Translational Equilibrium

Concurrent Forces

Characteristics of Forces

• A net force will change state of motion (1st law)
• Fores can be exerted over long distances (gravity)
• Forces always occur in pairs (3rd law)
• Force pairs always act in opposite directions (3rd law)
• Forces are vectors -- use vector addition

Concurrent forces:

Two or more forces acting on the same point at the same time.

Resultant force:

One single force which has the same effect as two or more combined concurrent forces.

Component forces:

Two forces at right angles to each other which would have the same effect as a single, original force are called the components of that force.

Equilibrant force:

One single force that produces equilibrium--equal and opposite to resultant of concurrent forces

Finding the Resultant Force

• If forces are in same or opposite directions, use algebraic sum.
• With a right angle between vectors, use Pythagorean theorem and trig functions.
• If angle between vectors is not a right angle, use cosine law and sine law to find the resultant.
• Geometric method (drawing) always works to find approximate value.

Equilibrium Requirements

• No change in motion
• No acceleration
• No net force or torque
• Body can be either motionless or moving at constant velocity

Translational equilibrium

• No unbalanced forces (no net force)
• Upward forces equal downward forces
• Forces to left equal forces to right
• Vector sum of all forces equals zero
• Either no motion or straight line motion at constant speed

Resolution of forces into components

• Choose a convenient coordinate system for orientation of components.
• Create two orthogonal component forces (at right angles to each other).
• Use trigonometry to find component magnitudes.
• Reverse of vector addition.
• Multiply sin or cos times the given vector.
• If given angle is measured to horizontal, then horizontal component will be adjacent side--use cos to find it; vertical component will be opposite the angle--use sin to find it
• If given angle is measured to vertical, then vertical component will be adjacent--use cos; horizontal component will be opposite--use sin

Statics

• No motion occurs
• Can have forces from supporting surfaces, ropes, beams, girders, etc.
• important in building structures where no motion is desired: bridges, buildings, etc.

Blocks and Inclined Planes

• Use coordinate system aligned with plane
• Find weight components of block parallel to and perpendicular with plane
• Perpendicular component equals normal force between surfaces
• Parallel component is force that causes motion down the plane
• Component magnitudes depend on elevation angle of plane
• Block on Plane (no friction)

Friction

• Force that resists motion
• Due to structure of materials in contact
• Practically independent of area of contact
• Depends on amount of force pressing sufaces together and the nature of the materials in contact
• Might be desirable or undesirable
• Can be decreased by lubricants: oil, grease
• Can be increased by traction increasing substances: sand, grit, rubber, adhesives

Starting (Static) Friction

• Maximum frictional force
• Must be overcome to start motion
• Equals applied net force in direction of eventual motion

Sliding (kinetic) friction

• Resists motion after it begins
• less than starting friction
• Symbol is F_f

Coefficient of Friction

• Ratio of frictional force to normal force between surfaces
• Different coefficients for starting and sliding friction
• Symbol is Greek letter mu: µ
• µ = F_f / F_N

Block on level surface

• Normal force equal in magnitude to weight
• Friction force = weight x m
• Applied force - friction force = net force
• If applied force > friction force, block accelerates

Block on Plane with friction

• Parallel component of weight - friction force = net force
• If net force > 0, block accelerates down plane
• If net force = 0, block is at rest or moves down plane at constant speed.

Vocabulary

• Concurrent force
• Equilibrant force
• Resultant force
• Component force
• Vector resolution
• Friction, starting & sliding
• Coefficient of friction

Summary

• When more than one force acts on an object, we use component vectors to simplify the situation
• Useful in statics and block-plane situations
• In equilibrium, no net force, so components in opposite directions must be equal.
• Friction always opposes motion