Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 5, Problem 97P
To determine

To Find: The safe range of speeds

Expert Solution & Answer
Check Mark

Answer to Problem 97P

  20.1km/hr to 56.1 km/hr

Explanation of Solution

Given Information:

Radius of the curve is 30m .

Mass of the car, m=950kg car

Speed of the car is 40.0km/h

The coefficient of static friction between the road and the tires is 0.300 .

Formula Used:

Newton’s second law of motion:

  F=ma

Where, m is mass and a is acceleration.

Calculation:

  Physics for Scientists and Engineers, Chapter 5, Problem 97P

From the Free body diagram is shown above. When the coefficient of static friction is zero along x-axis,

  Fnsinθ=mvmin2r...(1)

And along y-axis

  Fncosθmg=0Fncosθ=mg...(2)

Along x-axis

  Fnsinθfscosθ=mvmin2r...(3)

And along y-axis

  Fncosθ+fssinθmg=0...(4)

Now the force of static friction is given as

  fs=fs,max=μsFn...(5)

Substituting (5) in (3) and (4)

  Fn(μscosθsinθ)=mv min3r...(6)andFn(cosθ+μssinθ)=mg...(7)

Now dividing (6) and (7)

  Fn( μ s cosθsinθ)Fn( cosθ+ μ s sinθ)=m( v min 2 r )mg( μ s cosθsinθ)( cosθ+ μ s sinθ)=( v min 2 rg)vmin= rg( sinθ+ μ s cosθ ) ( cosθ+ μ s sinθ )vmin= ( 30 m )( 9 .81 m/s 2 )( sin 22.8 o 0.3cos 22.8 o ) ( cos 22.8 o +0.3sin 22.8 o )vmin=5.59m/svmin=20.1km/h

Now when the car is traveling at maximum speed:

Along x-axis

  Fnsinθ+fscosθ=mvmax2r...(8)

And along y-axis

  Fncosθfssinθmg=0...(9)

Now the force of static friction is given as

  fs=fs,max=μsFn...(10)

Substituting (10) in (8) and (9)

  Fn(μscosθ+sinθ)=mv max2r...(11)and Fn(cosθμssinθ)=mg...(12)

Now dividing (11) and (12)

  Fn( μ s cosθsinθ)Fn( cosθ+ μ s sinθ)=m( v max 2 r )mg( μ s cosθ+sinθ)( cosθ μ s sinθ)=( v max 2 rg)vmax= rg( μ s cosθ+sinθ ) ( cosθ μ s sinθ )vmax= ( 30 m )( 9 .81 m/s 2 )( 0.3cos 22.8 o +sin 22.8 o ) ( cos 22.8 o 0.3sin 22.8 o )vmax=15.6m/svmax=56.1km/h

Conclusion:

The safe range of speed is 20.1km/hr to 56.1 km/hr .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
An infinitely long conducting cylindrical rod with a positive charge λ per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of −2λ and radius r1, as shown in the figure. What is σinner, the surface charge density (charge per unit area) on the inner surface of the conducting shell? What is σouter, the surface charge density on the outside of the conducting shell? (Recall from the problem statement that the conducting shell has a total charge per unit length given by −2λ.)
A small conducting spherical shell with inner radius aa and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (Figure 1). The inner shell has total charge +2q, and the outer shell has charge −2q. What's the total charge on the inner surface of the small shell? What's the total charge on the outer surface of the small shell? What's the total charge on the inner surface of the large shell? What's the total charge on the outer surface of the large shell?
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius cc and outer radius d (Figure 1). The inner shell has total charge +2q, and the outer shell has charge −2q. What is the direction of the electric field for b<r<c? Calculate the magnitude of the electric field for c<r<d. Calculate the magnitude of the electric field for r>d.

Chapter 5 Solutions

Physics for Scientists and Engineers

Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - Prob. 42PCh. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 55PCh. 5 - Prob. 56PCh. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 65PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - Prob. 76PCh. 5 - Prob. 77PCh. 5 - Prob. 78PCh. 5 - Prob. 79PCh. 5 - Prob. 80PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - Prob. 84PCh. 5 - Prob. 85PCh. 5 - Prob. 86PCh. 5 - Prob. 87PCh. 5 - Prob. 88PCh. 5 - Prob. 89PCh. 5 - Prob. 90PCh. 5 - Prob. 91PCh. 5 - Prob. 92PCh. 5 - Prob. 93PCh. 5 - Prob. 94PCh. 5 - Prob. 95PCh. 5 - Prob. 96PCh. 5 - Prob. 97PCh. 5 - Prob. 101PCh. 5 - Prob. 102PCh. 5 - Prob. 103PCh. 5 - Prob. 104PCh. 5 - Prob. 105PCh. 5 - Prob. 106PCh. 5 - Prob. 107PCh. 5 - Prob. 108PCh. 5 - Prob. 109PCh. 5 - Prob. 110PCh. 5 - Prob. 111PCh. 5 - Prob. 112PCh. 5 - Prob. 113PCh. 5 - Prob. 114PCh. 5 - Prob. 115PCh. 5 - Prob. 116PCh. 5 - Prob. 117PCh. 5 - Prob. 118PCh. 5 - Prob. 119PCh. 5 - Prob. 120PCh. 5 - Prob. 121PCh. 5 - Prob. 122PCh. 5 - Prob. 123PCh. 5 - Prob. 124PCh. 5 - Prob. 125PCh. 5 - Prob. 126PCh. 5 - Prob. 127PCh. 5 - Prob. 128PCh. 5 - Prob. 129PCh. 5 - Prob. 130PCh. 5 - Prob. 131PCh. 5 - Prob. 132PCh. 5 - Prob. 133PCh. 5 - Prob. 134PCh. 5 - Prob. 135PCh. 5 - Prob. 136PCh. 5 - Prob. 137PCh. 5 - Prob. 138PCh. 5 - Prob. 139P
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
What Is Circular Motion? | Physics in Motion; Author: GPB Education;https://www.youtube.com/watch?v=1cL6pHmbQ2c;License: Standard YouTube License, CC-BY