## An automobile with a mass of 961.000 kg has 3.27 m between the front and rear axles. Its center of gravity is located 0.615 m behind the fro

Question

An automobile with a mass of 961.000 kg has 3.27 m between the front and rear axles. Its center of gravity is located 0.615 m behind the front axle. With the automobile on level ground, determine the magnitude of the force from the ground on (a) each front wheel (assuming equal forces on the front wheels) and (b) each rear wheel (assuming equal forces on the rear wheels).

in progress 0
1 year 2021-08-18T18:08:13+00:00 1 Answers 0 views 0

a)  3830 N

b) 887 N

Explanation:

WOW, you know the mass to within ± ½gram and position of CG to ± 0.5 mm! that’s some impressive measuring!!!

Let FR be the total rear wheels force

Let FF be the total front wheels force

Sum moments about the front wheels to zero

961(9.81)[0.615] – FR[3.27] = 0

FR = 1,773.045

so each rear tire supports

Fr = 1,773.045/2 = 886.5225 N

Fr ≈ 887 N when rounded to three significant digits

Sum moments about the rear wheels to zero

961(9.81)[3.27 – 0.615] – FF[3.27] = 0

FF = 7,654.365

so each front tire supports

Ff = 7,654.365/2 = 3,827.1825

Ff = 3830 N (to 3 s.d.)

verify by summing vertical forces to zero

7,654.365 + 1,773.045 – 961(9.81) ?=? 0

0 = 0   checks out