## 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(0
^{o}) = 1 → W = Fd. - Graphically, W = area under the F vs. d curve.

**Kinetic Energy:** - Kinetic energy (K) is defined as: K ≡ ½mV
^{2}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 V
_{f}. (Don't forget δV_{f}.) - Calculate ΔK = ½mV
_{f}^{2}being sure to propagate errors. (ΔK ± δ(ΔK)) - Compare with ΔK with W.