A basketball player makes a jump shot. The 0.580-kg ball is released at a height of 1.90 m above the floor with a speed of 7.18 m/s. The ball goes through the net 3.05 m above the floor at a speed of 4.23 m/s. What is the work done on the ball by air resistance, a nonconservative force?
To determine the work done on the ball by air resistance, we need to calculate the change in kinetic energy of the ball and then subtract the work done by other forces (like gravity).
First, let's calculate the initial kinetic energy of the ball when it is released:
Initial kinetic energy (KE₁) = 0.5 * mass * (initial velocity)²
Given:
Mass of the ball (m) = 0.580 kg
Initial velocity (v₁) = 7.18 m/s
Plugging in these values, we have:
KE₁ = 0.5 * 0.580 kg * (7.18 m/s)²
Next, let's calculate the final kinetic energy of the ball when it passes through the net:
Final kinetic energy (KE₂) = 0.5 * mass * (final velocity)²
Given:
Final velocity (v₂) = 4.23 m/s
Plugging in these values:
KE₂ = 0.5 * 0.580 kg * (4.23 m/s)²
Now, let's calculate the work done by gravity on the ball using the change in potential energy:
Change in potential energy (ΔPE) = mass * g * (Δh)
where:
g is the acceleration due to gravity (9.8 m/s²)
Δh is the change in height (initial height - final height)
Given:
Initial height (h₁) = 1.90 m
Final height (h₂) = 3.05 m
Δh = h₂ - h₁
Plugging in the values:
ΔPE = 0.580 kg * 9.8 m/s² * (3.05 m - 1.90 m)
Finally, subtract the work done by gravity from the change in kinetic energy to find the work done by air resistance:
Work done by air resistance = (KE₂ - KE₁) - ΔPE
Substitute the values we calculated into the formula to get the answer.