fun side of mechanics day 6 by jonathan abbott. review moment of inertia i = Σm i r i 2 : more mass...
TRANSCRIPT
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Fun Side of Mechanics Day 6By Jonathan Abbott
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Review• Moment of Inertia• I = Σmi ri
2 : more mass spread out = higher moment of inertia• Higher moment of inertia = harder to start spinning
• Torque• A force that changes an object’s rotation
• Angular Momentum• The bigger an object and the faster it spins, the greater its
angular momentum
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Homework Check• Did anyone try to
make a concept map?
• Would anyone like to share their work?
One Example:http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
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Impulse• Impulse (J) is a change in momentum (p)• Impulse J = Force * Time• So which of the following cases would have the greatest
impulse?
http://www.flickr.com/photos/trinity/164606648/sizes/m/in/photostream/
Stop the Red Line Subway Hit a baseball
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Then which has a greater impulse?
• A 1000 kg old car speeding up to 15 m/s starting from rest in a total time of 10 seconds.
• A 1000 kg sports car speeding up to 15 m/s starting from rest in a total time of 2 seconds.
• The change in momentum is the same.• This means the impulse must be the same for each.• Which case then has a greater net force?• The sports car has a greater net force because it has the same
impulse in less time.
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Stop a car• Stopping a car takes the same impulse whether you step on
the brake hard or just gradually slow down.
• Which method of braking is better for your car? Why?• Gradually slowing down: you give yourself more time. More
time means less net force. Less net force means easier on the brakes and safer for you.
• Good drivers anticipate braking and slow down early.
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What is the purpose of a Helmet?• Helmets keep you safer. But how?• As your head collides with the ground, the
helmet gives you more time for the collision. More time = less force.
• Less Force = less damage
I should have worn a helmet…
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Field Trip: How to survive a fall• We will go to this site to
explore how what we are talking about impulse applies to this topic.
• http://www.wikihow.com/Survive-a-Long-Fall
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What about these?• ‘Hard’ vs ‘Soft’ surface• Airbags• Seatbelts• Dismounting from a
giraffe• Jumping on a bed (so
much fun, I know)• Contact Juggling Balls• Hitting a baseball and
‘following through’• Dropping an egg on a hard
surface
• Car crash: crushed• Woodchips• Springs• Shoes• Sandpits• Glass cases (with padding)• Styrofoam Chips• Bubble Wrap• Track (as in track and field)• Basketball gym floors• Professional Clubs
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Calculate the total impulse:
0 1 2 3 40
2
4
6
8
10
12
14
Impulse
Time (in seconds)
Forc
e (in
New
tons
)
0 1 2 3 40
0.5
1
1.5
2
Impulse
Time (in seconds)
Forc
e (in
New
tons
)
0 1 2 3 40
0.20.40.60.8
11.2
Impulse
Time (in seconds)
Forc
e (in
New
tons
)
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Bicycle BumpWhy might larger tires be better for going over bumps?
More time = less force
Less force = less likely to fly up
Less likely to fly up/ back = less kinetic energy wasted
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Springs!• As you compress or stretch a string from
its relaxed length, it exerts a force to try to go back.
• This force is proportional to distance you stretch/compress the string and also depends on the spring constant
• F = - k x• Force = - spring constant * distance
stretched
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More about Springs• Similar to a spring is a rubber band.• Since when you release a stretched
rubber band or a compressed spring, what type of energy must be stored in springs?• Elastic Potential Energy
• The Elastic Potential Energy is:• PEe = ½ k x2
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Elastic Potential Energy• The Elastic Potential Energy is:• PEe = ½ k x2
• How much does the elastic potential go up if I stretch a spring or a rubber band twice as far as it was previously?• It now has four times as much energy.
Kinetic
translation
rotation
Potential
height
elastic
Other
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Spring Constant Lab!• Or we could call it rubber band constant lab…
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Mass on a Spring• This creates simple harmonic motion, which is the case when
something oscillates. You can get simply harmonic motion with many things besides springs:
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Uniform Circular Motion• Uniform Circular Motion is when an object sweeps out a
trajectory in a perfect circle. This is important because we can calculate the force needed to make this path easily.
• Force = m * v2 /r• Force = mass * speed2 / radius of the circle.• This force is ‘radially inwards’
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Uniform Circular Motion• A small object spins around a ring at a constant speed.• Which way is the acceleration and force at point 3?• Which way is the acceleration and force at point 2?
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Centripetal Force• We call this force that causes circular motion the centripetal
force.• ‘Centripetal’ means center seeking• Why might the rollercoaster passengers not fall out during the
loop shown below? [Hint: draw a free body diagram]
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Centripetal Forces Example• Conceptual Question: Why are roads banked?