A basketball player makes a jump shot. The 0.581 kg ball is released at a height of 2.02 m above the floor with a speed of 7.14 m/s. The ball goes through the net 3.10 m above the floor at a speed of 4.07 m/s. What is the work done on the ball by air resistance, a nonconservative force?
To calculate the work done on the ball by air resistance, we need to determine the change in mechanical energy of the ball.
The mechanical energy of an object is the sum of its kinetic energy and potential energy.
Given:
Mass of the ball (m): 0.581 kg
Initial height (h1): 2.02 m
Initial speed (v1): 7.14 m/s
Final height (h2): 3.10 m
Final speed (v2): 4.07 m/s
The initial mechanical energy (E1) of the ball is given by:
E1 = Potential energy + Kinetic energy
= m * g * h1 + (1/2) * m * v1^2
where g is the acceleration due to gravity (9.8 m/s^2)
The final mechanical energy (E2) of the ball is given by:
E2 = Potential energy + Kinetic energy
= m * g * h2 + (1/2) * m * v2^2
The change in mechanical energy (ΔE) is given by:
ΔE = E2 - E1
The work done on the ball by air resistance is equal to the change in mechanical energy.
Now, let's calculate the values:
Potential energy at h1:
PE1 = m * g * h1
Potential energy at h2:
PE2 = m * g * h2
Kinetic energy at v1:
KE1 = (1/2) * m * v1^2
Kinetic energy at v2:
KE2 = (1/2) * m * v2^2
Initial mechanical energy:
E1 = PE1 + KE1
Final mechanical energy:
E2 = PE2 + KE2
Change in mechanical energy:
ΔE = E2 - E1
Work done by air resistance (W):
W = ΔE
Substitute the given values into the formulas and calculate the result.