Energy, Work, and Power

By Matt Thrailkill,

Objective:

To measure the “man/woman power” of a student climbing stairs, and to investigate the relationship between potential and kinetic energy.

Introduction:

Work is force effected over a distance and power is work exerted over time. To perform work moving on an object vertically, all that is needed is enough force to counteract gravity acting on that object. Timing how long it took to effect a vertical displacement, the power used can be calculated.

Potential energy is the potential to perform work. Finding gravitational potential energy is relatively simple because the force exerted is simply gravity's effect on an given mass acting through an angle (since work is also performed through an angle) over a distance.

Kinetic energy is the energy associated with the actual doing of work. It is based on the mass and velocity of an object. In a conserving system, a system where a conservative force like gravity is all that is doing work, at any given moment the potential and kinetic energies of the system sum to the same value as at any other moment.

Work/Power: Kinetic/Potential energy: Velocity:

The final velocity of the system can also be predicted from the kinetic and potential energy pieces of the system – as will be done in the experiment.

Procedure:

The first part of the experiment aims to measure human-power in terms of horsepower. This is done through a vertical displacement, namely running up a few flights of stairs. This provides a way for a person to displace their own weight against gravity using their own muscles, over a period of time.

The second part of the experiment aims to predict the velocity of the system based on a known single source of potential energy. This is done by setting up a horizontal air track and moving the glider solely by the kinetic energy produced by a mass hanging at a height that will work out to give a specific amount gravitational potential energy to the system when not in motion.

The third part of the experiment aims to do the inverse of the second: determine the potential and kinetic energy of the system because the velocities involved are known. This is done by setting up the track so the glider moves through timing gates at the beginning and end. The gates measure the amount of time it took the glider to pass underneath. Taken with the length of the glider, the velocity can be calculated and having beginning and ending measurements yield an initial and final velocity. The track is inclined to make things interesting, but it is not necessary. Were it not inclined, a weight would have to be hanging off the end as with the first track, and this would complicate the calculations a little.

Observations and Data:

See data tables.

Sample Calculations:

Results:

See data tables.

Conclusions:

The first part of the experiment was just fun to perform. There's no theoretical figures to compare to, but it is interesting to note that 0.705hp wasn't too difficult to generate – although doing it for long periods of time would be difficult.

The theoretical calculations in part two most certainly agreed with experimental results. In the worst instances, the velocities disagreed only to a the third significant figure. This could likely be attributed to real-world frictions in the track – the calculations didn't take such variations into account.

Like the first part, there wasn't really any sort of theoretical vs. experimental comparison to be made in part three. One interesting thing is that the energy stolen by friction forces has been calculated: the change in kinetic energy. It is a small number, but it is still there. It provides justification for the small variance between measured velocity and calculated velocity in part two of the experiment. Were there no friction forces, the kinetic energy of the system should have remained the same until the glider's motion changed somehow.

2003-09-22T08:52:02