Sundance Simple Machines, Torque, Friction and Momentum ...



Introduction: Sabrina Cales (Bri), from UW, Physics & Astronomy Graduate Student, Name markers (Fold in half, name on one side, “Why you are ----“ on the other)

Simple Machines:

• Does anyone know what I mean when I say simple machines?

Simple machines are tools that make work easier.  They have few or no moving parts.  These machines use energy to do work.

• There are six of them can you name them, give an example and state how they make life easier?

Lever – Hammer – Prying, Lifting; Inclined Plane – Grades/Ramp on moving van – Can’t hop over the mountain or throw a refrigerator in the van; Wheel and Axle – Cars – Walk to Sundance??? Screw - ? - ?; Wedge – Saw – separate one object into two; Pulley - Crane – Loading heavy/bulky items.

Archimedes once said “Give me a place to stand and I can move the earth,” a comment in reference to the Lever, the simple machine he discovered. (Student Challenge?)

Our Simple Machines:

• Walk over to each machine and ask “Which machine this is an example of?”

i) Lever – Define: Fulcrum – The point on which the arm of the lever sits on so that it is free to rotate, Torque – Force times distance from fulcrum, Newton’s first law - An object will remain at rest, or continue to move at a constant velocity, unless a resultant force acts on it.

ii) Pulley – Ask: Why do some types of shoes stick to the ground better than others? There’s a word I’m looking for…, Define: Friction – The force of two surfaces in contact.

iii) Wheel and Axle – Ask: Does anyone know why when I hit the stationary car with another car it moves and the original car stops? Define: Momentum – The product of the mass and velocity of an object, Conservation of Momentum – Momentum is a conserved quantity for a closed system.

iv) Any more?

Free-Body Diagrams (X – Alternate):

• Does anyone know what a free-body diagram is?

Basically, just a picture of all the forces acting on the free body.

• Can anyone tell me what are the forces that act on the shoe in the pulley experiment?

Draw on the board.

[pic]

Activity (X – Alternate):

Students will get 15 minutes for each activity: i) Lever, ii) Pulley, iii) Wheel and Axle. Here are the sheets, follow directions carefully.

Alternate Activity (Groups of 2-4):

[pic]

Using Archimedes’ quote as inspiration, determine the logistics in order to “move the earth.” (i.e. Where would you stand, where would the fulcrum be…) Students have “15” minutes to make calculations and draw findings on poster board.

Good Numbers:

Mass of the earth = 5.9742 × 1024 kilograms

Radius of the earth = 6 378.1 kilometers

Earth-Moon distance = 384,403 kilometers

Earth-Sun distance = 1.496×108 kilometers

Mass of the earth * Radius of the earth / Mass of the moon = 517 ,718.003 kilometers = 81 times the radius of the earth

i) Lever – Lever to me

Set up:

Free-Body Diagram:

Draw the forces that act on the system on the diagram above. Also, note the length of the meter stick using L and the distances.

Directions:

1. Balance the meter stick with the wooden piece (fulcrum).

2. Write down the location where the fulcrum balances the meter stick perfectly: cm.

3. Is the balance point exactly 50.0 cm? Why or why not?

4. Discuss with your group and predict where Mass 2 should be placed if Mass 1 is placed 8.0 cm from the fulcrum.

M1 =

M2 =

D1 = 8.0 cm

D2 = cm

5. Test your hypothesis by placing Mass 1 at D1 = 8.0 cm and Mass 2 at your predicted value. Is the lighter mass (Mass 2) closer or farther away from the fulcrum?

6. Can you come up with an equation to predict the location that Mass 2 should be placed given that you know the location of Mass1? (HINT: Use M1, M2, D1 and D2.) If not go to step 7.

Equation:

7. Double the distance in step 5 from the fulcrum to object (i.e. D1 = 16.0 cm). If you found an equation in step 6 use it, if not use trial and error to find what D2 must be to balance the meter stick.

D2 = cm

Equations:

These equations show the relationship between mass and distance for the lever:

τ = F·D, Torque equals the acting force times the distance from the fulcrum (point of rotation.

∑τ= 0 Newton’s First Law for rotation. An object remains in a state of uniform rotational motion unless acted on by a net torque. (i.e. the lever is balanced therefore there is no acceleration, thus the sum of the torques should equal zero.)

F1 = M1g, F2 = M2g The forces that would cause rotation of the lever are just the force of gravity for each mass.

∑τ= τ1 – τ2 = F1D1 – F2D2 = M1gD1 - M2gD2 = 0

The minus sign comes from the fact that the two forces cause rotation in different directions. Therefore:

M1gD1 = M2gD2

ii) Pulley – If the shoe slips

Set up:

[pic]

Free-Body Diagram:

The free-body diagram is given above.

Directions:

1. Have one person volunteer their shoe to be used as Object A or use provided tennis shoe. Attach string securely to shoe and drape string over pulley. Form a loop to hang masses on as Object B.

2. Predict which shoe (Volunteered or Tennis Shoe) and surface (Table, Laminated Poster, Carpet) will require the most weight to move the shoe and state why you think so.

