## Experiment # 6: Work-Energy Theorem

Goal: We want to prove the work-energy theorem: ΔK = W.

### Theory

• The work (W) done on an object by a force (F) to move an object a distance d is given by: W = ∫F•dx = F cos(θ) ∫dx = F•d• cos(θ), where θ is the angle between F and d.
• For us, F is parallel to d → cos(0o) = 1 → W = Fd.
• Graphically, W = area under the F vs. d curve.

Kinetic Energy:
• Kinetic energy (K) is defined as: K ≡ ½mV2 where V is velocity.

Work-Energy Theorem:
• The work-energy theorem states theat the work done on an object is equal to the change in its kinetic energy: W = ΔK

### Experiment

• Using the setup shown above, release the hanging mass and the cart will accelerate to the right. Using Data Studio you will obtain a data table of the cart's velocity as well as a plot of force vs. distance. (F = Tension in the string.)
• Pay close attention to the force sensor calibration procedure. If you make a mistake you will need to start the procedure over.

Analysis:

• Calculate W from the plot of F vs. d using Data Studio. (Note: There is no δW given by Data Studio.)
• Calculate the average of the last 5 values of V from the velocity table. This average is Vf. (Don't forget δVf.)
• Calculate ΔK = ½mVf2 being sure to propagate errors. (ΔK ± δ(ΔK))
• Compare with ΔK with W.