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
𝑎 ∝
1
𝑚
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
𝑎 ∝𝐹
Combining the results of both labs…
𝐹
𝑎=
𝑚
- 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=
𝐹
𝑚
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
Fearth
(N)
m (kg)
• 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
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
A block of wood resting on a desktop
Normal Force
FN
Fg
Weight/Force due to Gravity
Example 2
A block of wood moving with a constant velocity across a surface
FN
Applied Force
FA
Friction
f
Fg
Example 3
A block of wood accelerating to the right across the surface
FN
FA
f
Fg
Example 4
A block of wood accelerating to the right when pulled by a
rope at an angle
Tension
FN
T
f
Fg
Example 5
A tetherball while swinging at a constant speed around a pole
Tension
T
Fg
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 equations
1. Draw a FBD to identify all forces and the directions
they act
1. 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
2. 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 components
60 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 mower
b) Calculate the normal force acting on the mower
Draw a force diagram of the mower:
FN
Write equations:
FAcos - f = 0
f
FA
Fg
FN - FAsin - Fg = 0
Use equations to solve problem:
b) FN - FAsin - Fg = 0
a) FAcos - f = 0
FN = FAsin + Fg
f = FAcos
FN = FAsin + mg
f = (100 N)cos 40.0
FN = (100 N)sin 40.0 + (15 kg)(10 m/s2)
f = 76.6 N
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?