forces

Topics: Force, Unit vector, Net force Pages: 29 (2812 words) Published: September 21, 2013
Chapter 2
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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