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Labs › exp Work & Energy › WE Introduction

- Use a Motion Detector and a force sensor to measure the position and force on a hanging mass, a spring, and a dynamics cart.
- Determine the work done on an object using a force
*vs.*distance graph. - Use the Motion Detector to measure velocity and calculate kinetic energy.
- Compare the work done on a cart to its change of mechanical energy.

*Work* is a measure of energy transfer. In the absence of friction, when positive work is done on an object, there will be an increase in its kinetic or potential energy. In order to do work on an object, it is necessary to apply a force along or against the direction of the object’s motion. If the force is constant and parallel to the object’s path, work can be calculated using

**W = F · s**

where *F* is the constant force and *s* the displacement of the object. If the force is not constant, we can still calculate the work using a graphical technique. If we divide the overall displacement into short segments, D *s*, the force is nearly constant during each segment. The work done during that segment can be calculated using the previous expression. The total work for the overall displacement is the sum of the work done over each individual segment:

This sum can be determined graphically as the area under the plot of force *vs.* distance. (If you know calculus, you may recognize this sum as leading to the integral
.)

These equations for work can be easily evaluated using a force sensor and a Motion Detector. In either case, the work-energy theorem relates the work done to the change in energy as

*W = *Δ*PE + *Δ*KE*

where *W* is the work done, Δ*PE* is the change in potential energy, and Δ*KE* the change in kinetic energy.

In this experiment you will investigate the relationship between work, potential energy, and kinetic energy.

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