## Analysis

### Work when the force is constant

- The work you did in lifting the mass did not change its kinetic energy. The work changed the potential energy of the mass. Calculate the increase in gravitational potential energy using the equation, Δ
*PE *=* mg*Δ*h* where Δ*h* is the distance the mass was raised. Compare this to the work done as calculated by the area under the force *vs.* distance graph as well as calculated from the average force over the distance. Record your values in the data table. Does the work done on the mass correspond to the change in gravitational potential energy? Should it?

### Work done to stretch a spring

- In this part you did work to stretch the spring. The graph of force
*vs.* distance depends on the particular spring you used, but for most springs will be a straight line. This corresponds to Hooke’s law, or *F* = – *kx*, where *F* is the force applied *by* the spring when it is stretched a distance *x*. *k* is the spring constant, measured in N/m. What is the spring constant of the spring? From your graph, does the spring follow Hooke’s law? Do you think that it would always follow Hooke’s law, no matter how far you stretched it? Why is the slope of your graph positive, while Hooke’s law has a minus sign?

- The elastic potential energy stored by a spring is given by Δ
*PE *= ½* kx*^{2}, where *x* is the distance. Compare the work you measured to stretch the spring to 10 cm, 20 cm, and the maximum stretch to the stored potential energy predicted by this expression. Should they be similar? Note:* *Use consistent units*.* Record your values in the data table.

### Work done to accelerate a cart

- In this part, you did work to accelerate the cart. In this case the work went to changing the kinetic energy. Since no spring was involved and the cart moved along a level surface, there is no change in potential energy. How does the work you did compare to the change in kinetic energy? Here, since the initial velocity is zero, Δ
*KE* = ½ *mv*^{ 2}* *where *m* is the total mass of the cart and any added weights, and *v* is the final velocity. Record your values in the data table.

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