A 0.579 kg basketball is dropped out of a window that is 6.22 m above the ground. The ball is caught by a person whose hands are 1.31 m above the ground. How much work is done on the ball by its weight?
To determine the work done on the basketball by its weight, we need to calculate the gravitational potential energy difference between its starting position (at the top of the window) and its final position (in the person's hands at a height of 1.31 m).
The gravitational potential energy (PE) is given by the formula:
PE = m * g * h
where:
m is the mass of the basketball (0.579 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
h is the difference in height (6.22 m - 1.31 m = 4.91 m).
So, the work done on the basketball by its weight is:
Work = PE_final - PE_initial
= (m * g * h_final) - (m * g * h_initial)
= (0.579 kg * 9.8 m/s^2 * 1.31 m) - (0.579 kg * 9.8 m/s^2 * 6.22 m)
Now, we can calculate the work done on the basketball:
Work = (0.579 kg * 9.8 m/s^2 * 1.31 m) - (0.579 kg * 9.8 m/s^2 * 6.22 m)
= 7.557 Joules
Therefore, the work done on the basketball by its weight is approximately 7.557 Joules.