Explanation Given information: The banked angle θ is 6 ° . The speed of the car ( v ) is 100 mi/h. The rated speed ( v R ) of the car is 60 mi/h. The frictional force ( F 0 ) at rated speed is 0. The side force is equal to 10% of passenger’s weights (0.1 W ). Calculation: Write the general equation mass ( m ). m = W g Here, m is the mass and g is the acceleration due to gravity. Write the general equation of acceleration ( a ) in curved path. a = v 2 ρ Here, v is the speed and ρ is the radius of curved path. Consider the car moves at rated speed. Find the radius ( ρ ) of the curve track using the equation: v R 2 = g p tan θ ρ = v R 2 g tan θ Substitute 60 mi/h for v R , 32.2 ft/s 2 for g , and 6 ° for θ . ρ = ( 60 mi h × 5 , 280 ft 1 mi × 1 h 3 , 600 s ) 2 ( 32.2 ) ( tan 6 ° ) = 2 , 288 ft Consider the x -axis is parallel to the floor of car. Sketch the free body diagram and kinetic diagram of the passenger as shown in Figure (1). Refer Figure (1): Find the magnitude of the side force felt by a passenger of weight W in a standard car with no tilt. Apply Newton’s law of equation along x -axis. Σ F x = m a x F s + W sin ( θ + ϕ ) = m a n cos ( θ + ϕ ) F s = m a n cos ( θ + ϕ ) − W sin ( θ + ϕ ) Substitute W g for m and v 2 ρ for a n . F s = ( W g ) ( v 2 ρ ) cos ( θ + ϕ ) − W sin ( θ + ϕ ) = W ( v 2 g ρ ) cos ( θ + ϕ ) − W sin ( θ + ϕ ) (1) Substitute 0.1 W for F s 100 mi/h for v , 32

12th Edition

ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 12.1, Problem 12.54P

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Find the required angle of tilt ϕ if passengers are to feel side forces equal to 10% of their weights.

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Chapter 12.1, Problem 12.53P

Chapter 12.1, Problem 12.55P

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Find the required angle of tilt ϕ if passengers are to feel side forces equal to 10% of their weights.

Solution Summary: The author calculates the required angle of tilt varphi for passengers to feel side forces equal to 10% of their weights.

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Find the required angle of tilt ϕ if passengers are to feel side forces equal to 10% of their weights.

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