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A car weighs 1800 kg the …

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A car weighs 1800 kg the distance between its front and back axles is 1.8m Its centre of gravity is 1.05 behind the front Excel determine the force exerted by the level ground on Each front wheel and each back wheel
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Sia ? 5 years, 11 months ago

Weight of car = 1800 Kg
Distance of COG from front axle = 1.05 m 
Distance of COG from back axle = 1.8 - 1.05 = 0.75 m 
Vertical forces are balanced , 
So,At translational equilibrium:
R1 + R2 = mg 
R1 + R2 = 1800 {tex}\times{/tex} 9.8 = 17640

R1 and R2 are the forces exerted by the level ground on the front and back wheels respectively.
Angular momentum about centre of gravity is zero.
So, 
R1(1.05) = R2(1.8 - 1.05)
{tex}R _ { 1 } \times 1.05 = R _ { 2} \times 0.75{/tex}
{tex}\frac { R _ { 1 } } { R _ { 2 } } = \frac { 0.75 } { 1.05 } = \frac { 5 } { 7 }{/tex}
{tex}\frac { R _ { 1 } } { R _ { 2 } } = \frac { 7 } { 5 }{/tex}
R1 = 1.4 R2 …..(ii)
Solving equations (i) and (ii), we get:
1.4 R2 + R2 = 17640
{tex}R _ { 2 } = \frac { 17640 } { 2.4 } = 7350 \mathrm { N }{/tex}
{tex}\therefore{/tex} R1 = 17640 - 7350 = 10290 N
Therefore, the force exerted on each front wheel {tex}=\frac { R_1 } { 2 }= \frac { 7350 } { 2 } = 3675 N{/tex}, and
The force exerted on each back wheel {tex}= \frac { R_2 } { 2 }=\frac { 10290 } { 2 } = 5145 N{/tex}

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