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Chapter 4: Problem 5

Explain why it's desirable to bank racetrack curves with the steeper angle on the outer part of the track.

Short Answer

Expert verified
Banking with a steeper outer curve provides additional centripetal force, enabling higher speed turns and reducing skidding risk.

Step by step solution

01

Understanding Centripetal Force

When a car travels around a curved racetrack, it requires a centripetal force to keep it moving in a circular path. This force acts towards the center of the circle and is typically provided by the friction between the car's tires and the track's surface.
02

Effect of Banking on Curve

Banking the track means tilting the track so that the outer edge is higher than the inner edge. This tilt helps vehicles make the turn because some of the gravitational force acting on the vehicle gets redirected towards providing the necessary centripetal force.
03

Outer Steeper Angle

A steeper angle on the outer part of the track allows vehicles to handle higher speeds while maintaining a stable path. The component of gravitational force on the steeper outer bank helps provide an increased centripetal force, reducing reliance solely on friction, which might not be sufficient at high speeds.
04

Reduction of Skidding Risk

A correctly banked turn with a steeper outer angle reduces the risk of skidding. When the friction force is not enough to provide the required centripetal force, the banking helps stabilize the car by transforming some of gravitational force component into centripetal force.

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Key Concepts

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

Centripetal Force
Centripetal force is an essential concept in the physics of racetrack design. When a car enters a curved path, it needs to stay on that path instead of sliding off it. To do this, it must experience a force that pulls it toward the center of the curve. This is what we call the centripetal force.
  • This force doesn't come from within the car; instead, it requires external support, primarily through the interaction between the car's tires and the road.
  • Friction between the tires and track surface is the most common provider of this force, preventing the car from drifting outwards.
  • Without adequate frictional support, additional measures such as banking curves are necessary to ensure stability.
Banking utilizes the gravitational force to contribute more naturally to the centripetal force needed, especially at high speeds.
Banked Curves
Banked curves are one of the smart engineering solutions in track design; they are tilted so the outer edge is higher than the inner edge. This inclination takes advantage of physics by redirecting forces.
  • Instead of relying solely on friction, banking allows the track itself to generate a component of the required centripetal force, leading to greater stability for vehicles.
  • This is possible because when a surface is inclined, part of the gravitational force helps push the car toward the center of the curve.
  • The steeper the bank, especially on the outer edge, the more significant this force component becomes. This feature is especially beneficial for enabling high-speed turns.
For racers, this can mean maintaining speed through turns, making banking a critical design factor on competitive racetracks.
Vehicle Dynamics
Understanding vehicle dynamics is crucial for appreciating how cars interact with racetrack designs, especially banked curves. Vehicle dynamics examines how forces affect the motion of vehicles, influencing their stability and performance.
  • When a car speeds through a curve, its dynamics are put to the test as it manages the forces that want to push it off the track.
  • The design of the track, including the angle and banking, can significantly influence these forces.
  • Banked curves reduce the dependence on tire friction, which can be insufficient at high speeds, thus lowering the chances of the car skidding.
By engineering tracks with these dynamics in mind, designers can ensure cars can handle curves more efficiently and safely, minimizing risks and enhancing both driver control and speed management.

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Most popular questions from this chapter

The " 20 -G" centrifuge at NASA's Ames Research Center is used to study the effects of large acceleration ("hypergravity") on astronauts and test pilots. Its 8.84 -m-long arm rotates horizontally about one end. The test subject is strapped onto a cot at the other end and rotates with it. A \(70.0-\mathrm{kg}\) astronaut who is \(1.70 \mathrm{~m}\) tall is strapped as shown in Figure GP4.120. The maximum rotation speed of the arm for human study is 35.55 rpm (rev/min). Typically, a person's head comprises \(6.0 \%\) of his weight, and his two feet together comprise \(3.4 \%\). (a) Draw force diagrams for the astronaut's head and for one foot during rotation. (b) Calculate the net force acting on the astronaut's head and on each of his feet when the arm is rotating at its maximum speed. Express your answer in newtons and as a multiple of the weight of the head and foot. Assuming negligible friction from the cot, what exerts the accelerating force on the head and feet? (c) Suppose instead that the arm were rotated at a constant rate in a vertical plane with the astronaut still strapped as shown. Find the maximum and minimum force on the astronaut's head.

The Sun exerts a gravitational force of \(5.56 \times 10^{22} \mathrm{~N}\) on Venus. Assuming that Venus's orbit is circular with radius \(1.08 \times 10^{11} \mathrm{~m},\) determine Venus's orbital period. Check your answer against the observed period, about 225 days.

A wooden block with mass \(0.300 \mathrm{~kg}\) rests on a horizontal table, connected to a string that hangs vertically over a frictionless pulley on the table's edge. From the other end of the string hangs a \(0.100-\mathrm{kg}\) mass. (a) What minimum coefficient of static friction \(\mu_{\mathrm{s}}\) between the block and table will keep the system at rest? (b) Find the block's acceleration if \(\mu_{k}=0.150 .\)

A car rounds a 210 -m-radius curve at \(11.5 \mathrm{~m} / \mathrm{s}\) (a) Draw a force diagram for the car. (b) If the horizontal force acting on the car is \(790 \mathrm{~N}\), what's the car's mass?

A 31 -kg golden retriever spots a squirrel and gives chase. The dog's legs provide an average force of \(170 \mathrm{~N}\). (a) What's the dog's acceleration? (b) How much time does it take the dog to go from rest to \(10.8 \mathrm{~m} / \mathrm{s} ?\)
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