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Chapter 6: Problem 14

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?

Short Answer

Expert verified
No, you should not feel yourself thrown to either side on an ideally banked curve, assuming no other external forces are acting. The force exerted on you by the car seat is directed towards the center of the curve due to the frictional force which acts as centripetal force.

Step by step solution

01

Understanding the Forces in a Turn

Whenever a car moves into a curve, it experiences a frictional force towards the center of the circle, along with the normal force due to gravity. This frictional force is the centripetal force that prevents the car from slipping.
02

Analysis of the Banked Curve

When a car is on an ideally banked curve, the frictional force becomes zero because the component of the gravitational force provides the necessary centripetal force. The angle of banking, car's speed, and the radius of the curve are so balanced that no lateral slipping occurs.
03

Force Exerted on the Driver

As for the driver, they would feel the force exerted on them by the car seat, which is directed towards the center of the curve. This results from the frictional force which resists the tendency of the driver to move in a straight line while the car is turning.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Centripetal Force
When a car navigates through a curve, it moves in a circular path. To maintain this circular motion, a special force is required - the centripetal force. This force acts towards the center of the curve, keeping the car from skidding outwards.

In simpler terms, centripetal force is what pulls the car towards the center of the curved path. Imagine swinging a ball tied to a string; the tension in the string acts as centripetal force, pulling the ball towards the center of the circle.

For a car moving along a curve, the centripetal force often comes from the friction between the tyres and the road, although, on a banked curve, this force is primarily provided by gravitational and normal forces. In the absence of sufficient centripetal force, the car would slide off the curve.
Frictional Force
Frictional force plays a critical role in maintaining a car's movement along a curve. It acts parallel to the surface of contact between the car's tyres and the road.

On a flat curve, the frictional force provides the necessary centripetal force that keeps the car on track, ensuring it doesn't slide off. However, on an ideally banked curve, the need for frictional force is minimized.

Here, the banking angle of the curve allows the gravitational component to provide the needed centripetal force. As a result, the frictional force can be zero. This reduces tyre wear and enhances safety, as the car relies less on friction to navigate the curve.
Gravitational Force
Gravitational force is the force with which the Earth attracts objects towards its center. This force plays an essential role in the dynamics of banked curves.

On an ideally banked curve, a component of gravitational force points towards the center of the curve. This means the curve鈥檚 angle and the gravitational pull work together to provide the centripetal force required to keep the car moving smoothly without skidding.

The careful balancing of gravitational force and the curve鈥檚 banking allows for this smooth motion. This balance ensures that even without a frictional force, the car can safely navigate the curve at a specified speed, reducing the chances of an accident due to skidding or slipping.

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Most popular questions from this chapter

A 30.0-g ball at the end of a string is swung in a vertical circle with a radius of \(25.0 \mathrm{cm} .\) The rotational velocity is \(200.0 \mathrm{cm} / \mathrm{s}\). Find the tension in the string: \((\mathrm{a})\) at the top of the circle, (b) at the bottom of the circle, and (c) at a distance of \(12.5 \mathrm{cm}\) from the center of the circle \((r=12.5 \mathrm{cm})\)

If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a problem on icy mountain roads). (a) Calculate the ideal speed to take a \(100.0 \mathrm{m}\) radius curve banked at \(15.0^{\circ} .\) (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at \(20.0 \mathrm{km} / \mathrm{h} ?\)

A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius \(7.00 \mathrm{m}\). At point A the speed of the car is \(10.0 \mathrm{m} / \mathrm{s},\) and at point \(\mathrm{B},\) the speed is \(10.5 \mathrm{m} / \mathrm{s}\) Assume the child is not holding on and does not wear a seat belt. (a) What is the force of the car seat on the child at point A? (b) What is the force of the car seat on the child at point B? (c) What minimum speed is required to keep the child in his seat at point A?

Many amusement parks have rides that make vertical loops like the one shown below. 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?

If you wish to reduce the stress (which is related to centripetal force) on high-speed tires, would you use largeor small-diameter tires? Explain.
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