How Do You Find the Center of Gravity of a Non-Uniform Plank?

In summary, the conversation discusses the calculation of the centre of gravity for a 4.00m long plank supported by three trestles. The vertical reactions at the ends and middle are given, and the use of an equation to calculate the centre of gravity is mentioned, though it may not be entirely accurate. The use of a moment of forces equation is also suggested as an alternative method.
  • #1
recoil33
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Solved, thank you.
 
Last edited:
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  • #2
Hi recoil33! :smile:
recoil33 said:
Three trestles support a 4.00m long plank, of non-uniform density, one at each end and one at the middle. These exert vertical reactions of 1.00 x 10^2N and 3.00 x 10^2N at the ends, and 4.00 x 10^2N at the middle. Calculate

A) The position of the centre of gravity.

Could i use this equation to calculate the centre of gravity?

R = (m1r1 + m2r2 + m3r3) / (m1 + m2 + m3)

Sort-of …

but you're not actually using masses, are you?

Technically, you should be using a moment of forces equation: the sum of the moments of the four forces on the beam (three reaction forces and the weight) has to be zero. :wink:
 

FAQ: How Do You Find the Center of Gravity of a Non-Uniform Plank?

What is the center of gravity?

The center of gravity, also known as the center of mass, is the point at which an object's weight is evenly distributed in all directions. It is the point where an object's weight can be considered to act.

Why is the center of gravity important?

The center of gravity is important because it affects an object's stability and balance. It is also a crucial factor in understanding the motion of objects and predicting their behavior.

How is the center of gravity calculated?

The center of gravity can be calculated by finding the weighted average of the individual masses and their distances from a reference point. This can be done through mathematical equations or by physically balancing the object on a pivot point.

What factors affect the center of gravity?

The location of an object's center of gravity is affected by its shape, size, and distribution of mass. Any changes in these factors can alter the position of the center of gravity.

How does the center of gravity differ from the center of mass?

The center of gravity and the center of mass are often used interchangeably, but they are not exactly the same. The center of mass refers to the point where an object's mass is evenly distributed, while the center of gravity takes into account the effects of gravity on the object's mass.

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