A basketball player makes a jump shot. The 0.600-kg ball is released at a height of 2.13 m above the floor with a speed of 7.55 m/s. The ball goes through the net 3.10 m above the floor at a speed of 3.95 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, we need to consider the change in the ball's kinetic energy.

The initial kinetic energy of the ball is given by:
KE_initial = 0.5 * m * v_initial^2
where m is the mass of the ball (0.600 kg) and v_initial is the initial speed (7.55 m/s).

The final kinetic energy of the ball is given by:
KE_final = 0.5 * m * v_final^2
where v_final is the final speed (3.95 m/s).

The work done by air resistance is the difference between the initial and final kinetic energies:
Work = KE_final - KE_initial

Calculating the initial kinetic energy:
KE_initial = 0.5 * 0.600 kg * (7.55 m/s)^2
KE_initial = 0.5 * 0.600 kg * 57.0025 m^2/s^2
KE_initial = 17.10125 Joules

Calculating the final kinetic energy:
KE_final = 0.5 * 0.600 kg * (3.95 m/s)^2
KE_final = 0.5 * 0.600 kg * 15.6025 m^2/s^2
KE_final = 4.68075 Joules

Calculating the work done by air resistance:
Work = KE_final - KE_initial
Work = 4.68075 Joules - 17.10125 Joules
Work = -12.4205 Joules

Therefore, the work done on the ball by air resistance, a nonconservative force, is -12.4205 Joules. The negative sign indicates that the work is done against the motion of the ball.

To find the work done on the ball by air resistance, we need to first calculate the change in mechanical energy of the ball. The mechanical energy of an object is the sum of its potential energy and its kinetic energy.

The potential energy of the ball at the initial height is given by the formula:
Potential energy = mass * gravity * height

where
mass = 0.600 kg (given)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 2.13 m (given)

Calculating the potential energy:
Potential energy = 0.600 kg * 9.8 m/s^2 * 2.13 m
Potential energy = 12.5568 Joules

The kinetic energy of the ball at the initial speed is given by the formula:
Kinetic energy = (1/2) * mass * velocity^2

where
mass = 0.600 kg (given)
velocity = 7.55 m/s (given)

Calculating the kinetic energy:
Kinetic energy = (1/2) * 0.600 kg * (7.55 m/s)^2
Kinetic energy = 17.1015 Joules

The total mechanical energy at the initial point is the sum of potential and kinetic energy:

Mechanical energy (initial) = Potential energy + Kinetic energy
Mechanical energy (initial) = 12.5568 Joules + 17.1015 Joules
Mechanical energy (initial) = 29.6583 Joules

Now, let's calculate the mechanical energy at the final point when the ball goes through the net.

The potential energy at the final height is given by the same formula:
Potential energy = mass * gravity * height

where
mass = 0.600 kg (given)
gravity = 9.8 m/s^2 (acceleration due to gravity)
height = 3.10 m (given)

Calculating the potential energy:
Potential energy = 0.600 kg * 9.8 m/s^2 * 3.10 m
Potential energy = 18.036 Joules

The kinetic energy at the final speed is given by the same formula:
Kinetic energy = (1/2) * mass * velocity^2

where
mass = 0.600 kg (given)
velocity = 3.95 m/s (given)

Calculating the kinetic energy:
Kinetic energy = (1/2) * 0.600 kg * (3.95 m/s)^2
Kinetic energy = 4.43775 Joules

The total mechanical energy at the final point is the sum of potential and kinetic energy:

Mechanical energy (final) = Potential energy + Kinetic energy
Mechanical energy (final) = 18.036 Joules + 4.43775 Joules
Mechanical energy (final) = 22.47375 Joules

Now, we can find the work done on the ball by air resistance by taking the difference in mechanical energy:

Work done = Mechanical energy (final) - Mechanical energy (initial)
Work done = 22.47375 Joules - 29.6583 Joules
Work done = -7.18455 Joules

The work done on the ball by air resistance is approximately -7.18455 Joules. Note that the negative sign indicates that the air resistance is doing work on the ball, causing a decrease in mechanical energy.