Introduction to Statics

ENGR 122

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Statics is the branch of mechanics concerned with the analysis of loads (forces, torque/moment) on physical systems in static equilibrium . . . when in static equilibrium, a system is either at rest, or its center of mass moves at constant velocity. Wikipedia.org

old railroad bridge (Leonard G. / Wikipedia)

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Units of MeasureMost units of measure can be broken down into the basic units of length (L), mass (M) and time (t).

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Units of Measure

L = length M = mass t=time

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Three Characteristics of a Force

x

y denotes a vector 1. Magnitude (F)• how hard you are pushing or pulling• graphically represented by the length of

the arrow

2. Direction ()• usually defined by an angle measured

relative to a coordinate system

3. Point of Application

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Components of a Force

x

y

Forces can be split into components that align with a coordinate system.The force is the vector sum of the components.

defined relative to the +x axis in this case

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ResultantsHow can we find the net effect of two or more forces that act on a body?

Geometric Solution: If all applied forces are arranged head to tail, a vector drawn from the tail of the first vector to the head of the last vector represents the resultant of all the forces.

Generally . . .

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Class Problem: Two ants are hitched to a beetle and pull with the forces shown:

a. Find the x and y components of the force exerted by ant 1.b. Find the x and y components of the force exerted by ant 2.c. Find the x component of the resultant force of the ants.d. Find the y component of the resultant force of the ants.e. Find the resultant force of the ants.f. What angle does the resultant force make with the x-axis?