Forces and the Laws of Motion
Section 1
Forces
• Forces can change motion.
– Start movement, stop movement, or change the direction of
movement
– Cause an object in motion to speed up or slow down
Forces and the Laws of Motion
Forces
• Contact forces
– Pushes or pulls requiring
physical contact between
the objects
– Baseball and bat
• Field forces
– Objects create force fields
that act on other objects.
– Gravity, static electricity,
magnetism
Section 1
Forces and the Laws of Motion
Section 1
Units of Force
• The SI unit of force is the newton (N).
– Named for Sir Isaac Newton
– Defined as the force required to accelerate a 1 kg mass at a rate of 1
m/s2
– Approximately 1/4 pound
• Other units are shown below.
Forces and the Laws of Motion
The Four Fundamental Forces
• Electromagnetic
– Caused by interactions between protons and electrons
– Produces friction
• Gravitational
– The weakest force
• Strong nuclear force
– The strongest force
– Short range
• Weak nuclear force
– Short range
Section 1
Forces and the Laws of Motion
Section 1
The Force Diagram
• Force Diagrams1. Represent forces using vector arrows
2. All forces are drawn as if they act on a central point
of the object
3. Free body diagrams show only forces acting on one
object
Forces and the Laws of Motion
Force Diagrams
• Forces are vectors (magnitude and direction).
• Force diagram (a)
– Shows all forces acting during an interaction
• On the car and on the wall
• Free-body diagram (b)
– Shows only forces acting on the object of interest
• On the car
Section 1
Forces and the Laws of Motion
Section 1
Free-Body Diagrams
• Three forces are shown
on the car.
– Describe each force by
explaining the source of the
force and where it acts on
the car.
– Is each force a contact
force or a field force?
Forces and the Laws of Motion
Force Diagram
Section 1
Forces and the Laws of Motion
Force Diagram
• Step for drawing a free body diagram
1. Identify forces acting on the object
– Tow truck exerts force on the car
– Road exerts force on the car
– Car is acted on by gravity
2. Draw a simple diagram
Section 1
Forces and the Laws of Motion
Section 1
Force Diagram
3. Add magnitude of forces to arrows
– Indicate force with a vector arrow on the car by the
tow truck (5800 N)
– Gravitational force acting on the car (14700 N)
– Road exerts an upward force on the car (13,690 N)
– Interaction between the road and the tires exert a
backward force of (775 N)
Forces and the Laws of Motion
Section 1
Force Diagram Practice
• Draw a force diagram of a crash test dummy in a
car at the moment of collision
• Forces acting on the car are
1. 19,600 N downward
2. 17,800 N forward
3. 25,000 N backward
Forces and the Laws of Motion
Section 2
Newton’s First Law
• Experimentation led Galileo to the idea that objects
maintain their state of motion or rest.
• Newton developed the idea further, in what is now
known as Newton’s first law of motion:
Forces and the Laws of Motion
Section 2
Draw a force diagram of a crash test dummy in a car at
the moment of collision
• Forces acting on the car are
1. 19,600 N downward
2. 17,800 N forward
3. 25,00 N backward
• Forces acting on the dummy are
1. 585 N downward
2. 175 N backward
3. 585 N upward
Forces and the Laws of Motion
Section 2
Newton’s First Law
• Called the law of inertia
• Inertia
– Tendency of an object to remain in its state of motion
– Tendency of an object not to accelerate or decelerate
– Mass is a measure of inertia
• More mass produces more resistance to a change in velocity
• Which object in each pair has more inertia?
– A baseball at rest or a tennis ball at rest
• Answer: the baseball
– A tennis ball moving at 125 mi/h or a baseball at rest
• Answer: the baseball
Forces and the Laws of Motion
Section 2
Net Force - the Sum of the Forces
• This car is moving with a
constant velocity.
– Fforward = road pushing the tires
– Fresistance = force caused by friction
and air
– Forces are balanced
• Velocity is constant because the
net force (Fnet) is zero.
