The Evergreen Gravito-Adobe Super Collider

 

Introduction: In fundamental physics, one pictures the world as composed of elementary particles of matter (quarks, electrons, neutrinos and the like) acting on each other through four kinds of influence (gravity, electromagnetism, weak interaction, and strong interaction)[1]. One things these interactions do is transfer momentum from one particle of matter to another. The Moore physics text discusses this concept at length, and from it you have heard that momentum is a vector associated with each isolated particle or group of particles, and specifically: (a) the vector points in the direction of the particle’s motion, and (b) the magnitude of the vector is equal to the product of the particle’s speed with its mass. A standard shorthand is

p = m v.

 

This lab investigates the transfer of momentum. It has two portions, involving you in two different kinds of experiment:

(1) investigating the momentum acquired by a pendulum as a function of its mass and the height from which it is released to swing; this is an inductive experiment, i.e. one which looks for a pattern in nature’s behavior;

and (2) investigating the transfer of momentum when two pendulum bobs travelling in different directions collide and stick together; this is a deductive experiment—it reasons from a theoretical claim (that the momentum of isolated systems stays constant) to make predictions about the direction of the combined motion after the collision—and the lab is to compare these predictions with observations.

 

Preparation: Read Moore C2 and C3, as well as all of this lab description. Make sure to read the footnotes, too.

 

Part I of the lab uses a computer-linked photogate to measure speed. There are only enough set-ups for about half the program at a time, so half will need to start with Part II. Either Part can be done first.

 

The instructions in this lab leave you to work out details of the procedure. It is a good idea for you and your partner to do a full “dry run” of each Part before taking data, and looking for improvements in procedure that make things more convenient or reliable.

 

Part I: Transfer of Momentum Into a Pendulum

The basic idea is simple: a ball of clay, swinging on the end of a string, gains momentum from gravity when it is released from a position away from its rest position at the bottom. You can find out the magnitude of the ball’s momentum by measuring its mass and speed. Your task is to look for simple patterns (if any) in the way momentum at the bottom of the swing (where the ball is moving fastest) is a function of the ball’s mass and of the height at which it is released.

 

Equipment: § ceiling hook

§ nylon string or equivalent

§ modeling clay or equivalent

§ screw eyes, plain screws, or equivalent, to serve as anchors in the bobs for attaching string

§ balance

§ photogate, data interface, and computer

§ ring stand and clamp

§ meter stick or equivalent

§ calipers

§ protractor or equivalent

§ straws

§ scissors

 

Theory: The pendulum will swing so that a small segment of straw, protruding from the bottom of the bob, will briefly interrupt a beam of light in the photogate. The photogate measures the time the beam is interrupted; from the measured width of the straw and the definition of speed, one can calculate what speed of the bob corresponds to the measured time.

 

Procedure: (A) The photogate, interface, and computer should already be hooked up; log onto the computer, start the Vernier software (Logger Pro, inside the Data Acquisition entry of Programs in the Start menu), and follow the instructions (Open File>Probes & Sensors>Photogates) to open the Vernier experiment template called One Gate Timer. This should open with two graph windows and a data table showing. Click the Collect button on the computer screen and check that the photogate is working by interrupting the light beam briefly with a finger. Figures should appear in the data table. (Note that the Velocity column does not give true results until you have entered the right width for your straw, which you do by measuring the straw then select the Velocity column and under the ‘Column Definitions” tab manually enter your value for length in the column equation (originally 0.05/”gate time”; change the 0.05 to your value of straw length.)

 

Before proceeding, make sure you understand the Collect/Stop button (not hard, but essential) and also that you can clear data from the table.

 

Use modeling clay and an anchor to make a roughly spherical pendulum bob about 300 g in mass. (It is a good idea from this point on to have different people handling clay and using the computer: the computer isn’t made to handle clay between the keys.) Measure the bob’s mass. Suspend it from the ceiling hook and arrange the photogate in such a way that a small segment of plastic straw stuck in the bottom will pass through the photogate at the bottom of the pendulum’s swing. Swing the bob back and up to a known height above the lowest point [[10 centimeters or so]], and release.[2] Use the time recorded by the photogate, and the basic definition of speed, to calculate the speed of the pendulum bob at the bottom of its swing. Be sure to do this by hand with at least the first several data points, rather than trusting the computer. If the numbers agree, use the computer’s thereafter, if you like. Record this data by hand in your notebook.[3] Repeat for several release heights, well spaced between 5 and 25 cm, and for several different masses between 100 and 500 g.

