Centripetal Story Problems Physics

Play Ground Toys This is an aerial view of a spinning playground wheel. It completes one turn every 5 seconds. There are NO safety rails for the poor orphans. If the acceleration exceeds 3 m/s2 their shoes will lose traction and they will be flung off the ride into a tank of piranhas. Time Around Circle: Distance Around Circle: Speed of Child: Centripetal Acceleration: Time Period T Circumference = 2πr distance/time v2/r

Let’s calculate the centripetal acceleration for each orphan.

CHILD A Time Period T = 5 s d= 2π(0) = 0 m v = d/T = 0/5 = 0 m/s a = v2/r = 02/0 = 0 m/s2 SAFE

CHILD B Time Period T = 5 s d= 2π(1) = 6.28 m v = d/T = 6.28/5 = 1.26 m/s a = v2/r = 1.262/1 = 1.58 m/s2 SAFE

CHILD C Time Period T = 5 s d= 2π(2) = 12.6 m v = d/T = 12.6/5 = 2.51 m/s a = v2/r = 2.512/2 = 3.16 m/s2 AT RISK

CHILD D Time Period T = 5 s d= 2π(3) = 18.8 m v = d/T = 18.8/5 = 3.77 m/s a = v2/r = 3.772/3 = 4.73 m/s2 PIRANHA FOOD

Fictitious Forces Sometimes it appears like a force is pushing or pulling you, but it is NOT really there.

Centrifugal Force: Center Fleeing The force that throws objects away from spinning circles. IT DOES NOT EXIST! Inertia carries the object forward in a straight line. (Inertia is NOT a force! It is a property of matter.)

Examples: Playground Circle Cake Beaters Spin Cycle on the Washing Machine Centrifuge Get a rag wet and spin it over your head. Everyone get’s sprayed. Talk about the circle ride at Lagoon where it feels like there is a force pushing you out to the edge. Image from: www.aaastateofplay.com

Story Problems SPINNING RIDES: Distance = 2πr Velocity = d/T Acceleration = 2πr d/T v2/r

What is the furthest from the center a child can stand and still be safe? Remember that the time for one turn is 5 seconds and the maximum acceleration their shoes can provide is 3 m/s2. Time Period T = 5 s d= 2πr = 6.28r v = d/T = 6.28r/5 = 1.26r a = v2/r = 1.262r2/r = 1.58r max acceleration = 3 m/s2 1.58r = 3 r = 3/1.58 = 1.89 m

Somebody gives the circle a quick push and it speeds up Somebody gives the circle a quick push and it speeds up. It now completes a full circle every 3 seconds. What is the furthest out that a child could safely stand? They do this on their own.

Story Problems VERTICAL TURNS: (up/down) Powered by… Therefore acceleration = gravity 9.8 m/s2

You are driving your car over a hill with a radius of curvature of 35 meters. How fast can you safely drive in order to remain firmly on the ground? Inertia a= 9.8 m/s2 v = want r = 35 m a = v2 r = 18.5 m/s r r r a = v2 = √(35)(9.8) √ √ v = √r a Notice we use an inequality. Any faster and you will jump off the hill. Exactly 18.5 and you feel like you are floating. v ≤ 18.5 m/s

Bob is skiing in the mountains Bob is skiing in the mountains. He approaches a hill with a radius of curvature of 12 meters. How fast does Bob need to be going in order to get some air? They do this on their own

Story Problems HORIZONTAL TURNS: (left/right) Use the equation: a = v2/r

Bob is driving to school one morning. He is driving 9 m/s Bob is driving to school one morning. He is driving 9 m/s. What is the tightest turn that he can safely make at these speeds if the maximum acceleration his car can handle without sliding or rolling is 2 m/s2? Arial view a= 2 m/s2 v = 9 m/s r = want a = v2 r r r a = v2 r __ a __ a r = v2 a = 92 2 r = 40.5 m

The speed limit on the freeway is about 27 m/s The speed limit on the freeway is about 27 m/s. What is the sharpest turn that should be built if you want cars to be safe? (Remember that the maximum acceleration = 2 m/s 2 .) They do this on their own.