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If centripetal force is directed toward the center, why do you feel that you are ‘thrown’ away from the center as a car goes around a curve? Explain.

Race car drivers routinely cut corners as shown in [link] . Explain how this allows the curve to be taken at the greatest speed.

In the figure, two paths are shown inside a race track through a steep curve, approximately equal to ninety degrees. Two cars are shown. One car is on the path one, which is the inside path along the track. The path of this car is shown with an arrow through the inside path. The second car is shown overtaking the first car, while taking a left turn, showing it to be crossing into the inside path from the second path. The path of this car is also shown with an arrow throughout.
Two paths around a race track curve are shown. Race car drivers will take the inside path (called cutting the corner) whenever possible because it allows them to take the curve at the highest speed.

A number of amusement parks have rides that make vertical loops like the one shown in [link] . For safety, the cars are attached to the rails in such a way that they cannot fall off. If the car goes over the top at just the right speed, gravity alone will supply the centripetal force. What other force acts and what is its direction if:

(a) The car goes over the top at faster than this speed?

(b)The car goes over the top at slower than this speed?

In the given line diagram, a circular amusement ride is shown from the front with a boat having four people seated in it going upward from the left to the right. The ride starts from the left in a horizontal direction, then goes upward, then turns sideways to the left, comes down from the right and moves horizontal to the right and then ends. It looks like a single knot of a thread, viewed from sideways. Some square iron blocks are also shown below the ride path.
Amusement rides with a vertical loop are an example of a form of curved motion.

What is the direction of the force exerted by the car on the passenger as the car goes over the top of the amusement ride pictured in [link] under the following circumstances:

(a) The car goes over the top at such a speed that the gravitational force is the only force acting?

(b) The car goes over the top faster than this speed?

(c) The car goes over the top slower than this speed?

As a skater forms a circle, what force is responsible for making her turn? Use a free body diagram in your answer.

Do you feel yourself thrown to either side when you negotiate a curve that is ideally banked for your car’s speed? What is the direction of the force exerted on you by the car seat?

Suppose a mass is moving in a circular path on a frictionless table as shown in figure. In the Earth’s frame of reference, there is no centrifugal force pulling the mass away from the centre of rotation, yet there is a very real force stretching the string attaching the mass to the nail. Using concepts related to centripetal force and Newton’s third law, explain what force stretches the string, identifying its physical origin.

In the figure a table is shown. On the table a mass is attached to a nail at the center with the help of a string. The mass is moving on a circular path in counterclockwise direction.
A mass attached to a nail on a frictionless table moves in a circular path. The force stretching the string is real and not fictional. What is the physical origin of the force on the string?

Problems exercise

(a) A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?

(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rev/min if she is 8.00 m from its center?

(c) Compare each force with her weight.

a) 483 N

b) 17.4 N

c) 2.24 times her weight, 0.0807 times her weight

Calculate the centripetal force on the end of a 100 m (radius) wind turbine blade that is rotating at 0.5 rev/s. Assume the mass is 4 kg.

What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 105 km/h speed limit (about 65 mi/h), assuming everyone travels at the limit?

4 . 14º size 12{4 "." "14"°} {}

Practice Key Terms 5

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Source:  OpenStax, Introductory physics - for kpu phys 1100 (2015 edition). OpenStax CNX. May 30, 2015 Download for free at http://legacy.cnx.org/content/col11588/1.13
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