AP Physics lab practical (simple harmonic motion): "Kiss the egg"

Question

The lab is called "kiss the egg". I am pretty sure it will come up if you google it in case it does not make sense how I explain it.

I am given a random length of rubber band. The goal of the lab is to drop a bag of rocks attached to this band and have it barely touch (ie kiss) the egg that is sitting on the floor directly beneath it. We do not get the rocks until after we have figured out how to solve for the height to drop it from.

The first step is to solve for k. I did this using a 0.2kg mass on the end of the rubberband. I measured the rubber band with out the mass and then measured it with the mass. I used the euqation mg=kx to solve for k using m=0.2 g=9.8 and x= the difference between the two measured lengths.

My teacher told us to set height=0 at the floor. Given that height is zero at the floor, the mass spring system will have gravitational potnetial at the point that we release it from, kinetic energy and gravitational (i think) at the point where the band is stretched just by the mass, and only spring potential at the instant that it barely touches the egg.

If all I know is the k constant of the spring, how do we solve for the height (above the floor/egg) to drop the rocks from??? My teacher's hint was "you have to decide as a group whether you want to keep the length of the band or height constant, one or the other must be constant". My group is of no help and spent the class period playing with the mass set and rubber band. I am very confused and most likely overthinking this.

Please help me! If you could answer in detail that would be extra helpful as I will be the only person carrying out the experiment and only have one more shot to do it. Again: I will have a bag of rocks and the k constant of a band (but will not be able to pracitce with the band once i recieve the rocks). From this, I have to know how high to lift the bag of rocks after attaching it to the rubber band. I will then tie the rock bag to the rubber band, lift it the height I solved for, and let go. When I drop this bag it will have to fall down, barely hit the egg (ensuring it touches but does not smash or break the shell) and rebound back up.

 

Also a related question. If we solved for k of the rubber band using say 0.2 kg at the beginning, would we have to resolve for it for the bag of rocks? Because it will weigh more. And if so, how would we do this with out using the rubber band as I will not have it after I get the bag of rocks until I am ready to test for the final grade. 

Thank you so much!!

Answer 1

Hi Abigail,

 

To determine the height, you will use you can proceed the way you elaborated above with minor adjustments

You test mass is m = 0.2kg

Tie the test mass m =0.2 kg to the rubber band, measure the length of the rubber band from where you will be holding it to the bottom of the test mass when taut but not stretched or slack and call it L₁.  

Hold the rubber band up and let the test mass stretch it, again measure the length of the stretched rubber band from the point where you are holding it to the bottom of the mass call it L₂.

m  = 0.2 kg

g   = 9.8 m/s²

L₁ = ___ cm        (multiply by 0.01 m/cm to convert to meters)

L₂ = ___ cm        (multiply by 0.01 m/cm to convert to meters)

x = L₂ - L₁

 

mg = kx

0.2*9.8 = kx              k = 1.96/x

 

To answer one of your questions is whether find it for the mass in the bag. The answer is NO, k is the property of the material the rubber is made from, so it will remain the same for your purpose as long as the mass in the bag is within a certain limit. NOTE: Overstretching the rubber band will cause it to yield, i.e it will lose its elasticity and the k value will not work because the molecular structure of the band has changed.

 

To determine the height from which to release the mass in the bag, you do the same calculation this time to the top of the egg on the floor.

 

**** Point of release of mass M in the bag

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|                                                  

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|   height = h                                                 

|

|

|

|

Ο  egg -----------------------------------Floor

 

Mg = kh

M(9.8) = (1.96/x)h

M(9.8)(x/1.96) = h

h =5Mx ,  you have measured the value for x above

 

h= 5M(L₂ - L₁)    

This is the height in meters if L₁, L₂ are in meters and M is in kilograms. As you can see if you have already figured out k or have written down the value of the length of the stretched  rubber band with the test mass 0.2 kg and the unstretched length of the rubber band you can calculate the height if you are given the mass in the bag M.