Lab 11: Work-Kinetic Energy Theorem

According to theory, the work done to move an object turns into kinetic energy, therefore, if we limit the amount of air resistance and friction, we should be able to find a direct identity relationship between work and kinetic energy.

To do this, we need a motion and force sensor, since kinetic energy is a function of velocity, and work is a function of force. We deduce the kinetic energy after capturing velocity and figuring out the mass of the system, applying the formula for it. We find work by noting the integral of force and, by plotting both against the distance, we could compare work and kinetic to see if they are indeed the same, such that:

W = F * d = (m v²) / 2

The force sensor is clamped to the far end of the picture above, connected to a spring and a weighted cart over a track. The motion sensor is on the near end. First, we measure and zero the sensors with the spring uncompressed. Then, we pull the cart, such as to extend the spring an arbitrary amount--this will be recorded as positive distance. Thus, the chronological order of events will appear in reverse when the graph is plotted against position. When released, the stretched spring should be at maximum force, reaching zero at uncompressed (neutral) position,while velocity increases. Work is converted to kinetic energy.

This is our data:

The data points of negative position are crossed out, telling Logger Pro to ignore what happens after the spring reaches uncompressed position, and begins to be compressed. We create a calculated column for kinetic energy. And we use Logger Pro to find the area under the force curve between certain limits, and analyze the value of kinetic energy at that point. To illustrate, here are a few points. Note the similarity between the values:

Please excuse the moire, the resolution of the phone doesn't capture computer screens well. More importantly, note that work and kinetic energy as reported by Logger Pro diverges as time goes by, revealing the faults in our experiment. First, our spring isn't ideal, and hangs to one side off the track, even at rest, which could distort the zeroing of our sensors. Second, there are other forces at work in reality, such as friction. Our measurement time is brief, exacerbating error. Nevertheless, we see clear signs of a correlation, so we consider that the relationship between work and kinetic energy confirmed.