# Conservation of Energy

Photo 1 of Lab
Photo 2 of Lab
Photo 3 of Lab

We have discussed today in class the concept of energy. What we have seen is that energy takes many forms and that it transforms back and forth between these various forms. One definition of energy is that it is something (some "stuff") that if you measure the "stuff" at various times you always get the same result. The form of the "stuff" may change with time but its amount is always the same. When something stays the same we say that it is conserved. So if energy is some "stuff" that regardless of its form and transformations stays the same then energy must be conserved. While this may sound quite abstract talking about some "stuff" that stays the same this is a very important concept in Physics and it is called the Conservation of Energy.

This is what we will examine in lab today using a rubber band, a metal hook, a balance to measure the mass of the hook and a meter stick.

In this lab you must be very careful in writing down your data and in performing your measurements and calculations. The idea behind todays lab is that work is done on the rubber band to stretch it so that it then has elastic potential energy. The metal hook is placed on the rubber band and stretched a distance, then it is released and the elastic potential energy is turned into kinetic energy which is the energy of motion. As the hook rises it slows down so its kinetic energy decreased but the hooks gravitational potential energy inreases until it reaches its maximum value which is when all the kinetic energy is transformed into gravitational potential energy. So we will observe that the elastic potential energy is turned into kinetic energy which is then turned into gravitational potential energy but the total energy of the system of the rubber band and metal hook stays the same.

In equation form this is:

Work done to stretch rubber band = maximum kinetic energy of hook

maximum kinetic energy of the hook = maximum gravitational potential energy

So the work done to stretch the rubber band equals the maximum gravitational potential energy.

Part 1: Measure the mass of the metal hook in units of grams and label this mH, for mass of Hook.

Part 2: Now we need to measure a property of the rubber band which we will need. What we are going to measure is how stretchable is the rubber band to be used. This property we will call the spring constant k. Place a metal weight hanger of mass 50 g over the rubber band and add masses until the rubber band is stretched 2 cm. Be careful in making sure that it stretches 2 cm. Record this mass and remember to add the 50 g of the hanger, call this total mass m. Now lets obtain k. The spring constant k is equal to the mass m times g (980 cm/s^2) all divided by 2 cm. Perform this calculation and write down the result for k.

Part 3: Now lets calculate the work done in stretching the rubber band. The work done is equal to:

Work = 1/2 * k * (how far the rubber band is stretched)squared or

W = 1/2 * k x^2.

Now calculate this number and call it W, remember the rubber band was stretched 2 cm.

Part 4: Now we can do a really neat thing. Knowing the conservation of energy and the work done in pulling down the hook we can predict how high the hook will travel straight up once it is released. This is because the highest it will go is where the hook has its maximum gravitational potential energy and this is equal to the work calculated in part 3. The position it which the metal hook sits on the rubber band and is not stretching it is where its gravitational potential energy is zero. However once it is pulled down and released as it travels upward it gains gravitational potential energy as the distance from its rest increases. The maximum value for the gravitational potential energy is when it is at its highest height from rest which we will call the distance h. This distance h is what we will predict and then measure. We have seen in class that the gravitational potential energy (PE) is equal to:

PE = mass of the object * g * height of the object

or in our case

PE = mH*g*h = mHgh

Since this PE is equal to W calculated in part 3 to get the height h the metal hook will travel upward we set PE = W so that now we get

mHgh = W and this then means

h= W/(mHg)

Using yours results from part 1 for mH and part 3 for W calculate h which is your prediction for how high the hook will go once released.

Part 5: Now let's measure h, or how high the hook goes. Here you must be careful to pull the metal hook down 2 cm and to also make sure the hook goes straight up once launched. Make five such measurements for straight up motion and write down the results. Also calculate the average of your results.

Part 6: Does your average measured value for h obtained in part 5 agree with your prediction? If not, why might they not agree?