1. Centripetal Story Problems
Physics

2. 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

3. Let’s calculate the centripetal acceleration for each orphan.

4. 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

5. 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

6. 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

7. 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

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

9. 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.)

10. 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:

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

12. What is the furthest from the center a child can stand and still be safe? Remember that the time for one turn is 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

13. 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.

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

15. 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 ≤ m/s

16. 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

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

18. 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

19. 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.