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Chapter 6: Q6.3-7CQ (page 218)

A number of amusement parks have rides that make vertical loops like the one shown in Figure. 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?

Short Answer

Expert verified

The car goes over the top at faster than this speed becausecentripetal acceleration is more than gravity and the centripetal acceleration will cause a net upward force.

The car goes over the top at slower than this speed because centripetal acceleration is less than gravity and the gravity will cause a net downward force.

Step by step solution

01

Definition of centripetal force

The centripetal force causes a body to follow a curved path. It always moves in the opposite direction of the body, towards the fixed point of the path's instantaneous centre of curvature.

Centripetal force is present when a body moves in circular path or in circle .It always works toward the centre.

02

Determine the Condition when the car goes over the top faster than this speed (a)

The centripetal acceleration is more than gravity and the centripetal acceleration will cause a net upward force.

A very high normal force acts on the car making it push harder against the rails. The passengers experience a force higher than 1g.

03

Determine the Condition when the car goes over the top slower faster than this speed (b)

If it goes slower then centripetal acceleration is less than gravity and the gravity will cause a net downward force.

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Most popular questions from this chapter

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components鈥攆riction parallel to the road (this must supply the centripetal force), and the vertical normal force (which must equal the system鈥檚 weight).

(a) Show that\(\theta \)(as defined in the figure) is related to the speed v and radius of curvature r of the turn in the same way as for an ideally banked roadway鈥攖hat is,\(\theta = {\tan ^{ - 1}}\,{v^2}/rg\)

(b) Calculate \(\theta \) for a \(12.0{\rm{ m}}/{\rm{s}}\) turn of radius \(30.0{\rm{ m}}\) (as in a race).

Figure 6.36 A bicyclist negotiating a turn on level ground must lean at the correct angle鈥攖he ability to do this becomes instinctive. The force of the ground on the wheel needs to be on a line through the center of gravity. The net external force on the system is the centripetal force. The vertical component of the force on the wheel cancels the weight of the system while its horizontal component must supply the centripetal force. This process produces a relationship among the angle \(\theta \), the speed \(v\), and the radius of curvature \(r\) of the turn similar to that for the ideal banking of roadways.

Two friends are having a conversation. Anna says a satellite in orbit is in freefall because the satellite keeps falling toward Earth. Tom says a satellite in orbit is not in freefall because the acceleration due to gravity is not 9.80 m/s2. Who do you agree with and why?

If centripetal force is directed toward the centre, why do you feel that you are 鈥榯hrown鈥� away from the centre as a car goes around a curve? Explain.

Microwave ovens rotate at a rate of about 6rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?

(a) A \(22.0{\rm{ kg}}\) child is riding a playground merry-go-round that is rotating at \(40.0{\rm{ rev}}/{\rm{min}}\). What centripetal force must she exert to stay on if she is \(1.25{\rm{ m}}\) from its centre? (b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at \(3.00{\rm{ rev}}/\min \) if she is \(8.00{\rm{ m}}\) from its center? (c) Compare each force with her weight.
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