^2 x 40m = 784 m^2/s^2

Taking the square root of both sides, we find:

v = √784 m^2/s^2 = 28m/s

Substituting the values for mass and velocity into the equation for kinetic energy:

KE = 1/2 x 8kg x (28m/s)^2 = 6272 Joules

Finally, the total energy after falling a distance of 40m is the sum of the potential energy and the kinetic energy:

Total energy = PE + KE = 7840 Joules + 6272 Joules = 14112 Joules