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Amusement Park Physics

The Patriot!

Four forces cause centripetal acceleration:

At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of the circle do not fall out? Assume a radius of curvature of 8.6 m?

  • Climbs up to 149 ft (45 m)
  • Maximum speed: 65 mph (29 m/s)

**Assuming you travel at this speed and travel in a perfect circle, how many "g's" could you experience on the ride?

Draw free body diagrams for a person at each of the following locations on a roller coaster. What forces contribute to the centripetal force?

3.

2.

1.

On the ripcord, you free fall for 30 m before the tension in the 40 m cord causes centripetal acceleration.

a) What's your velocity after the free fall?

b) What is the force of tension on the rope at the bottom of the swing? (Assume you have a mass of 45 kg)

  • Gravity
  • Normal Force
  • Friction
  • Tension

A 1000 kg go-kart is going around a curve with radius 30 meters. If the coefficient of friction between the car's tires and the road is 0.5, what is the maximum speed at which the car can make the turn?

Suppose that the coefficient of friction between a typical tire and a particular highway surface is u. What should be the minimum radius for curves on this highway if the speed limit is v?

Riders in an amusement park ride shaped like a Viking ship hung from a large pivot are rotated back and forth like a rigid pendulum of radius 14m. Sometime near the middle of the ride, the ship is momentarily motionless at the top of its circular arc. The ship then swings down under the influence of gravity.

(a) What is the magnitude of the centripetal acceleration at the bottom of the arc?

(b) Draw a free-body diagram of the forces acting on a rider at the bottom of the arc.

(c) Find the magnitude of the force exerted by the ride on a 60.0 kg rider and compare it to her weight.

(d) Discuss whether the answer seems reasonable.

The Finnish Fling

If the room radius is 5.5 m, and the rotation frequency 0.5 revolutions per second when the floor drops out, what minimum coefficient of static friction keeps the people from slipping down?

People on this ride said they were "pressed against the wall" Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides scary)?

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