A basketball player makes a jump shot. The 0.585 kg ball is released at a height of 2.14 m above the floor with a speed of 7.15 m/s. The ball goes through the net 3.10 m above the floor at a speed of 4.19 m/s. What is the work done on the ball by air resistance, a nonconservative force?
To find the work done on the ball by air resistance, you need to calculate the change in kinetic energy of the ball as it moves from its initial position to its final position. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
First, determine the initial kinetic energy (KE initial) and the final kinetic energy (KE final) of the ball. Kinetic energy is given by the formula KE = 1/2 * m * v^2, where m is the mass of the ball and v is its velocity.
Given data:
Mass of the ball (m) = 0.585 kg
Initial velocity (v initial) = 7.15 m/s
Final velocity (v final) = 4.19 m/s
Calculating KE initial:
KE initial = 1/2 * m * v initial^2
KE initial = 1/2 * 0.585 kg * (7.15 m/s)^2
Calculating KE final:
KE final = 1/2 * m * v final^2
KE final = 1/2 * 0.585 kg * (4.19 m/s)^2
Now, find the difference between KE final and KE initial to determine the change in kinetic energy (ΔKE).
ΔKE = KE final - KE initial
Substitute the calculated values into the formula to calculate the change in kinetic energy.
Finally, the work done on the ball by air resistance is equal to the change in kinetic energy.
Work done on the ball by air resistance = ΔKE
Plug in the calculated values and perform the necessary calculations to determine the work done on the ball by air resistance.
consider U = 0 at 2.14 m height
total energy at bottom = Ke = (1/2).585(7.15)^2 = 15 J
height gained = 3.1 - 2.14 = .96 m
total energy at top
= .585 g (.96)+.5(.585)(4.19)^2
= 10.6 J
difference = energy lost to friction = 15-10.6 = 4.4 J