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Fun Side of Mechanics Day 6

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

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Fun Side of Mechanics Day 6

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  1. Fun Side of Mechanics Day 6 By Jonathan Abbott

  2. Review • Moment of Inertia • I = Σmi ri2 : 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

  3. 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

  4. Impulse • Impulse (J) is a change in momentum (p) • Impulse J = Force * Time • So which of the following cases would have the greatest impulse? Stop the Red Line Subway Hit a baseball http://www.flickr.com/photos/trinity/164606648/sizes/m/in/photostream/

  5. 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.

  6. 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.

  7. What is the purpose of a Helmet? I should have worn 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

  8. 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

  9. 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

  10. Calculate the total impulse:

  11. Bicycle Bump Why 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

  12. 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

  13. 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

  14. 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.

  15. Spring Constant Lab! • Or we could call it rubber band constant lab…

  16. 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:

  17. 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’

  18. 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?

  19. 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]

  20. Centripetal Forces Example • Conceptual Question: Why are roads banked?

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