# forces

Forces

To study the effect of forces acting on particles.

2.1 Equilibrium of a Particle

2.2 Free Body Diagram

2.3 Force Vectors

2.4 Forces in a Plane

2.5 Forces in Space

Expected Outcomes

• Understand the condition for a particle to be in static

equilibrium

• Able to construct free body diagrams

• Able to solve for the forces acting on a static particle

2.1

Equilibrium

of a Particle

www.classical.com/features

2.1.1 Condition for the

Equilibrium of a Particle

• Particle is at equilibrium if it is

a) At rest

b) Moving at constant a constant velocity

2.1.1 Condition for the Equilibrium

of a Particle

(a) Equilibrium at rest

• Newton’s first law of motion

∑F = 0

where ∑F is the vector sum of all the forces acting on the particle

Even Univ.

Graduates

(a) Equilibrium at rest

• Newton’s Law of

Motion

• 1st law – a particle

originally at rest, or

moving in a straight

line with constant

velocity, tends to

remain in its state

provided the particle

is not subjected to an

unbalanced force.

http://www.jameslogancourier.org/index.php?blogid=1&archive=2006-3-21

2.1.1 Condition for the

Equilibrium of a Particle

(b) Equilibrium at motion

• Newton’s second law of motion

∑F = ma

• When the force fulfill Newton's first law of motion,

ma = 0

a=0

therefore, the particle is moving in constant velocity or at rest

2.1.1 Condition for the Equilibrium of

a Particle

Forces in equilibrium

2.1.1 Condition for the

Equilibrium of a Particle

• Methods to solve for force equilibrium:

• graphical solution yields a closed polygon

• algebraic solution R F 0

2.2 Free Body Diagram

2.2 The Free-Body Diagram (FBD)

• ~ the best representation of all the unknown forces (∑F) which acts on a body

• ~ a sketch showing the particle “free” from the

surroundings with all the forces acting on it

• Two common connections which are usually replaced as

forces in FBD

• Spring

• Cables and Pulleys

2.2.1 The Free-Body Diagram: Spring

• Linear elastic spring:

• change in spring length, s force acting on it, F

• The magnitude of force F = ks

• k = spring constant or stiffness - defines the elasticity of the spring

• Direction of force depends on the spring (compressed or

elongated) - in the direction of the spring force is acting

(or, against the compressed or elongated direction of the

spring)

2.2.2 The Free-Body Diagram: Cables

and Pulley

• Cables (or cords) are assumed negligible weight and cannot stretch

• Tension always acts in the direction of the cable

• For any angle θ in the figure, the cable is subjected to a constant tension T

2.2.3 Procedure for Drawing a FBD

1. Draw outlined shape

- Identify the shape of interest

2. Show all the forces

- Active forces: particle in motion

- Reactive forces: constraints that prevent motion

3. Identify each forces

- Known forces with proper magnitude and direction

- Letters used to represent magnitude and directions

Example

Determine the

forces in the cables.

Space Diagram: A sketch

showing the physical

conditions of the problem.

Free-Body Diagram: A sketch

showing only the forces on the

selected particle.

2.3 Force Vectors

force: action of one body on another; characterized by its

point of application, magnitude, line of action

2.3.1 Scalars & Vectors

• Scalar – a physical quantity that is completely described by a real number

• E.g. Time, mass

• Vector – a physical quantity that is described by magnitude & direction

• E.g. Displacement, forces

• Represented by boldfaced letters: U, V, W, …

• Magnitude of vector U = |U|

2.3.2 Vectors

• Graphical representation: Arrow

• Direction of arrow = direction of vector

• Length of arrow magnitude of vector

• Example:

• rAB = position of point B relative to point A

• Direction of rAB = direction from point A to point B

• |rAB| = distance between 2 points

2.3.2 Vectors

• Equal...

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