MCE222_LN_Sec_13-4 - EQUATIONS OF MOTION: RECTANGULAR...

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EQUATIONS OF MOTION: RECTANGULAR COORDINATES (Section 13.4) Today’s Objectives: Students will be able to apply Newton’s second law to determine forces and accelerations for particles in rectilinear motion.
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APPLICATIONS If a man is pushing a 100 lb crate, how large a force F must he exert to start moving the crate? What would you have to know before you could calculate the answer?
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APPLICATIONS (continued) Objects that move in any fluid have a drag force acting on them. This drag force is a function of velocity. If the ship has an initial velocity v o and the magnitude of the opposing drag force at any instant is half the velocity, how long it would take for the ship to come to a stop if its engines stop?
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EQUATION OF MOTION The equation of motion, F = m a, is best used when the problem requires finding forces (especially forces perpendicular to the path), accelerations, velocities or mass. Remember, unbalanced forces cause acceleration! Three scalar equations can be written from this vector equation . The equation of motion, being a vector equation, may be expressed in terms of its three components in the Cartesian (rectangular) coordinate system as F = m a or F x i + F y j + F z k = m(a x i + a y j + a z k ) or, as scalar equations, F x = ma x , F y = ma y , and F z = ma z .
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PROCEDURE FOR ANALYSIS Free Body Diagram Establish your coordinate system and draw the particle’s free body diagram showing only external forces . These external forces usually include the weight, normal forces, friction forces, and applied forces. Show the ‘m a ’ vector
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MCE222_LN_Sec_13-4 - EQUATIONS OF MOTION: RECTANGULAR...

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