Fun Side of Mechanics Day 6 By Jonathan

Fun Side of Mechanics Day 6 By Jonathan Abbott

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

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

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 http: //www. flickr. com/photos/trinity/164606648/sizes/m/in/photostream/ Hit a baseball

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.

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.

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…

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

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

Calculate the total impulse: Force (in Newtons) Impulse 1, 2 1 0, 8 0, 6 0, 4 0, 2 0 Impulse 0 1 2 Time (in seconds) Force (in Newtons) 14 12 10 8 6 4 2 0 0 1 2 3 Time (in seconds) 4 3 4 Impulse 2 1, 5 1 0, 5 0 0 1 2 3 Time (in seconds) 4

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

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=-kx • Force = - spring constant * distance stretched

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 x 2

Elastic Potential Energy • The Elastic Potential Energy is: • PEe = ½ k x 2 • 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 Potential translation height rotation elastic Other

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

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:

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 * v 2 /r • Force = mass * speed 2 / radius of the circle. • This force is ‘radially inwards’

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?

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]

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