A basketball player makes a jump shot. The 0.610-kg ball is released at a height of 1.90 m above the floor with a speed of 7.08 m/s. The ball goes through the net 3.04 m above the floor at a speed of 4.29 m/s. What is the work done on the ball by air resistance, a nonconservative force?
initial PE+initial KE-frictionloss=finalKE+final PE
mg*1.9+1/2 m 7.08^2-frictionwork=mg*3.04+1/2 m 4.29^2
solver for the term frictionwork.
To determine the work done on the ball by air resistance, we need to find the change in kinetic energy of the ball.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be expressed as:
Work = Change in Kinetic Energy
Since the work done by air resistance is considered a nonconservative force, we can ignore other forms of energy like potential energy.
To calculate the change in kinetic energy, we first need to find the initial kinetic energy (K_i) and the final kinetic energy (K_f) of the ball.
The initial kinetic energy (K_i) can be calculated using the formula:
K_i = (1/2) * m * v_i^2
Where:
m = mass of the ball = 0.610 kg
v_i = initial velocity = 7.08 m/s
Plugging in the given values, we get:
K_i = (1/2) * 0.610 kg * (7.08 m/s)^2
Next, we need to find the final kinetic energy (K_f) using the same formula, but with the final velocity (v_f):
K_f = (1/2) * m * v_f^2
Where:
v_f = final velocity = 4.29 m/s
Plugging in the values, we get:
K_f = (1/2) * 0.610 kg * (4.29 m/s)^2
Once we have the initial and final kinetic energy, we can calculate the change in kinetic energy (∆K) using the formula:
∆K = K_f - K_i
Finally, the work done on the ball by air resistance can be calculated as:
Work = ∆K
Substituting the calculated values for ∆K, we get the answer to the question: the work done on the ball by air resistance, a nonconservative force.