Finding the Center of Mass of a Triangle

In summary, the problem involves a thin uniform wire bent to form a triangle ABC with two equal sides of length 5cm and a third side of length 6cm made from wire with twice the density. The question asks for the distance of the center of mass from point A. Using the equations for center of mass and uniform density, the x coordinate of the center of mass can be calculated as 12λ*lenght of rod BC/2, but the y coordinate requires further calculations and mathematical reasoning.
  • #1
Acemave
2
0

Homework Statement


a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ?

Homework Equations


x centre of mass = m1R1+m2r2/ sum of masses(where r= centre of mass of particle in sys.)λ=m/l ( where m= mass of object , l=length ) uniform density formula

The Attempt at a Solution


i was able to calculate the X c.o.m which is = 12λ*lenght of rod BC/2
but was unable to calculate its y coordinate ?
 
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  • #2
Acemave said:

Homework Statement


a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ?

Homework Equations


x centre of mass = m1R1+m2r2/ sum of masses(where r= centre of mass of particle in sys.)λ=m/l ( where m= mass of object , l=length ) uniform density formula

The Attempt at a Solution


i was able to calculate the X c.o.m which is = 12λ*lenght of rod BC/2
but was unable to calculate its y coordinate ?
I don't think that's the solution this problem is looking for.

Once the wire is formed into the triangle, you are supposed to calculate the (x,y) coordinates of the center of mass from point A.
 
  • #3
Make a drawing. Mark on it the centre of mass of each rod. One of the co-ordinates (say x) is trivial by symmetry. The other (say distance y from point A) needs some maths.

Acemave said:
but was unable to calculate its y coordinate ?

Show your working (forum rules).
 

What is the center of mass of a triangle?

The center of mass of a triangle is the point at which the entire mass of the triangle is evenly distributed. It is also known as the centroid, and it is the intersection point of the three medians of the triangle.

How do you find the center of mass of a triangle?

To find the center of mass of a triangle, you can use the formula (x,y) = ((x1+x2+x3)/3, (y1+y2+y3)/3), where x1, x2, and x3 are the x-coordinates of the three vertices of the triangle, and y1, y2, and y3 are the y-coordinates of the three vertices. You can also use the geometric method of drawing the medians and finding their intersection point.

Why is finding the center of mass of a triangle important?

Finding the center of mass of a triangle is important in physics and engineering, as it helps in determining the balance and stability of a structure. It is also used in calculating the moments of inertia for rotation and in finding the center of gravity of an object.

Can the center of mass of a triangle be outside of the triangle?

No, the center of mass of a triangle will always be inside the triangle. This is because the medians of a triangle will always intersect within the triangle, and the center of mass is the intersection point of the medians.

Does the shape of a triangle affect the location of its center of mass?

Yes, the location of the center of mass of a triangle is affected by its shape. For example, an equilateral triangle will have its center of mass at the intersection of the medians, while an isosceles triangle will have its center of mass closer to the longer side.

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