A 1 490-kg automobile has a wheel base (the distance between the axles) of 3.10 m. The automobile’s center of mass is on the centerline at a

Question

A 1 490-kg automobile has a wheel base (the distance between the axles) of 3.10 m. The automobile’s center of mass is on the centerline at a point 1.10 m behind the front axle. Find the force exerted by the ground on each wheel.

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Tryphena 1 day 2021-07-21T21:28:41+00:00 1 Answers 0 views 0

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    2021-07-21T21:30:39+00:00

    Answer:

    Force on each front wheel = 4711 N

    Force on each back wheel = 2591 N

    Explanation:

    Weight of car = 1490 Kg

    Distance of COG from front axle= 1.1 m

    Distance of COG from back axle = 3.1 – 1.1 = 2 m

    Vertical forces are balanced ,

    So, R1 + R2 = mg

    R1 + R2 = 1490× 9.8

    Thus; R1 + R2 = 14602 – – – eq1

    Where

    R1 is force on front wheel

    R2 is force on back wheel

    Now, we know that;

    Angular momentum about centre of gravity is zero.

    Therefore,

    R1 × 1.1 = R2 × 2

    R1 = (2/1.1)R2

    Put this into equation1, to get;

    (2/1.1)R2 + R2 = 14602

    R2(2.818) = 14602

    R2 = 14602/2.818

    R2 = 5182 N and R1 = (2/1.1)5182 = 9422 N

    Hence, force on each back wheel = R2/2 = 5182/2 = 2591 N

    Force on each front wheel = R1/2 = 9422/2 = 4711 N

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