Finding the load mass to shift a car's center of mass to the midpoint between axles

[will_1688]

Homework Statement

the centre of mass for a 2D car is 1.125m towards the rear wheels from the front wheels, there is then 1.675m to the rear wheels. If a load with a centre of mass 0.4m from the rear wheels towards the back of the car is added how heavy does this load need to be to move the centre of mass to the middle of the front and rear wheels i.e 1.4m backwards from the front wheels.

Can someone please give me an idea of how to do this question

 

[ZharAngel]

Use turning moments of force, take moments about the front wheels.

 

[ZharAngel]

Front wheels - A
Rear wheels - B
Centre of Gravity - X
Load - Y

Taking moments about A:

Initially:

$$F_B = \frac{45}{112} F_X$$

Add the load:

$$F_X = 2F_B + \frac{12}{7} F_Y$$

$$F_X = \frac{45}{56} F_X + \frac{12}{7} F_Y$$

$$F_Y = \frac{11}{96} F_X$$

 

[RANDHIR SINGH]

please see the solution on the attached doc file

 

[will_1688]

thanks a lot that is perfect i understand it now