Forces

Summarizing a few things we know…

From the Bowling Ball activities we have evidence that…

• Forces are responsible for changes in motion– F same direction as v: Speed up– F opposite direction as v: slow down– F perpendicular to v: changing direction– Forces cause acceleration

• When there is no net force, motion does not change in any way… a = 0 m/s2

Newton’s First Law

• Objects at rest will stay at rest, and objects in motion with constant velocity will stay in motion with constant velocity unless an unbalanced external force causes it to change.

Acceleration Lab I:

• How does the acceleration of a system depend on the mass of the system?–Acceleration is inversely

proportional to mass

Acceleration Lab II:

• How does the acceleration of a system depend on the force applied to the system?–Acceleration is directly proportional to

the force applied

Combining the results of both labs…

- acceleration is directly proportional to force-acceleration is inversely proportional to mass

Newton’s Second Law

• The acceleration of an object is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

A conceptual comparison of the 1st and 2nd laws of Newton…

Newton’s First Law Newton’s Second Law

From the Force of the Earth activity we have evidence that…

• The force the earth on an object is directly proportional to the mass of the object.

Fearth = (10 N/kg)m

• The intercept is zero…zero mass feels no force from earth• The slope is called the gravitational field strength, g

» All objects in the same location experience the same gravitational field strength

• The “force of the earth” on an object is more commonly known as the object’s weight

Fearth

(N)

m (kg)

Mass vs. Weight• Mass – a measure of the quantity of matter in an object,

a property of the object, NOT a force.• This value is the same regardless of location• A measure of an object’s inertia• SI unit is the kilogram (kg)

• Weight – a measure of the force of gravity on an object.• This value depends on the object’s location in a gravitational field.• SI unit is the Newton (N)

• Weight = mass x gravitational field strength

Fg = mg

*Near the surface of Earth, a 1 kg mass weighs 10 N

Newton’s 3rd Law• For every action, there is an equal but

oppositely directed reaction.– Action/reaction = forces between 2 objects– Forces always occur in pairs– Action/Reaction forces are always the same size– Action/reaction forces always point in opposite

directions– Action and reaction pairs NEVER ACT ON THE SAME

OBJECT…• Object A pushes object B• Object B pushes object A

Free Body Diagrams

A Free Body Diagram (FBD) is a visual representation of all the forces acting

on a single object

FBDs are extremely powerful problem solving tools that bridge the gap between

qualitative analysis and a quantitative mathematical representation

Drawing a FBD…

• A simple dot can be used to represent the object in question

• Identify the forces acting ON that object only• Draw one arrow to represent each force acting

ON the object– All arrows should be drawn from the dot or the center

of the object– The arrows point in the direction of the force.– The length of the arrow represents the relative

magnitude of the force…ie longer arrows = larger force

Example 1

Normal ForceFN

Fg

Weight/Force due to Gravity

A block of wood resting on a desktop

Example 2A block of wood moving with a constant velocity across a surface

FN

Fg

Applied ForceFA

Frictionf

Example 3A block of wood accelerating to the right across the surface

FN

Fg

FAf

Example 4A block of wood accelerating to the right when pulled by a rope at an angle

FN

Fg

TensionT

f

Example 5A tetherball while swinging at a constant speed around a pole

Fg

TensionT

Notice there is nothing in the original description that says the tetherball is being hit. A diagram for the ball as it is being hit would show an additional force acting on the ball.

Try it…Draw a FBD for a lawn mower being pushed at a

constant speed as shown in the picture

Writing force equations1. Draw a FBD to identify all forces and the directions

they act

2. Write an equation to sum up the horizontal forces making sure all forces that affect the object horizontally are accounted for in the equation.

- algebraic signs are used to indicate directions- Keep in mind F = 0 when there is no

acceleration

3. Write an equation for the vertical forces making sure all forces that affect the object vertically are accounted for in the equation

Let’s try it…

A book is pushed to the right across the desktop at a constant speed.

Before going further, we need a little vector review…

• Forces are vectors. They have size and direction.• Forces that act at an angle have components in the vertical

and horizontal directions.• Every vector can be visualized as the hypotenuse of a right

triangle with its components as the other sides. See the diagrams below.

• Trigonometry allows us to determine the values of those components to use in force equations.

Resolving vectors into components60 N

40°

What are the horizontal and vertical components of the tension in the chain?

Remember this…Let’s write the equations that go along with the FBD we

did earlier. Assume the woman pushes at an angle compared to the horizontal and the mower is accelerating to the left.

Draw the FBD and write F equations for the following example…

• A crate is being dragged to the right at a constant speed along a level surface by a rope that makes an angle of 30° as measured from horizontal.

One more time…Now with numbers!

A 15 kg lawn mower is pushed at a constant speed by a force of 100.0N directed along the handle at 40.0° to the horizontal. a) Determine the frictional force acting on the mowerb) Calculate the normal force acting on the mower

Draw a force diagram of the mower:

FN

f

Fg

FA

Write equations:

FAcos - f = 0

FN - FAsin - Fg = 0

Use equations to solve problem:

a) FAcos - f = 0 f = FAcos f = (100 N)cos 40.0 f = 76.6 N

b) FN - FAsin - Fg = 0 FN = FAsin + Fg FN = FAsin + mg FN = (100 N)sin 40.0 + (15 kg)(10 m/s2) FN = 214.3 N

Friction• Friction is a force that opposes the motion, or

tendency of motion, of an object.

• Friction is caused mostly by the electromagnetic interactions of particles within molecules at the surfaces of objects in contact.

Two Basic Types of Friction– Static friction

• exists between the surfaces of non-moving objects that are trying to move

• Maximum static friction refers to the most force that can be applied before the object starts to move

– Kinetic friction (also called sliding friction)• Exists between the surfaces of objects when there is

relative motion between the objects

***Part I of lab shows that static friction is larger than kinetic friction

Friction vs. Normal Force• Part II of lab shows us that friction is directly

proportional to normal force:

f = (slope)FN

• The slope of a friction vs. normal force graph for two given surfaces is called the coefficient of friction (μ)

f = μFN

Coefficient of Friction

• The coefficient of friction has no units. It is a ratio of two forces (Newtons divided by Newtons)…

μ = f / FN

• This relationship gives us a common substitution used in problem solving… f = μFN. – If working with static friction, this equation represents a

maximum possible value.

Example – kinetic, constant speed

• The coefficient of friction between a 12 kg wooden crate and the floor is 0.32. How much force is needed to push this crate across the floor at a constant speed?

Example – accelerated motion

• A 5.0 kg box is pushed horizontally across the floor with a force of 25.0 N. If the coefficient of kinetic friction is 0.24, what is the acceleration of the box?