# Calculating Center of Gravity: Bethany, Serendipity & Cardinal Glick

• joel amos
In summary, Bethany and Serendipity are each exerting a force of 350 N on the 1.25 m arms of a wheelbarrow while carrying Cardinal Glick, who weighs 1,050 N, in the bucket. The center of gravity of the bucket and the Cardinal is where the downward force is applied to the arm, which is located at the end of the 1.25 m arms. This can be visualized by looking at pictures of a wheelbarrow and understanding that the arm acts as a lever.
joel amos

## Homework Statement

If Bethany and Serendipity each exert a force of 350 N on each arm of a wheelbarrow with 1.25 m arms and carry Cardinal Glick in the bucket, who has a weight of 1,050 N, where is the center of gravity of the bucket and the Cardinal with respect to the wheel?

Pointers would be nice, as I'm not sure how to go about this. All help is welcome.

Last edited:
The wheelbarrow's arm is a lever.

Yes, I realize this bit. The part I don't get is how to find the center of gravity, especially since the bucket was never assigned a length.

The length is given - this is the arm's length. Google for "wheelbarrow" and look at pictures if that is not clear. The center of gravity of the bucket + load is where the downward force applies to the arm.

To calculate the center of gravity in this scenario, we can use the formula:

CG = (ΣFx * dx + ΣFy * dy) / ΣF

Where CG is the center of gravity, ΣFx and ΣFy are the sum of the forces in the x and y directions respectively, dx and dy are the distances from the center of the wheel to the point where the force is applied, and ΣF is the sum of all the forces.

In this case, we have two forces acting in the x direction (from Bethany and Serendipity) and one force acting in the y direction (from Cardinal Glick). The distances for the x direction will be the length of the arms (1.25 m) and for the y direction, it will be the distance from the center of the wheel to the bucket (let's say 0.5 m for simplicity).

So, our equation becomes:

CG = ((350 N * 1.25 m) + (350 N * 1.25 m) + (1050 N * 0.5 m)) / (350 N + 350 N + 1050 N)

Simplifying, we get:

CG = (437.5 N * m + 525 N * m) / 1750 N

CG = 962.5 N * m / 1750 N

CG = 0.55 m

Therefore, the center of gravity of the bucket and Cardinal Glick with respect to the wheel is 0.55 m from the center of the wheel.

Pointers:

- When calculating the center of gravity, it is important to consider both the magnitude and direction of the forces.
- The distance used in the equation should be the perpendicular distance from the center of the wheel to the point where the force is applied.
- If there are multiple forces acting in the same direction, we can simply add them together to get the sum of the forces in that direction.
- In this scenario, we have ignored the weight of the wheelbarrow itself, assuming it is negligible compared to the other forces.
- Practice with different scenarios and forces to get a better understanding of how to calculate the center of gravity.

## 1. What is the center of gravity?

The center of gravity is the point at which the weight of an object is evenly distributed and the object will balance perfectly. It is also known as the center of mass.

## 2. How is the center of gravity calculated?

The center of gravity can be calculated by finding the product of the mass of each part of the object and its distance from a reference point, and then dividing the sum of these products by the total mass of the object.

## 3. How do you find the center of gravity for irregularly shaped objects?

For irregularly shaped objects, the center of gravity can be found by suspending the object from different points and marking the plumb line. The point where all the plumb lines intersect is the center of gravity.

## 4. How does the center of gravity affect stability?

The lower the center of gravity, the more stable an object is. This is because the weight of the object is more evenly distributed and there is less chance of it toppling over.

## 5. How is the center of gravity important in physics and engineering?

The center of gravity is important in physics and engineering because it helps determine the stability and balance of objects. It is also a crucial factor in designing structures and vehicles to ensure they are safe and functional.

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