A 0.564-kg basketball is dropped out of a window that is 5.85 m above the ground. The ball is caught by a person whose hands are 1.89 m above the ground. (a) How much work is done on the ball by its weight? What is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) What is the change (PEf - PE0) in the ball's gravitational potential energy?
(a) Weight*(distance fallen)
= M*g*3.96 m = ___ J
(b) M*g*Ymax = PEo = PEoriginal
(c) M*g*Ymin = PEf = PEfinal
(d) (c) - (b)
It will be a negative number.
To calculate the work done on the basketball by its weight, we can use the equation:
Work = Force x Distance
The force acting on the basketball is its weight, which is given by the equation:
Weight = Mass x Acceleration due to gravity
Acceleration due to gravity (g) is approximately 9.8 m/s^2. Given that the mass of the basketball is 0.564 kg, we can calculate the weight as:
Weight = 0.564 kg x 9.8 m/s^2 = 5.5152 N
Now, we need to calculate the distance over which the basketball falls. The basketball is dropped from a window that is 5.85 m above the ground, and it is caught by a person whose hands are 1.89 m above the ground. Therefore, the distance over which the basketball falls is:
Distance = (5.85 m + 1.89 m) = 7.74 m
Now, we can calculate the work done by the weight of the basketball using the equation:
Work = Force x Distance
Work = 5.5152 N x 7.74 m = 42.668 N·m or Joules (J)
(a) Therefore, the work done on the basketball by its weight is 42.668 Joules.
To calculate the gravitational potential energy (PE) of the basketball, we can use the equation:
PE = Mass x Gravity x Height
(b) When the basketball is released, the height from the ground is 5.85 m. Therefore, the gravitational potential energy of the basketball when it is released is:
PE = 0.564 kg x 9.8 m/s^2 x 5.85 m = 30.0327 J
(c) When the basketball is caught, the height from the ground is 1.89 m. Therefore, the gravitational potential energy of the basketball when it is caught is:
PE = 0.564 kg x 9.8 m/s^2 x 1.89 m = 10.7609 J
(d) The change in the ball's gravitational potential energy (PEf - PE0) is the difference between the potential energy when the basketball is caught and when it is released:
Change in PE = PEf - PE0 = (10.7609 J - 30.0327 J) = -19.2718 J