 

Analysis for Part I: The goal is to find simple functions, if possible, that give the way pendulum speed depends on pendulum mass for a given height, and the way pendulum speed depends on release height, for any given mass. First, “eyeball” the data to see if any patterns are quickly apparent; then use your calculator’s “power law” fitting routine (called PwrReg on the TI-83) to find the parameters of a function in the form axb that approximates your data.

 

Calculate the momentum of the bob at the bottom of its swing for each of your combinations of mass and release height.[4]

 

Part II: Momentum Transfer in Collisions

 

Additional Equipment:

§ Velcro tape, both kinds

§ large plain paper sheets

 

Theory: Two pendulums will collide at the bottom of their swing and stick together. During the time of the collision, they are essentially isolated from outside influences (in the sense that the collision interaction is much stronger than anything else, like small air currents that may be acting on them at that time). Therefore, their total momentum vector (the vector sum of their two individual momenta) does not change in the collision, and the resulting combined object has the same momentum, in magnitude and in direction. This experiment measures the direction of the momentum after the collision, by finding the line of swing of the combined mass, and compares it with the direction predicted by conservation of momentum. You make the prediction by finding the vector sum of the two individual momenta, as indicated in the diagram:

 

 

 

 

To define the two vectors, you need a coordinate system in which each direction can be specified. You also need the mass and speed of each bob. You can measure the mass directly, and you can determine the speed from your results in Part I. (As you read through the procedure, you will see that you can record all the data you need for this part before you do Part I; you just can’t do all the calculations until Part I is complete.)

 

(B) You do not need the photogate/interface/computer rig for this part of the lab. Make a second bob, to be suspended from the same support as the first. Measure its mass. The two pendulums are to be released from different locations so as to collide at the bottom, stick together, and move off at some new direction. You will measure the direction for a series of different mass combinations, and compare with the predictions of momentum conservation. Wrap the Velcro tape around each of the two bobs, so they will reliably stick together when they collide. Devise a way of recording the directions of the two swings before the collision and also of the direction the combined mass moves afterward. (Suggestion: the analysis is simplest when the two bobs come in along perpendicular lines.)

 

After practicing so that you can reliably get the two bobs to collide, record the initial conditions (release heights and directions) and the results of a series of collisions of bobs of different masses.

 

Analysis for Part II: Notice that your results from part (A) will allow you to know the magnitude of the momentum of either of your bobs, provided you measure their release heights and masses. Since the two bobs are moving in different directions here, their momentum vectors are different even if their masses and release heights are the same. Conservation of momentum predicts that the total momentum of the two bobs, i.e. the vector sum of their momenta, does not change in the collision. And since there is only one body after the collision, the stuck-together lump of clay, it must move in the direction of that total momentum vector, if conservation of momentum is right.

 

Choose a coordinate system; calculate the momentum vector for each bob; find their vector sum, specifically its x and y components, as outlined in the Theory section.  Compare with your observations.

 

Optional Dessert Course

 

The Logger Pro software allows a number of graphing options and has a built-in curve-fitting routine. If you like, explore these and other features of the interface.

 

Clean-up: Return clay to the supply table and make sure your desktop is clean.

 

Write-up: Follow the format of previous labs. Write out a typical example of each calculation, but there is no need to show additional calculations in detail when they repeat a typical example with different numbers.

 

 



[1]Influence” is a purposely general word (not to say vague), chosen to give one a way of referring to all the different effects that the four basic interactions can have.

[2]  Since the bob is a blob, not a mathematical point, you have to decide what feature of it to measure the height of. Note also that it is the height above the bottom of the swing, and not the height above the floor, desktop, or sea level, that counts.

[3]  You will also be able to save this data in a file, but it is important that the raw data appear in your notebook, and we strongly advise direct recording until you become thoroughly familiar with data saving in this lab environment. Lost electronic data is nearly impossible to recover.

[4]  Note that you can use your data directly for this step; you don’t need to use your fitted power function.