This week we'll finish the Newton's Second Law lab and initiate our bridge building contest.

Second Law lab -- data collection finishes Monday. If you are having trouble getting all the trials I've suggested try these six as a bare minimum: with the empty cart try with 10 grams (2 clips), 30 grams (2 clips + 20) and 50 grams (2 clips + 2 -20s). Then with the .5 kg mass on the cart try the same three masses on the clips.

Product for submission: 2 graphs, one for the empty cart and one for the loaded cart. Graph paper here. Each graph should have two lines. The axes are accelerating force on the y-axis and rate of change of momentum for the x- axis. Draw two lines, a dotted line to show the theoretical (no friction) prediction and another to show the real data. Use a ruler to put in both lines. The theoretical line should have a slope of 1 and a y-intercept at the origin. The experimental line should be labeled with its slope and its y-intercept determined (it may be negative so leave room on your graph to accomodate that possibility. Due Friday. Last day of the quarter so no use getting this one in late.

Bridge Contest

Every year the Illinois Institute of Technology hosts a contest to see who can build the most efficient model bridge from a particular set of materials. Tinley Park will send four representatives to the contest in February. We will have two rounds of competition to choose our representatives. It is my hope that our four representatives will receive some training from a professional structural engineer prior to building their contest bridge.

Our first round will be a class assignment. To save the costs associated with using basswood, we'll use pasta for our first bridge. This will be first of all a class assignment and second of all a talent search for TPHS contest reps.

Assignment. Using fetuccini noodles build a bridge to the following specifications:

1. Use only fettucine noodles and glue. I'll provide the first 1 oz of noodles and the glue that we'll use in class.

2. The mass of your finished bridge may not exceed 35 grams.

3. Your bridge must span 15.0 cm (so make it at least a little longer so the ends can rest on the provided supports).

4. Your bridge must be at least 3.0 cm wide.

5. Your bridge must accomodate a block 2.54 cm wide x 2.54 cm high x 10.16 cm long (1 inch x 1 inch x 4 inches).

6. It must be possible to place the center of the block at the center of your bridge's support plane (that is centered both lengthwise and across the width of your bridge).

7. Your bridge must accomodate a 1/2" in diameter rod vertically through the center point.

8. Scoring: you get 5 pts for satisfying steps 1 - 7. Efficiency is determined by dividing mass supported by mass of bridge. You get 1 extra point for each 40X efficiency (that is: efficiency = 40 then +1, 80 +2, 120 +3 160 +4 and 200 +5). No additional points towards the standard.

9. We will work Thursday and Friday in class to build a first bridge. If you would like to build a second bridge (or a third or a fourth) you have until November 1st to submit. This must be made of materials (fettucini noodles) that you obtain yourself (and your own glue of choice).

10. The ten highest scoring (as of November 1) will be invited to participate in the second round and will build bridges of basswood.

http://www.pghbridges.com/basics.htm

http://www.en.wikipedia.org/wiki/Lattice_truss_bridge

http://www.britannica.com/EBchecked/topic/79272/bridge/72070/Truss-bridges

http://www.jhu.edu/~virtlab/bridge/bridge.htm

Assignment

Read sections 18.3 and 18.4 of your textbook.

Answer review questions 9 - 15 and think and explain questions 5 and 7 at the end of chapter 18.

RQ9a: Steel is used to make springs, that compress or stretch and then return to their original shape.

RQ9b: If putty is deformed it stays deformed until you reshape it.

RQ10: Hooke's Law states that the amount of deformation (for instance the elongation experienced by a spring) will be directly proportional to the force that acts to stretch it.

RQ11: The amount of force that can be exerted against an elastic system without causing permanent deformation.

RQ12: Proportion could be read as: 2-kg is to 3-cm as 6-kg is to 9-cm.

RQ13: Yes. It is compressed by its own weight.

RQ14:In between the two chords. (In material called the webbing where there is little or no compression or tension)

RQ15: The long, thin, vertical part is much lighter than the upper and lower chords because it doesn't have to resist nearly so much tension or compression.

T&E5: Since less material is needed in the neutral part, removing that material makes the beam lighter and cheaper. Ultimately, the weight removed doesn't have to be supported.

T&E7: To scale up, each dimension, height, width and length must be scaled: 50 •100•100•100 = 50,000,000 N. Since the strength depends on the cross-section and is only •100•100 = 10,000 times as strong, we can expect much more sagging under the larger weight.

Explain the difference between tension and compression.

Compression occurs when a vertical load causes the structure supporting it (such as a pillar) to shorten. Tension occurs when a vertical load causes the structure supporting it (such as a cable) to lengthen.

Look up stress and strain on the Internet (maybe here: http://en.wikipedia.org/wiki/Stress–strain_curve) and explain the difference between them.

Stress is an expression of the force exerted on a system -- often as pressure, which is determined by dividing the total force by the area over which the force is distributed: P = F÷A.

Strain is an expression for the deformation of the system under stress -- for instance elongation divided by the length of the system under tension (strain = ∆L/L)

Look up the term "chord" within the context of a bridge "truss" and explain how the terms are related. (Maybe here to start: http://en.wikipedia.org/wiki/Truss).

Chords are the long upper and lower members of a truss. If the depth (distance between the upper and lower chords) is large, the truss is more efficient. The upper chord tends to experience compression during loading while the lower chord experiences tension. The material between the chords is referred to as webbing, and is often made of lighter, weaker material than the chords.

Using the data below, calculate the percentage difference between the theoretical force provided by the hanging mass and the experimental force verified by the rate of change of momentum of the accelerating cart. Speculate on the origin of the difference.

hanging mass = 25 grams

Theoretical force is the weight = .025 kg • 9.8 m/s/s = .245 N

mass riding on track = .500 kg

total mass = .5 kg + .025 kg

during acceleration: t1 = 0.22 s, v1 = 0.18 m/s, t2 = 1.45 s v2 = 0.73 m/s

∆v = (.73 m/s - .18 m/s) = .50 m/s so m∆v = .50 • .525 kg = .263 kg•m/s

∆p/t = 0.263 kg•m/s ÷ (1.45 - .22)s = 0.213 N

∆F = .245 - .213 = .032 N and (.032/.245)• 100 = 13 %

The most likely origin for the difference is the inevitable presence of friction. The carts experience friction where the wheels contract the track and where the axles turn against the cart itself. Also the wheels have some rotational inertia that must be produced in order to accelerate the cart.