Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
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.
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
N
Ffriction
T
T
mBg
mBg
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):
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
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
i) Lever – Lever to me
Set up:
M1
M2
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:
3. Is the balance point exactly 50.0 cm? Why or why not?
cm.
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
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
Equations:
L
M2
M1
M2g
M1g
D1
D2
These equations show the relationship between mass and distance for the lever:
τ = F·D,
∑τ= 0
F1 = M1g, F2 = M2g
Torque equals the acting force times the distance from the fulcrum
(point of rotation.
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.)
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
M1D1 = M2D2
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
ii) Pulley – If the shoe slips
Set up:
N
Ffriction
T
T
mBg
mBg
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
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
Challenge:
The super shoe - Which group can come up with the most mass needed to make the shoe slip?
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
iii) Wheel and Axle –
Set up:
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?
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
Equations:
pBlue,Before + pRed,Before = pBlue,After + pRed,After
p = mv
mBlue = mRed
Conservation of Momentum Equation for two objects
The momentum of an object is equal to its mass times
its velocity.
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
vBlue,Before = vRed,After
Collision Types:
Equal Masses (mBlue = mRed)
Before
After
Different Masses (mBlue = 2mRed)
Before
After
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
Group Challenge - Lever – Lever to me
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 earthlever system and label your results.
Set up:
M1
M2
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.
Sundance Simple Machines, Torque, Friction and Momentum – Sabrina L. Cales
November 5, 2007
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:
L
M2
M1
M2g
M1g
D1
D2
These equations show the relationship between mass and distance for the lever:
τ = F·D,
∑τ= 0
F1 = M1g, F2 = M2g
Torque equals the acting force times the distance from the fulcrum
(point of rotation.
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.)
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
M1D1 = M2D2