Calculating Centre of Mass for 2D Car with Added Load: Homework Help

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Discussion Overview

The discussion revolves around calculating the center of mass for a 2D car when an additional load is introduced. Participants explore the implications of this load on the overall center of mass, specifically aiming to determine the weight required to shift the center of mass to a specified position between the front and rear wheels.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents a homework problem involving the calculation of the center of mass for a car with an added load.
  • Another participant suggests using turning moments of force and proposes taking moments about the front wheels to analyze the problem.
  • A detailed mathematical approach is provided, involving equations for forces at the front and rear wheels and the load, with specific ratios and relationships expressed.
  • A document is referenced for a solution, indicating an additional resource for participants.
  • One participant expresses gratitude and indicates understanding after reviewing the provided solution.

Areas of Agreement / Disagreement

There appears to be a progression towards understanding the problem, with one participant confirming comprehension after receiving assistance. However, the discussion does not explicitly resolve any disagreements or alternative approaches.

Contextual Notes

Limitations include the lack of detailed assumptions regarding the forces involved and the specific conditions under which the calculations are made. The mathematical steps leading to the final solution are not fully elaborated in the thread.

Who May Find This Useful

Students or individuals interested in mechanics, particularly in the context of calculating center of mass in physics problems, may find this discussion beneficial.

will_1688
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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
 
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Use turning moments of force, take moments about the front wheels.
 
Last edited:
Front wheels - A
Rear wheels - B
Centre of Gravity - X
Load - Y

Taking moments about A:

Initially:

[tex] F_B = \frac{45}{112} F_X[/tex]

Add the load:

[tex] F_X = 2F_B + \frac{12}{7} F_Y[/tex]

[tex] F_X = \frac{45}{56} F_X + \frac{12}{7} F_Y[/tex]

[tex] F_Y = \frac{11}{96} F_X[/tex]
 
please see the solution on the attached doc file
 

Attachments

thanks a lot that is perfect i understand it now
 

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