• Net external force can be
determined by a change in
motion
Forces and the Laws of Motion
Equilibrium
• The state in which the net
force is zero.
– All forces are balanced.
– Object is at rest or travels with
constant velocity.
• In the diagram, the bob on
the fishing line is in
equilibrium.
– The forces cancel each other.
– If either force changes,
acceleration will occur.
Section 2
Forces and the Laws of Motion
Net External Forces
• Net external forces =
vector sum of all the
forces acting on the
object
Section 2
Forces and the Laws of Motion
Section 2
Practice Problems
• A man is pulling on his dog with a force of 70.0N
directed at an angle of 30.0º to the horizontal.
– Find the x and y component.
Forces and the Laws of Motion
Section 2
Practice Problems
• The man pulls a box with a force of 25.0N at
angle of 18.0º to the horizontal.
– Find the x and y component
Forces and the Laws of Motion
Section 2
Practice Problems
• A crate is pulled to the right with a force of 85N,
to the left with a force of 115N, upward with a
force of 565 N, and downward with a force of
236N.
– Find the net external force of x
– Find the net external force of y
– Find the magnitude and direction of the net external
force on the crate
Forces and the Laws of Motion
Section 2
Classroom Practice Problem
• An agricultural student is designing a support
system to keep a tree upright. Two wires have
been attached to the tree and placed at right
angles to each other (parallel to the ground).
One wire exerts a force of 30.0 N and the other
exerts a force of 40.0 N. Determine where to
place a third wire and how much force it should
exert so that the net force on the tree is zero.
• Answer: 50.0 N at 143° from the 40.0 N force
Forces and the Laws of Motion
Section 3
Newton’s Second Law
• Increasing the force will increase the acceleration.
– Which produces a greater acceleration on a 3-kg model airplane, a force
of 5 N or a force of 7 N?
• Answer: the 7 N force
• Increasing the mass will decrease the acceleration.
– A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg
and one with a mass of 4 kg. Which has a greater acceleration?
• Answer: the 3 kg airplane
Forces and the Laws of Motion
Section 3
Newton’s Second Law (Equation Form)
• F represents the vector sum of all forces acting on an
object.
– F = Fnet
– Units for force: mass units (kg)  acceleration units (m/s2)
– The units kg•m/s2 are also called newtons (N).
Forces and the Laws of Motion
Section 3
Practice Problems
• The net external force on the propeller of a 0.75
kg model airplane is 17 N forward. What is the
acceleration of the plane?
• The net external force on a golf cart is 390 N
north, if the cart has a total mass of 270 kg, what
are the magnitude and direction of its
acceleration?
Forces and the Laws of Motion
Section 3
Practice Problems
• A car has a mass of 1500 kg. What force is
required to accelerate the car at 4.5m/s2 to the
east?
• A 2.0 kg mass starts from rest at the top of an
inclined plane 85 cm long and slides down to the
bottom is 0.50s. What net external force acts on
the mass along the incline?
Forces and the Laws of Motion
Section 3
Classroom Practice Problem
• Space-shuttle astronauts experience
accelerations of about 35 m/s2 during takeoff.
What force does a 75 kg astronaut experience
during an acceleration of this magnitude?
• Answer: 2600 kg•m/s2 or 2600 N
Forces and the Laws of Motion
Section 3
Classroom Practice Problem
• The muscle responsible for closing the mouth is the
strongest muscle in the human body. It can exert a force
greater than that exerted by a man lifting a mass of 400
kg. Richard Hoffman of Florida recorded the force of
biting at 4.33  103 N. If each force has a magnitude
equal to the force of Hoffman’s bite, determine the net
force. One force is along the horizontal, the second force
is -90º from the horizontal, and the third force is -60 º
from the horizontal.
•
•
Forces and the Laws of Motion
Section 3
Classroom Practice Problem
• In 1994, Vladimir Kurlovich, from Belarus, set the record
as the world’s strongest weightlifter. He did this by lifting
and holding above his head a barbell whose mass was
253 kg. Kurlovich’s mass at the time was roughly 133 kg.
