Physics Lesson 8

Static Equilibrium

Eleanor Roosevelt High School

Chin-Sung Lin

Net Force

Net Force

Net Force – Sum of all Forces

The combination of all forces acting on an object is called the net force

Net Force

Calculate Net Force – Vector Addition

Vector addition can be used to calculate the net force

Net Force

Calculate Net Force – Vector Resolution/Addition

Since vector addition by graphical method is not precise, it is preferred to resolve all the force vectors into horizontal and vertical components, and then add them respectively

x

y

F

Fx

Fy

Fx = F cos θFy = F sin θ

Net Force

Calculate Net Force

BA

Net Force

Calculate Net Force

BA

A + B

Net Force

Calculate Net Force

B A

Net Force

Calculate Net Force

B A A + B

Net Force

Calculate Net Force

B A

Net Force

Calculate Net Force

B A A – B

Net Force

Calculate Net Force

B A

Net Force

Calculate Net Force

B A A – B

Net Force

Calculate Net Force

A A

Net Force

Calculate Net Force

A A 0

Net Force

Calculate Net Force

A A

Net Force

Calculate Net Force

A A 0

Gravitational Force (Fg)

The gravitational force (Fg) is the attraction force exerted by Earth on the block

Fg

Normal Force (FN)

The normal force (FN) is the reaction force exerted by ground on the block

Fg

FN

Normal Force (FN)

Normal force is always perpendicular to the surface

Fg

FN

FN = Fg

Friction Force (Ff)

The friction force (Ff) is the reaction force exerted by ground on the block

Friction force is always against the motion

FFf

Friction Force (Ff)

When the net force is equal to zero, friction force (Ff) is equal to the the force (F) exerted on the block

FFfFf = FF

Tension Force (FT)

The tension force (FT) is the force exerted by the rope on the block

Fg

FT

Tension Force (FT)

When the net force is equal to zero, tension force (FT) is equal to the the gravitational force (Fg) exerted on the block

Fg

FT

FT = Fg

Equilibrium

Statics

Statics is the branch of mechanics concerned with the analysis of force on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems are at rest, or where components and structures are at a constant velocity

Equilibrium

When an object is at rest, or at constant velocity, with the net force on it being zero, the object is in a state of equilibrium

Free-Body Diagram

A diagram showing all the forces acting on an object is called a free-body diagram

Drawing a free-body diagram should always the first step in solving physics problems involving forces

Free-Body Diagram

We isolate, or free the object of concern from everything else, and represent that object by a dot. We then draw all the forces vectors acting on the object with its tail starting on the dot. We label each vector to indicate what type of force it represents –

• W (or Fg) for a gravitational force

• N (or FN) for a normal force

• f (or Ff) for a friction force, and

• T (or FT) for a tension force Fg

FT

Vector Addition & Vector Resolution

Vector Addition

An object of 10 N hangs from two spring scales

When the spring scales hang at 60o from the vertical, their readings are 10 N each

When the angle has increased to 75.5o, the readings are 20 N each

Vector Addition

As the angle between the scales increases, the tension in the scales must increase for the resultant to remain 10 N

Vector Addition

For any pair of scales, ropes, or wires supporting a load, the greater their angles from the vertical, the larger the tension force in them. The resultant of the tension forces, or the diagonal of the parallelogram they describe, must be equal and opposite to the load being supported

Vector Resolution

2 FT cos = 2 x 10 N x cos 60o = 2 x 10 N x 1/2 = 10 N

2 FT cos = 2 x 20 N x cos 75.5o = 2 x 20 N x 1/4 = 10 N

Q & A

The End