PPT Activity Levers

Developer Notes1. I’m trying to balance spending some time on simple machines (levers only – mention the

others) with other needs. 2. Do we still want to mention other simple machines? (sc 6/16)

Version Date Who Revisions03 04 2004/03/15 dk Changed to new format

changed concept definition for force and distance in simple machines

expanded the goals

Goals1. Students will understand how bones, joints, and muscles work together as levers.2. Students will know the three classes of levers.3. Students will know the formula for levers.4. Students will know that force and distance are inversely proportional in simple machines.5. Students will know that levers are one kind of simple machine.

Concepts & Skills Introduced

Area Conceptphysics simple machines physics in simple machines, force and distance are inversely proportional physiology our musculo-skeletal system operates by levers

Time Required1.5 hours (probably more?)

PresentationStart the students off with a continuation of the physiological discussion of joints, ligaments, muscles, and tendons.

Do a demo. Have several volunteers hold a mass of about 10 kg. Have them place their elbow near the edge of a table. Place the weight in their hand first, then hold the weight so their forearm is horizontal. Then move the weight halfway up their forearm. It should be significantly easier when it is on their forearm. For the large mass, you can use a bucket with a bowling ball in it. Attach a strap to the handle of the bucket so that the bucket can rest on the floor and the strap is long enough to reach the bench top. This allows you to raise the bucket without fear of dropping it far.

Scientists like to simplify in order to see patterns more clearly. We can simplify the arm by modeling it. The arm makes a lever. Introduce the four parts of a lever and discuss the vocabulary.

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PPT Activity Levers

Vocabulary Lever – a simple machine consisting of a bar, fulcrum, resistance, and effort. There are three

classes of lever, depending on whether the fulcrum, resistance, or effort is in the middle:Class 1, fulcrum, Class 2, resistance, Class 3, effort.

Fulcrum – part of a lever. It is the fixed part of the lever on which the bar rotates. Resistance – in mechanics, the force inhibiting motion. Effort – in mechanics, the force applied. Simple machine – one of a small number of mechanical devices which make work easier.

More complicated machines are made by combining simple machines. Simple machines include levers, inclined planes, screws, pulleys, and wheels and axles. (The list varies between authors.)

Set up three demos and take volunteers before starting the lab. You’ll need a 2” x 12” x 8’ (knot free) board as the lever bar and a 12” piece of 2” x 2” board (or 2” x 4”, or a broomstick…) to serve as the fulcrum. This will help the students to see the three types of levers. If you can organize it, it would be good to have everyone try the demos, especially the class 2 demo. Class 1 – Set the board over the fulcrum so the fulcrum is closer to one end. Have two people

(resistance) stand on the short end, and have the third person (effort) stand on the long end so that they can lift the other two.

Class 2 – The floor is the fulcrum here. Have one of the students (resistance) stand near one end of the board. Have another student (effort) try lifting the board from various locations, starting farthest away from the resistance/fulcrum and moving closer. It helps to put something under the non-fulcrum end of the board so people can get their fingers under it.

Class 3 – To create the fulcrum, either put one end of the board under a cabinet edge, or have someone hold down the very end. Have another person try lifting (effort) the board (resistance), moving from the middle toward the fulcrum. It helps to put something under the non-fulcrum end of the board so people can get their fingers under it.

Start the lab. This activity should remind the students of their work on center of mass, where they used the same setup. The balance in that lab is a class 1 lever. The formula is ∑Fd = ∑Fd. Levers are actually easier than that if you ignore the weight of the bar (meter stick). Hanging the meter stick at the balance point eliminates having to take into account the meter stick’s mass. For a class 1 lever, using masses as the effort eliminates having to account for the mass of the scale and the mass of the ruler.

The paper clips may need to be bent into this shape for strength, but it takes time. A simpler bend is shown in the activity.

Don’t give them the formulas until they’ve completed the lab summary. For a lever, Fede = Frdr . The force of the effort times its distance from the fulcrum equals

the force of the resistance times its distance from the fulcrum.

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PPT Activity Levers

If you want to hang the meter stick off-center to make it more interesting, the formula for class 2 and 3 levers is Fede = Frdr + Fmdm, where m is for the resistance of the meter stick. The measured weight of the meter stick times the distance from the fulcrum will be the same in all cases. It’s interesting to graph, as it forms a hyperbola; as you get infinitely close to the fulcrum, the resistance gets infinitely great (and vice versa, except you can’t get infinitely far, because the meter stick ends).

Also, for a class 1 lever, if you use the scale to measure the downward force required, you must add the weight of the scale to its reading. Thus the equation is Fede = (Fr+Fs)dr, where Fs is the weight of the scale.

POEThis is a nice think-piece which combines Fd and conservation of momentum. Set up a large board (1" x 10" x 8' or so) as a teeter-totter. Use a small board (1" wide) for the fulcrum so the board is easy to balance but still tippy. Set up two mass carts (one with a spring) with different amounts of weight on them so that they are balanced in the middle of the board. Have the students predict whether the board will stay balanced once you release the spring and set the carts rolling. Release the spring so the carts go apart. The board should balance. Why? Momentum is conserved - it started at zero, and mv on one side will equal mv on the other side. Since the carts travel for the same amount of time after the spring is released, time falls out of the equation and md = md. Mass is directly related to force (through gravity, 9.8 m/s2), so Fd on one side will equal Fd on the other side, and the board will balance.

