Inv 6.3 Equilibrium of Forces and

Hooke’s Law

Investigation Key Question:

How do you predict the force on a spring?

6.3 Applications of equilibrium

If an object is not moving,

then you know it is in

equilibrium and the net

force must be zero.

You know the total upward

force from the cables must

equal the downward force of

the sign’s weight because

the sign is in equilibrium.

What is the upward

force in each cable?

6.3 Applications of equilibrium

Real objects can move in three directions: up-down, right-left, and front-back.

The three directions are called three dimensions and usually given the names x, y, and z.

When an object is in equilibrium, forces must balance separately in each of the x, y, and z dimensions.

6.3 The force from a spring

A spring is a device designed to

expand or contract, and thereby

make forces in a controlled way.

Springs are used in many devices

to create force.

There are springs holding up the

wheels in a car, springs to close

doors, and a spring in a toaster

that pops up the toast.

6.3 The force from a spring

The most common type of spring is a coil of

metal or plastic that creates a force when it is

extended (stretched) or compressed

(squeezed).

6.3 The force from a spring

The force from a spring has

two important

characteristics:

The force always acts in a

direction that tries to return

the spring to its

unstretched shape.

The strength of the force is

proportional to the amount

of extension or

compression in the spring.

6.3 Restoring force and Hooke’s Law

The force created by an extended or

compressed spring is called a

“restoring force” because it always

acts in a direction to restore the spring

to its natural length.

The change a natural, unstretched

length from extension or compression

is called deformation.

The relationship between the restoring

force and deformation of a spring is

given by the spring constant (k).

6.3 Restoring force and Hooke’s Law

The relationship between force, spring constant,

and deformation is called Hooke’s law.

The spring constant has units of newtons per

meter, abbreviated N/m.

6.3 Hooke's Law

The negative sign indicates that positive

deformation, or extension, creates a restoring

force in the opposite direction.

F = - k x

Spring constant N/m

Force (N)Deformation (m)

1. You are asked for force.

2. You are given k and x.

3. Use F = - kx

4. Substitute values: F = - (250 N/m)(0.01 m) F = - 2.5 N

Calculate the force from a spring

A spring with k = 250 N/m is extended

by one centimeter. How much force

does the spring exert?

6.3 More about action-reaction and normal

forces

The restoring force

from a wall is always

exactly equal and

opposite to the force

you apply, because it

is caused by the

deformation resulting

from the force you

apply.

1. You are asked for the deformation, x.

2. You are given force, F and spring constant, k.

3. Use F = - kx, so x = - F ÷ k

4. Substitute values: x = - (500 N/m) ÷ (1 × 108 N/m)

5. x = - 5 × 10-6 meters (a very small deformation)

Calculate the restoring force

The spring constant for a piece of solid wood is 1 × 108

N/m. Use Hooke’s law to calculate the

deformation when a force of 500 N (112 lbs) is applied.

We are surrounded by structures.

To design a structure well, you first need to know what forces

act and how, and where the forces are applied.

Engineering is the application of science to solving real-life

problems, such as designing a bridge.

The Design of Structures

An object on a spring is

pulled to the right of the

equilibrium position and

released from rest.

The diagram shows the

direction of the spring

force at five different

positions over the

course of the object's

path.

If we analyze the position vs time of the object, we

observe a sinusoidal variation.

This is called oscillatory or simple harmonic motion.

If we analyze the velocity vs time of the object, we observe again a

sinusoidal variation, with an offset of ¼ of the cycle.

Notice the speed is maximum at the equilibrium position, and zero at the

turning points.

One complete cycle is

called an oscillation

• The time it takes to complete one oscillation is

called the period P.

• The maximum displacement (positive or negative)

from equilibrium is called the amplitude

Equilibrium

position