Find the coordinates x, y of the center of gravity of a mass of density f(x, y)
Question:
Find the coordinates x̅, y̅ of the center of gravity of a mass of density f(x, y) in the region R. Sketch R, show details.
f = x2 + y2, R: x2 + y2 ≤ α2, y ≥ 0
Step by Step Answer:
x fx y dx fx y d...View the full answer
Related Video
The Centre of gravity is a theoretical point in the body where the body’s total weight is thought to be concentrated. It is important to know the centre of gravity because it predicts the behaviour of a moving body when acted on by gravity. It is also useful in designing static structures such as buildings and bridges.In a uniform gravitational field, the centre of gravity is identical to the centre of mass. Yet, the two points do not always coincide. For the Moon, the centre of mass is very close to its geometric centre. However, its centre of gravity is slightly towards the Earth due to the stronger gravitational force on the Moon’s near side.
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