# Lab 9: Work-Energy

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Lab 9: Work-Energy

Group Report

PHYS 211L-046

**Theory/Procedure**

Objective: To verify the generalized work-energy theorem.

The work-kinetic energy theorem states that, “When one or more forces act on a particle as it is displaced from an initial position to a final position, the net work done on the particle by these forces causes the particle’s kinetic energy to change by .” This means that the difference between an object’s final kinetic energy and its initial kinetic energy is equal to the amount of work you do on the object.

Summary of Procedure:

- Measure and record mass of the cart, force probe and string.
- Make sure the track is level and free of dust. Connect to the RMS device and place a mass on the end. Make sure the mass will hit the floor before the cart reaches the end of the track.
- Launch Logger Pro, calibrate the RMS device so that it is measuring position. Enter the diameter.
- Turn on the force probe and zero it with no tension on the string.
- Add some mass to the hangar so that the cart accelerates smoothly. Integrate the force vs distance graph that is generated to get the experimental value for the net work done on the cart, . Record the standard deviation of this integral.
- Calculate the change in the cart’s kinetic energy, , using the initial and final velocity values from the RMS.
- Calculate the percent difference between this and .
- Include a copy of the logger pro plot.

Free-body diagram for cart/probe:

**Data, Graphs and Equations**

** **

To calculate the percent error, Δ%, of our data, we will use the mean, *μ*, with the standard value:

Equation relating the change in kinetic energy to the work done by the net force:

(1)

Equation for the kinetic energy of an object of mass *m* with velocity *v*:

(2)

Net force on the string in terms of the mass, *m*, of the cart and acceleration, *a* (this will be measured by Logger Pro):

(3)

Mass of the cart and probe:

629 g (.6053)

Mass of the string:

0.4 g

Fig 1: Example of Logger Pro graphs

Table 1: Data gathered and calculations for

Trial |
Mass of Cart/Probe, m (kg) |
Initial Velocity, v_{i }(m/s) |
Final Velocity, v_{f} (m/s) |
Change in KE, ∆K (J) |
Integral of Force vs Distance, W_{net} (J) |
W_{net} Standard Deviation (J) |

1 | 0.629 | 0.357792 | 0.632973 | 0.0857 | 0.2011 | 0.0105 |

2 | 0.629 | 0.764454 | 1.150754 | 0.2327 | 0.204 | 0.03057 |

3 | 0.629 | 0.457858 | 0.734 | 0.1035 | 0.1058 | 0.007888 |

4 | 0.629 | 0.249419 | 0.744092 | 0.1546 | 0.1911 | 0.02076 |

5 | 0.629 | 0.3456 | 0.602 | 0.07625 | 0.08944 | 0.008934 |

**Summary Table**

Table 2: Percent error using mean of the averages of and

Average ∆K (J) |
Average W_{net} (J) |
Mean of ∆K and W_{net} (J) |
Percent Error |

0.130550108 | 0.158288 | 0.144419054 | 9.60% |

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