Lecture 14

# Lecture 14 - Lecture 14 CENTER OF GRAVITY CENTER OF MASS...

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Statics: Lecture Notes for Sections 9.1-9.2 1 Lecture 14 CENTER OF GRAVITY CENTER OF MASS CENTROID FOR A BODY Section 9.1-9.2 Ehab Zalok Today’s Objective : Students will: a) Understand the concepts of center of gravity, center of mass, and centroid. a) b) Be able to determine the location of these points for a system of particles or a body.

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Statics: Lecture Notes for Sections 9.1-9.2 2 APPLICATIONS To design the structure for supporting a water tank, we will need to know the weights of the tank and water, as well as the locations where the resultant forces representing these distributed loads are acting. 3 How can we determine these weights and their locations? APPLICATIONS (continued) One concern about a sport utility vehicle (SUVs) is that it might tip over while taking a sharp turn. 4 One of the important factors in determining its stability is the SUV’s center of mass . Should it be higher or lower for making a SUV more stable? How do you determine its location?
Statics: Lecture Notes for Sections 9.1-9.2 3 CONCEPT OF CG & CM The center of gravity (G) is a point which locates the resultant weight of a system of particles or body 3m 4N 1m AB particles or body. From the definition of a resultant force, the sum of moments due to individual particle weight about any point is the same as the moment due to the resultant weight located at G. For the figure above, try taking moments about A and B. 1 N 3 N G 5 Also, note that the sum of moments due to the individual particle’s weights about point G is equal to zero. Similarly, the center of mass is a point which locates the resultant mass of a system of particles or body. Generally, its location is the same as that of G. CONCEPT OF CENTROID The centroid coincides with the center of The centroid C is a point which defines the geometric center of an object. The centroid coincides with the center of mass or the center of gravity only if the material of the body is homogenous (density or specific weight is constant throughout the body).

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Lecture 14 - Lecture 14 CENTER OF GRAVITY CENTER OF MASS...

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