How Does Adding a Steamer Trunk Affect the Plane's Center of Gravity?

In summary, the partial loading of a plane with a 300 pound steamer trunk in the rear cargo hold, 250 inches behind the center of gravity, shifts the center of gravity 0.65 inches towards the rear.
  • #1
mathguy2
16
0

Homework Statement


A partially loaded plane weighs 115,000 pounds. A famous actor's steamer trunk, weighing 300 pounds, is put into the rear cargo hold 250 inches behind the center of gravity. How much does this extra hold shift the center of gravity.

Homework Equations


W1 = W x (L2 / L)

W2 = W x (L1 / L)

W = 115300
W1 = 115000
W2 = 300
L = 250

The Attempt at a Solution


I did this:
W2 = W x (L1 / L)
so...
300 = 115300 x (L1 / 250)
so...
300 = 461.2L1
divide both sides by 461.2

L1 = .6504770165

The center of gravity of the plane shifts .6504770165 inches toward the rear. Your input is encouraged.
 
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  • #2
Looks good, but get rid of some of those figures after the decimal point, maybe just say 0.65 inches
 
  • #3
Thank you for the input. Would you mind taking a look at the more advanced center of gravity problem I posted. It's really frustrating me at the moment.
 

Related to How Does Adding a Steamer Trunk Affect the Plane's Center of Gravity?

1. What is the center of gravity problem?

The center of gravity problem, also known as the centroid problem, is a mathematical problem that deals with finding the center of mass or balance of a physical object or system. It is often used in fields such as engineering, physics, and architecture.

2. How is the center of gravity calculated?

The center of gravity is calculated by taking into account the weight and distribution of all the individual components of an object or system. It is usually found by taking the average of all the individual masses and their distances from a reference point.

3. Why is the center of gravity important?

The center of gravity is important because it helps determine the stability and balance of an object or system. It is also used in designing structures and vehicles, as well as in predicting their behavior under different conditions.

4. Can the center of gravity be outside of an object?

Yes, the center of gravity can be outside of an object. This usually occurs when the weight distribution of the object is uneven and causes the center of mass to shift away from the physical object.

5. What are some real-world applications of the center of gravity problem?

The center of gravity problem has many practical applications, such as in the design of airplanes and other vehicles, the construction of buildings and bridges, and the analysis of sports equipment and body positioning in sports. It is also used in determining the stability of structures during earthquakes and in understanding the movement of celestial bodies in space.

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