Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 5, Problem 28P

(a)

To determine

The frictional force on the car.

(a)

Expert Solution
Check Mark

Answer to Problem 28P

The frictional force on the car is 2300N_.

Explanation of Solution

Given that the radius of the curved path is 410m, the speed of the car is 32m/s, the banking angle of the road is 5.0°, and the mass of the car is 1400kg.

Let the the x-axis point horizontally toward the the center of curvature and y-axis point upward.

The Free-body diagram of the car in the given situation is shown in Figure 1.

Physics, Chapter 5, Problem 28P

Write the condition for equilibrium of forces in the x and y directions.

Fx=0 (I)

Fy=0 (II)

Apply the condition in equation (II) to the free-body diagram of the car.

Ncosθmgfsinθ=0 (III)

Here, N is the magnitude of normal force, θ is the angle of banking, m is the mass of the car, g is the acceleration due to gravity, and f is the magnitude of the frictional force.

Solve equation (III) for N.

N=fsinθ+mgcosθ (IV)

Apply the condition in equation (I) to the free-body diagram of the car.

Nsinθ+fcosθmv2r=0 (V)

Here, mv2/r represents the centripetal force.

Use equation (IV) in (V) and solve for f.

(fsinθ+mgcosθ)sinθ+fcosθmv2r=0(fsinθ+mg)(sinθcosθ)+fcosθ=mv2rf=(mv2/r)mg(sinθcosθ)(sinθ(sinθcosθ)+cosθ)=m(v2cosθrgsinθ) (VI)

Conclusion:

Substitute 32m/s for v, 5.0° for θ, 410m for r, 9.80m/s2 for g, and 1400kg for m in equation (VI) to find f.

f=(1400kg)((32m/s)2cos5.0°410m(9.80m/s2)sin5.0°)=2287N2300N

Therefore, the frictional force on the car is 2300N_.

(b)

To determine

The speed with which one must drive the car so that the force of friction is zero.

(b)

Expert Solution
Check Mark

Answer to Problem 28P

The speed with which one must drive the car so that the force of friction is zero is 19m/s_.

Explanation of Solution

Write the expression for the force of friction for the given track.

f=m(v2cosθrgsinθ)

The force of friction to be zero, the term f in the above equation has to be replaced by 0.

0=m(v2cosθrgsinθ) (VII)

Solve equation (VII) for v.

v2=rgsinθcosθv=rgtanθ (VIII)

Conclusion:

Substitute 410m for r, 9.80m/s2 for g, and 5.0° for θ in equation (VIII) to find v.

v=(410m)(9.80m/s2)(tan5.0°)=18.74m/s19m/s

Therefore, the speed with which one must drive the car so that the force of friction is zero is 19m/s_.

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Chapter 5 Solutions

Physics

Ch. 5.4 - Prob. 5.8PPCh. 5.4 - Prob. 5.4CPCh. 5.4 - Prob. 5.9PPCh. 5.4 - Prob. 5.10PPCh. 5.5 - Prob. 5.5CPCh. 5.5 - Prob. 5.11PPCh. 5.5 - Conceptual Practice Problem 5.12 Analysis of the...Ch. 5.6 - Prob. 5.6CPCh. 5.6 - Prob. 5.13PPCh. 5.7 - Prob. 5.14PPCh. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQCh. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Multiple-Choice Questions 1-4 and Problem...Ch. 5 - Questions 1–4: A satellite in orbit travels around...Ch. 5 - 3. What is the direction of the satellite’s...Ch. 5 - 4. What is the direction of the satellite’s...Ch. 5 - 5. An object moving in a circle at a constant...Ch. 5 - 6. A spider sits on a DVD that is rotating at a...Ch. 5 - 7. Two satellites are in orbit around Mars with...Ch. 5 - Questions 8-9: A boy swings in a tire swing....Ch. 5 - 9. When is the tension in the rope the...Ch. 5 - Questions 10–11 concern these three...Ch. 5 - 11. An object is in nonuniform circular motion...Ch. 5 - 12. An astronaut is out in space far from any...Ch. 5 - 1. A carnival swing is fixed on the end of an 8.0...Ch. 5 - 2. Convert these to radian measure: (a) 30.0°, (b)...Ch. 5 - 3. Find the average angular speed of the second...Ch. 5 - 4. An elevator cable winds on a drum of radius...Ch. 5 - 5. A wheel of radius 30 cm is rotating at a rate...Ch. 5 - 6. A soccer ball of diameter 31 cm rolls without...Ch. 5 - 7. A bicycle is moving at 9.0 m/s. What is the...Ch. 5 - 8. Dung beetles are renowned for building large...Ch. 5 - 9. In the construction of railroads, it is...Ch. 5 - Problems 10–12. Five flywheels are spinning as...Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - 13. Objects that are at rest relative to Earth’s...Ch. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - 21. A conical pendulum consists of a bob (mass...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - 25. A roller coaster car of mass 320 kg (including...Ch. 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 - 56. Find the tangential acceleration of a freely...Ch. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 60PCh. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 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. 81PCh. 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 - 94. Two blocks are connected by a light string...Ch. 5 - Prob. 95PCh. 5 - Prob. 96P
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