Assessment

Writing Prompts

RelevanceWhen the lab is complete, have the students identify different types of levers in their bodies. Or name muscles or joints and have them identify the class of lever. (The quadriceps and the outside of fingers are tricky – I think they’re class 3. Look at the insertion point of the muscle/tendon.) Class 1 – elbow extension (triceps), ankle extension (calf), neck-head looking up Class 2 – non-existent. You can’t have the resistance between the joint (fulcrum) and the

muscle (effort). Some people think ankle extension is a class 2 lever, using the ball of the foot as the fulcrum, and the weight of the leg as the resistance.

Class 3 – elbow flexion (biceps), knee flexion (hamstring), ankle flexion (shin), finger flexion

Also lead a discussion on where levers are used in every-day life. Example: nail puller, gas pedal, wheelbarrow, seesaw, crowbar, shovel, automatic door…

Answers to Exercises

Answers to Challenge/ extension

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BackgroundWe’ve learned about bones, their strength, and how they form the framework for our bodies. We’ve learned about joints and how they allow us to move. And we’ve learned about muscles and how they make us move. But how strong are we? What determines how much we can lift?

When you pick up a book, you use your biceps muscle, your forearm, and your elbow joint to raise it. That makes a lever. A lever consists of four things: a resistance (book), an effort (biceps), a bar (forearm), and a fulcrum (elbow joint). Levers are classified into three types, depending on whether the fulcrum, the resistance, or the effort is in the middle.

Class 1 – fulcrum in the middle

Class 2 – resistance in the middle

Class 3 – effort in the middle

123, FRE

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ProblemFor each of the three classes of levers, find the formula that describes its behavior.

Materials1 meter stick1 2000 g spring scale1 mass set3 jumbo paper clips (bent as shown)1 ring stand

Procedure1. Work in groups of two.2. Set up your apparatus to model each kind of lever as shown below.

a. For all the setups, put the Fulcrum at the 50 cm (balance) point and leave it there.b. For all the setups, use a mass (about 200 g is good) as the Resistance.c. For a class 1 lever, use masses from the mass set (not the scale) as the Effort.d. For class 2 and 3 levers, use the scale as the Effort.e. For a class 3 lever, reverse the Fulcrum so it holds the meter stick down. (Try it.)

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Class 2

Class 3

Class 1

R

F

E

E

E

F

F

R

R

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3. Make a table for each class of lever and record data in your table.4. For each setup, take at least four readings – two by moving the Resistance, and two by

moving the Effort (you may take more). Take the readings when the meter stick is level. For each reading, record

a. the location of the fulcrum, b. the location and amount of the resistance (mass), and c. the location and amount of the effort (scale reading).

5. If you want more data, try changing the amount of resistance. 6. Analyze your data and come up with a formula for each class of lever.

Summary 1. In all three classes, if you increase the distance between the fulcrum and the resistance, what

do you have to do with the effort?2. In all three classes, if you increase the amount of resistance, what do you have to do with the

effort?3. What is the formula for a class 1 lever?4. What is the formula for a class 2 lever?5. What is the formula for a class 3 lever?6. Draw a picture of a first class lever in a human. Identify the fulcrum, resistance, and effort.7. Draw a picture of a third class lever in a human. Identify the fulcrum, resistance, and effort.

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Reading

Exercises1. Apes’ biceps are attached to their forearms farther away from their elbows than humans’.

Assuming everything else is the same (size and speed of muscles, etc.), who is stronger?2. If you’re trying to move a boulder using a pry bar (class 1 lever), which end of the bar should

the fulcrum be closest to, the boulder or you?3. If you’re trying to move a load with a wheelbarrow (class 2 lever), how can you make the

load easier to lift?4. Why would things always seem heavier with a class 3 lever than without any lever at all?5. You want to lift a 500 kg boulder, so you decide to use a big bar as a class 1 lever. The

distance from the bottom of the boulder to the fulcrum is 0.40 m. You weigh 50 kg. In order to lift the boulder, how long must the bar be from the fulcrum to where you pull on it? How long must whole bar be so that you can lift the boulder? Neglect the weight of the bar.

6. For levers, if you want to exert the same amount of effort but move a heavier load, what do you have to do?

Challenge/ extension1. What is the particular advantage of a class 3 lever when you compare the distance the effort

moves versus the distance the resistance moves?2. Assuming muscles contract at the same rate, what advantage would that give humans over

apes to compensate for the apes’ greater strength?3. Move the fulcrum in the lab setup to 25 cm and test what force is needed at 0 cm to balance

it. How does that compare to the weight of the meter stick? Why?

Glossary Simple machine – a mechanical devices that multiplies or changes the direction of a force.

More complicated machines are made by combining simple machines. Simple machines include levers, inclined planes, screws, pulleys, and wheels and axles. (The list varies between authors.)

Lever – a simple machine consisting of a bar, fulcrum, resistance, and effort. There are three classes of lever, depending on whether the fulcrum, resistance, or effort is in the middle:Class 1, fulcrum, Class 2, resistance, Class 3, effort.

Fulcrum – part of a lever. It is the fixed part of the lever on which the bar rotates. Resistance – in mechanics, the force inhibiting motion. Effort – in mechanics, the force applied.

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