Lecture 1-5

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

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Engineering Mechanics: Statics Mechanics is the branch of the physical sciences d ith th t t f t ti f b di concerned with the state of rest or motion of bodies subjected to forces.

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Engineering Mechanics • Mechanics Mechanics – Rigid-body mechanics • Dynamics – the study of objects in motion Dynamics – the study of objects in motion – F = ma Statics - the study of objects in equilibrium – Also F = ma, but a = 0 – Deformable-body mechanics – Fluid mechanics
Newton’s Laws 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 acting on an object is not zero, the sum of the forces is equal to the product of the mass and its acceleration. F = ma 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. For every action, there is an equal and opposite reaction

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S l V t Scalar vs. Vector Physical quantity described by a real number Magnitude and direction (magnitude , but no direction) Ex. mass, speed Ex. weight, velocity & F F & F (magnitude of a vector ) F & (textbook may use bold F )
Vector Addition Head to tail or Triangle Rule Head-to-tail or U + V = V + U

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Product of Scalar and Vector

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Vector Vector Subtraction
Unit Vectors

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Vector Components Sum of two vectors can be found by simply summing the components.
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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Th t l l i t d b t bl hi h t d f th t f 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
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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