Final answer:
The work done on the spelunker by the lifting force is 1000 J for acceleration, 7840 J for the constant-speed lift, and -1000 J for deceleration.
Step-by-step explanation:
Stage (a): Acceleration
To accelerate the spelunker from 0 m/s to 5.00 m/s, we can calculate the work done using the work-energy principle, which states that the work done is equal to the change in kinetic energy.
The initial kinetic energy is 0 because the spelunker is stationary, and the final kinetic energy is given by KE = 1/2mv². Substituting the values, we have:
Work = ∆KE = 1/2(80.0 kg)(5.00 m/s)²
= 1000 J
Stage (b): Constant Speed
When the spelunker is lifted at a constant speed, the only force doing work is the lifting force against gravity.
Since the speed is constant, the net work done is simply the work done to overcome the gravitational force, which is equal to the change in gravitational potential energy. Using GPE, the work done is:
Work = GPE = (80.0 kg)(9.8 m/s²)(10.0 m)
= 7840 J
Stage (c): Deceleration
Decelerating the spelunker to zero speed involves doing negative work on the spelunker’s kinetic energy, reducing it back to zero. Thus, the work done during deceleration is the negative of the work done during acceleration, which is:
Work = -1000 J
Note that the negative work done by the force during deceleration indicates that the force is taking energy out of the system, hence slowing down the spelunker.