The standard test to determine the maximum lateral acceleration of a car is to drive it around a 200-ft-diameter circle painted on a level a

Question

The standard test to determine the maximum lateral acceleration of a car is to drive it around a 200-ft-diameter circle painted on a level asphalt surface. The driver slowly increases the vehicle speed until he is no longer able to keep both wheel pairs straddling the line. A 3000 lb car is traveling at 25 mi/hr when the driver applies the brakes, and the car continues to move along the circular path. What is the maximum deceleration possible if the tires are limited to a total horizontal friction force of 2400 lb?

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Mít Mít 3 years 2021-08-18T20:48:37+00:00 1 Answers 51 views 0

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  1. Nho
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    2021-08-18T20:50:13+00:00
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    Answer:

    a=25.736\ lb.ft.s^{-2} is the maximum deceleration from this top speed keeping-up with the grip of friction.

    Explanation:

    Given:

    diameter of the track, d=200\ ft

    mass of the car, m=3000\ lb

    speed of the car, v=25\ mi.hr^{-1}=36.6667\ ft.s^{-1}

    maximum horizontal frictional force between the surfaces, f=2400\times 32.17=77208\ lb.ft.s^{-2}

    Now the maximum speed attained by the car according to the frictional force:

    f=m.\frac{v^2}{r} also f=m.a

    where:

    • a = acceleration; \frac{v^2}{r} =a
    • r=\frac{d}{2} =100\ ft

    77208=3000\times \frac{v^2}{r}

    a=25.736\ lb.ft.s^{-2} is the maximum deceleration from this top speed keeping-up with the grip of friction.

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