Emily has a master's degree in engineering and currently teaches middle and high school science.
Understand the meaning of the center of gravity (CG) and its effect on the stability of an object. Learn how to calculate the CG of different systems of objects with a series of examples.
Center of Gravity Defined
Have you ever heard someone say that one of the advantages of being short and stocky is that you're less likely to get knocked over? They might have even mentioned that it's because the short and stocky person has a lower center of gravity. The center of gravity (CG) of an object is the point at which weight is evenly dispersed and all sides are in balance. A human's center of gravity can change as he takes on different positions, but in many other objects, it's a fixed location.
Follow me through a quick experiment. You'll need the following:
A #2 pencil
A fine edge like a ruler or a credit card
A permanent marker
A ruler (if you don't have one, you may be able to eyeball it)
Step 1: Attempt to balance the pencil on the edge you have selected.
Balancing the pencil may take some trial and error. The point at which the pencil balances may not be where you first thought. If it begins to tip in one direction, move the pencil back slowly in the opposite direction until it will stay there on its own.
Step 2: Once the pencil is balanced, mark the location of the balancing point with a permanent marker.
Step 3: Measure the distance between the ends of the pencil and the balancing point you have marked. Are the two lengths equal? On my pencil, the length from the eraser to the balancing point was actually 1.25 inches less than the length from the pencil tip to the balancing point. Why would this be the case?
In our experiment, the balancing point was another word for the center of gravity of this pencil. In other words, if we cut the pencil in two at the mark we made in the experiment, the two parts would be equal in weight. However, they are not equal in length. As you may have already figured out, the metal piece that houses the eraser contributes more to the weight of the pencil, so the CG is closer to that side of the pencil.
Keeping Up with that Center
The center of gravity is an important concept in determining the stability of a structure. It's the reason why a good homeowner will keep the top branches of his trees trimmed. It's also the reason why a pick-up truck might not be the best vehicle choice for a first time driver. Stability is maximized in objects with a lower center of gravity and a wide base. The taller and more top-heavy an object, the more likely it is to tip over when it is tilted by a force. This figure demonstrates a bus driving on two different grades; the second one is steep enough to cause the center of gravity to fall outside of the base of the vehicle, which will cause it to topple over.
Center of Gravity Equation
The center of gravity of an object is calculated by taking the sum of its moments divided by the overall weight of the object. The moment is the product of the weight and its location as measured from a set point called the origin.
One Dimensional Example
To make more sense of our CG equation, let's see it applied in a simple one-dimensional example that I like to call the Confused Weightlifter.
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Jack goes to the gym and loads a bar for his workout. The bar is 60 inches long, with a weight of 45 pounds. He picks out a 35 pound weight to load onto the left side of the bar but accidentally grabs a 25 pound weight for the right side of the bar. Before he realizes his mistake, he has already lifted the bar over his head with one hand. Where does Jack have to hold his hand to prevent the bar from tipping?
You're going to have to find the moment of both weights and the barbell itself. Divide by the total mass of all three components.
Two Dimensional Example
Now that we are more comfortable with the concept of center of gravity, we can attempt a two-dimensional problem.
Finley is delivering a tray of drinks to a group of thirsty happy hour customers at her restaurant, but she only has one free hand. In her rush, she didn't arrange the drinks in the most convenient way. Find the best location underneath the tray for her to position her hand to make sure the drinks do not tip over. Assume the tray and the drinks are one pound each.
To solve this, Finley should hold the tray slightly to the left and downward from the center (blue star). More simply, split up the problem. Solve for the x-coordinate of the center of gravity first, then solve for the y-coordinate.
Note: In this solution, the moments of each object were calculated moving clockwise from the y-axis. The moment of the tray itself is zero because it is centered at the origin.
In this lesson, we learned that the center of gravity (GC) is the point at which the weight of an object is evenly dispersed and all sides are in balance. We saw how center of gravity is an important concept in many situations, including sports and vehicle safety. The center of gravity can be calculated if information has been provided about an object's weight and how that weight is positioned. You should now have enough information to practice calculating CG in the quiz section of this lesson.
Center of Gravity Definition & Equation
Center of gravity: The point of an object at which the weight is evenly dispersed and all sides are in balance.
Center of gravity equation: Take the sum of an object's moments and divide by the overall weight of the object.
Moment: Product of the weight and its location as measured from a set point called the origin.
As you complete the lesson, you should be able to:
Define the center of gravity
Explain the real-world importance of the center of gravity
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