Chapter 2. CONCENTRATED FORCES AND THEIR EFFECTS

a.

Representing Interactions Between Bodies

Objective: Define interaction. Recognize attributes of interactions that can be represented by concentrated forces and the implications of Newton's 3rd law of motion.

Objective: Identify attributes of forces acting between frictionless contacting bodies.

Objective: Identify attributes of forces acting between a body and an attached cable.

Objective: Identify attributes of forces acting between a body and an attached spring.

Objective: Recognize that all the interactions between bodies that are in contact or attached to one another can be represented as vectors. Be able to draw force vectors on bodies to reflect their attributes.

b.

Effects of a Force

Objective: Distinguish between various motions produced by forces on bodies

Objective: Recognize qualitatively that the translational effects of a force depend on force magnitude, direction and sense, but do not depend on the point of application of the force

Objective: Recognize qualitatively that the rotational effects of a force depend on force magnitude, direction and sense, and on the line of action of the force

Objective: Define the tendency of the force to create rotation as the moment, and determine the moment of a force by identifying the perpendicular distance from the axis of rotation to the line of action of the force in 2D situations

Objective: Determine the moment of a force in 3D situations that can be modeled in 2D

c.

Effects of Multiple Forces

Objective: Recognize that translational effects of forces combine as in vector addition

Objective: Determine the components of force vectors

Objective: Determine the sum of concurrent forces by summing their components.

Objective: Recognize that rotational effects of forces combine through the addition of moments.

Objective: Add moments due to known forces when their moment arms are given.

Objective: Find the force that balances the moment created by several other forces when moment arms are given.

Objective: Determine the moment of a force as a sum of the moments of its vertical and horizontal components.

Objective: Determine the moment of a force as a sum of the moments of its components parallel and perpendicular to the line between the moment center and the point of application of the force.

Objective: Judiciously choose method of calculating the moment of a force

Objective: Forces translated into a moment

Objective: Shear and bending moment in beams

d.

Introduction to Free Body Diagrams

Objective: Explain the purpose and philosophy of drawing FBDs

Objective: Demonstrate the procedure of drawing FBDs

Objective: Identify the factors which affect the choice of subsystem, and choose an appropriate subsystem in simple cases

e.

Equilibrium Under 2D Concentrated Forces

Objective: Recognize the equilibrium conditions under which bodies have no tendency to translate or rotate

Objective: Impose the conditions of equilibrium when the equilibrium of moments on the body is trivially satisfied in systems with collinear forces for which the net moment about any point on the line is zero

Objective: Impose the conditions of equilibrium when the equilibrium of moments on the body is trivially satisfied in systems with concurrent forces for which the net moment about a point of intersection is zero

Objective: Impose the conditions of equilibrium when both force and moment equilibrium need to be explicitly satisfied in systems where all forces act in one direction

Objective: Impose the conditions of equilibrium when both force and moment equilibrium need to be explicitly satisfied in systems with general coplanar forces