Prediction:

3. Test your hypothesis. Add weight as Object B until your shoe slips. Write down the weight just before and just after the shoes slips in the chart below.

|Volunteer Shoe |Table |Laminate Poster |Carpet |

|Mass Just Before Slip |g |g |g |

|Mass Just After Slip |g |g |g |

|Tennis Shoe |Table |Laminate Poster |Carpet |

|Mass Just Before Slip |g |g |g |

|Mass Just After Slip |g |g |g |

Challenge:

The super shoe - Which group can come up with the most mass needed to make the shoe slip?

iii) Wheel and Axle –

Set up:

[pic]

Place the cars on the metal track, making sure that the magnetic ends face each other so that they repel each other on impact.

Directions:

1. Take a minute or two to practice colliding the cars. The cars only need a gentle push in order to make a successful collision. Find what speed you should push at in order to have a “smooth” collision (smooth meaning both cars stay on the track and bounce away from each other).

2. Give one car (the blue car) a push in the direction of the other (the red car). What happens when the car you pushed (the blue car) hits the stationary one (the red car)? Describe the speed of the cars before and after the collision. Make a diagram of what happens after the collision using arrows to indicate the relative magnitude and direction of the speed of the two cars.

Before: After:

3. What other types of collisions can you think of? Draw them in diagram form like above and test them. What can you say about the momentum of the cars before and after the collisions? Does this mean that momentum is conserved for this system?

Challenge:

Which group can come up with the most collision types?

Equations:

pBlue,Before + pRed,Before = pBlue,After + pRed,After Conservation of Momentum Equation for two objects

p = mv The momentum of an object is equal to its mass times its velocity.

mBlue = mRed The mass of the blue cart equals the mass of the red cart.

pBlue,Before + pRed,Before = pBlue,After + pRed,After Conservation of Momentum for step 2 show that the velocity of the blue cart before collision equals the velocity of the red cart after the collision.

mBluevBlue,Before + mRedvRed,Before = mBluevBlue,After + mRedvRed,After

mBluevBlue,Before + 0 = 0 + mRedvRed,After

mBluevBlue,Before = mRedvRed,After

Collision Types:

|Equal Masses (mBlue = mRed) |Different Masses (mBlue = 2mRed) |

|Before |After |Before |After |

| | | | |

| | | | |

| | | | |

Group Challenge - Lever – Lever to me

[pic] Archimedes once said “Give me a place to stand and I can move the earth,” a comment in reference to the Lever, the simple machine he discovered.

Using Archimedes’ quote as inspiration, determine the logistics in order to “move the earth.” (i.e. Where would you stand, where would the fulcrum be…)

Mass of the earth = 5.9742 × 1024 kilograms

Radius of the earth = 6 378.1 kilometers

You can use the set up below to explore the mechanics of the lever, but remember you only have 15 minutes. Display your findings on a sheet of poster board. Draw the free-body diagram of the earth-lever system and label your results.

Set up:

Free-Body Diagram:

Draw the forces that act on the system on the diagram above. Also, note the length of the meter stick using L and the distances.

Directions:

1. Balance the meter stick with the wooden piece (fulcrum).

2. Write down the location where the fulcrum balances the meter stick perfectly: cm.

3. Is the balance point exactly 50.0 cm? Why or why not?

4. Discuss with your group and predict where Mass 2 should be placed if Mass 1 is placed 8.0 cm from the fulcrum.

M1 =

M2 =

D1 = 8.0 cm

D2 = cm

5. Test your hypothesis by placing Mass 1 at D1 = 8.0 cm and Mass 2 at your predicted value. Is the lighter mass (Mass 2) closer or farther away from the fulcrum?

6. Can you come up with an equation to predict the location that Mass 2 should be placed given that you know the location of Mass1? (HINT: Use M1, M2, D1 and D2.) If not go to step 7.

Equation:

7. Double the distance in step 5 from the fulcrum to object (i.e. D1 = 16.0 cm). If you found an equation in step 6 use it, if not use trial and error to find what D2 must be to balance the meter stick.

D2 = cm

Equations:

These equations show the relationship between mass and distance for the lever:

τ = F·D, Torque equals the acting force times the distance from the fulcrum (point of rotation.

∑τ= 0 Newton’s First Law for rotation. An object remains in a state of uniform rotational motion unless acted on by a net torque. (i.e. the lever is balanced therefore there is no acceleration, thus the sum of the torques should equal zero.)

F1 = M1g, F2 = M2g The forces that would cause rotation of the lever are just the force of gravity for each mass.

∑τ= τ1 – τ2 = F1D1 – F2D2 = M1gD1 - M2gD2 = 0

The minus sign comes from the fact that the two forces cause rotation in different directions. Therefore:

M1gD1 = M2gD2

-----------------------

T

mBg

T

N

mBg

Ffriction

M1

M2

M1

M2

M1g

M2g

M1D1 = M2D2

D2

D1

L

N

T

Ffriction

mBg

T

mBg

vBlue,Before = vRed,After

M2

M1

L

M1

M2

M2g

M1g

D1

D2

M1D1 = M2D2

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