Lecture 1-5

Lecture 1-5 - Engineering Mechanics: Statics Engineering...

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Engineering Mechanics: Statics •M e c h a n i c s i s t h e b r a n c h o f t h e p h y s i c a l s c i e n c e s concerned with the state of rest or motion of bodies subjected to forces.
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Engineering Mechanics • Mechanics Mechanics –R ig id-body mechan ics Dynamics – the study of objects in motion • Dynamics – the study of objects in motion –F = ma •S ta t -the s tudy o f ob jec ts in equ i l ib r ium –A lso F = , bu t a = 0 –Deformab le-body mechan – Fluid mechanics
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Newton’ sLaws Newton s Laws 1 st Law – If an object is in motion, it will remain in motion. If an object is at rest, it will remain at rest, unless a force acts upon it. – When the sum of forces acting on an object is zero, the object will remain at rest if initially at rest. 2 nd Law –When the sum of forces act ing on an ob ject is not zero, the sum of the forces is equal to the product of the mass and its acceleration. –F = m a 3 rd Law – The forces exerted by two objects on each – The forces exerted by two objects on each other are equal in magnitude and opposite in direction. o r e v e r y a c t i o n , t h e r e i s a n e q u a l a n d o p p o s i t e r e a c t i o n
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Scalar vs. Vector Physical quantity described by a real numbe Magnitude and direction by a real number (magnitude , but no direction) Ex. mass, speed Ex. weight, velocity & F F & F (magnitude of a vector ) F & (textbook may use bold F )
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Vector Addition Vector Addition Head to tail or Triangle Rule Head-to-tail or U + V = V + U
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Vector Addition Vector Addition Parallelogram Rule
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Product of Scalar and Vecto Product of Scalar and Vector
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Vector Vector Subtraction
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Unit Vectors
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Vector Components Sum of two vectors can be found by simply summing the components.
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A man exerts a 60-lb force F to push a crate onto a truck. (a) Express F in terms of components using the coordinate system shown. (b) The weight of the crate is 100-lb. Determine the magnitude of the sum of the forces exerted by the man and the crate’s weight.
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The steel column is supported by two cables which extend from the top of the column to the ground and lie in the same plane. The tensions in cables A and B are 13 kips and 10 kips, respectively. What is the magnitude and direction of the resultant force exerted on the top of the column by the cables? 50 o 60 o A B
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Position Position Vector A position vector can be formed between two physical locations in space. The magnitude of the magnitude of the position vector is the distance between the two points (length).
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A surveyor finds that the length of the line OA is 1500 m and the length of the line OB is 2000 m.
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Lecture 1-5 - Engineering Mechanics: Statics Engineering...

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