Calculating Center of Gravity: Bethany, Serendipity & Cardinal Glick

[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.

 

[voko]

The wheelbarrow's arm is a lever.

 

[joel amos]

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.

 

[voko]

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.

 

[Nickie]

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.