AP Physics
Work and Potential Energy Lab

Discussion:

Suppose that you hang a mass from a spring. If you raise the mass, you do (positive) work on it, while gravity is doing negative work - we say that the work that you do is saved as gravitational potential energy.

When you let go of the mass, it falls. As it falls, its gravitational potential energy decreases, and its elastic potential energy increases (because the spring is stretched).

How does the increase in the elastic potential energy compare to the decrease in the gravitational potential energy?

Equipment:

ring stand	spring	ring-stand clamp	c-clamp
meter stick	clothespins	0.5 and 1.0 kg. masses

Safety Notes:

• Be sure to keep your feet out of the area in which the mass will fall if it comes off the spring, or the spring breaks!
  
  
• Be sure to clamp the ring stand to the lab table, or weight it with several books so that the mass does not pull it off the table.
  
  
• You need to hang enough mass to the end of the spring to get a measurable stretch, but too much force will permanently damage the spring. (An engineer would say that it has exceeded its "elastic limit"). "You break it, you bought it."
  

Procedure:

1. Assemble the spring and mass apparatus as shown in the diagram.
   
   
2. First, in order to determine the work done in stretching the spring, you need to determine the spring constant, k. Remember Hooke's Law (F = kx)? You can determine k by measuring the stretch of the spring for a known force. Of course, you will want to try a few different forces as a check on the precision of the calculation. Record your measurements in a data table.
   
   
3. Now, attach a 1.0 kg. mass to the spring. Hold the mass 20 cm or so below the normal unstretched length (that is the length when no mass is hanging from it) of the spring. Let go of the mass, and note the position of maximum stretch of the spring. It helps to mark the 3 positions with clothespins on the ring stand or a meter stick. Repeat until you are confident you have located the maximum-stretch position. Record your measurements in a data table.
   
   
4. Repeat for a few other starting heights.
   
   
5. Replace the 1.0 kg. mass with the 0.5 kg. mass, and repeat.

Results:

1. Knowing the spring constant, k, you can calculate the work done in stretching the spring from the starting position to the position of maximum stretch in each trial. (This is the increase in the elastic potential energy.) Be sure to show a sample calculation.
   
   
2. Knowing the mass and the distance that the mass falls you can calculate the work done by gravity as the mass falls in each trial. (This is the decrease in the gravitational potential energy.) Show a sample calculation.

Conclusions:

1. How does the work done in stretching the spring compare to the work done by gravity as the mass falls? Why is this so?