Introduction Mechanics: deals with the responses of the bodies to the action of forces. Objectives: To give students an introduction to engineering mechanics with an emphasis on engineering problem solving Question: What are the mechanical issues involved in the design of a bridge crossing a river?

Fundamental quantities of Mechanics -- : the geometry region in which the physical events of interest in mechanics occur. : the interval between two events. : a quantitative measure of inertia. : the action of one body upon another body.

Principles --- Newton’s laws of Motion Law 1: - foundation for the study of statics Law 2: - foundation for the study of dynamics Law 3: - foundation of understanding the concept of a force In the absence of external forces, a particle originally at rest or moving with a constant velocity will remain at rest or continue to move with a constant velocity along a straight line. If an external force acts on a particle, the particle will be accelerated in the direction of the force and the magnitude of the acceleration will be directly proportional to the force and inversely proportional to the mass of the particle. For every action there is an equal and opposite reaction. The forces of action and reaction between bodies are equal in magnitude, opposite in direction, and collinear.

Vectors Mechanical Quantities: scalars and vectors Vectors: Notation: F or F Representations: is an unit vector

Vectors Addition: parallelogram law Dot product: Law of Sine: Law of Cosine:

Cross Product of Vectors Where, is the unit vector in a direction perpendicular to the plane containing vectors A and B. A B 

Particle Equilibrium Forces: magnitude; direction; point of application Effects: external effects: internal effects: Equilibrium of a particle:

Example 1: In a Cartesian coordinate system illustrated as follows, point A is located at (5, 10, 2). A force F with a magnitude of 10 N is applied at a body located at the origin (O), along the direction of vector OA. Determine the x, y, and z scalar components of the force. x y z o A F

Equilibrium of a System of Particles Key step: selection of your “free body” 1) Given W 1, W 2, r 1, r 2,  what are the reaction forces coming from the supporting wedge? 2) What is the force between two cylinders?

Example 2: The 900-lb platform illustrated in the following figure is supported by a light cable and pulley system. Find the tension inside the cable over pulley A and the tension inside the cable over pulley B. Assume the mass center location so that the platform remains horizontal.

Test 1)Draw the free-body diagram of cylinder 1 2)Draw the free-body diagram of two cylinders as one body Assume all surfaces are smooth.