Fun Side of Mechanics Day 6

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Fun Side of Mechanics Day 6 By Jonathan Abbott

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Fun Side of Mechanics Day 6. By Jonathan Abbott. Review. Moment of Inertia I = Σ m i r i 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 - PowerPoint PPT Presentation

Transcript of Fun Side of Mechanics Day 6

Page 1: Fun Side of Mechanics Day 6

Fun Side of Mechanics Day 6By Jonathan Abbott

Page 2: Fun Side of Mechanics Day 6

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?