Draw a free-body diagram showing the various forces in
the problem. Calculate the normal force exerted on each
of Kurlovich’s feet during the time he was holding the
barbell.
•
•
Forces and the Laws of Motion
Section 3
Classroom Practice Problem
• The net force exerted by a woodpecker’s head when its
beak strikes a tree can be as large as 4.90 N, assuming
that the bird’s head has a mass of 50.0 g. Assume that
two different muscles pull the woodpecker’s head
forward and downward, exerting a net force of 4.90 N. If
the forces exerted by the muscles are at right angles to
each other and the muscle that pulls the woodpecker’s
head downward exerts a force of 1.70 N, what is the
magnitude of the force exerted by the other muscle?
Draw a free-body diagram showing the forces acting on
the woodpecker’s head.
•
Forces and the Laws of Motion
Section 3
What do you think?
• Two football players, Alex and Jason, collide
head-on. They have the same mass and the
same speed before the collision. How does the
force on Alex compare to the force on Jason?
Why do you think so?
– Sketch each player as a stick figure.
– Place a velocity vector above each player.
– Draw the force vector on each and label it (i.e. FJA is
the force of Jason on Alex).
Forces and the Laws of Motion
Section 3
What do you think?
• Suppose Alex has twice the mass of Jason. How
would the forces compare?
– Why do you think so?
– Sketch as before.
• Suppose Alex has twice the mass and Jason is
at rest. How would the forces compare?
– Why do you think so?
– Sketch as before.
Forces and the Laws of Motion
Section 3
Newton’s Third Law
• When two objects interact, the magnitude
of the force exerted on object 1 by object 2
is equal to the force exerted on object 2 by
object 1. These two forces are equal as
well as opposite.
Forces and the Laws of Motion
Section 3
Newton’s Third Law
• Forces always exist in pairs.
– You push down on the chair, the chair pushes
up on you
– Called the action force and reaction force
– Occur simultaneously so either force is the
action force
Forces and the Laws of Motion
Section 3
Newton’s Third Law
• For every action force there is an equal and opposite
reaction force.
• The forces act on different objects.
– Therefore, they do not balance or cancel each other.
– The motion of each object depends on the net force on that object.
Forces and the Laws of Motion
Hammer Striking a Nail
• What are the action/reaction pairs for a
hammer striking a nail into wood?
– Force of hammer on nail = force of nail on
hammer
– Force of wood on nail = force of nail on
wood
• Which of the action/reaction forces above
act on the nail?
– Force of hammer on nail (downward)
– Force of wood on nail (upward)
• Does the nail move? If so, how?
– Fhammer-on-nail > Fwood-on-nail so the nail
accelerates downward
Section 3
Forces and the Laws of Motion
Section 3
Hammer Striking a Nail
• What forces act on the hammer?
– Force of nail on hammer (upward)
– Force of hand on hammer (downward)
• Does the hammer move? If so, how?
– Fnail-on-hammer > Fhand-on-hammer so the hammer
accelerates upward or slows down
• The hammer and nail accelerate in opposite
directions.
Forces and the Laws of Motion
Section 3
Action-Reaction: A Book on a Desk
Action Force
Reaction Force
• The desk pushes up on
the book.
• The book pushes down
on the desk.
• Earth pulls down on the
book (force of gravity).
• The book pulls up on
Earth.
Forces and the Laws of Motion
Section 3
Action-Reaction: A Falling Book
Action
• Earth pulls down on the
book (force of gravity).
Reaction
• The book pulls up on
Earth.
• What is the result of the
action force (if this is the
only force on the book)?
• What is the result of the
reaction force?
– Unbalanced force
produces an acceleration
of -9.81 m/s2.
• Unbalanced force produces
a very small upward
acceleration (because the
mass of Earth is so large).
Forces and the Laws of Motion
Newton’s Third Law
• Field forces also act as pairs
Section 3
Forces and the Laws of Motion
Section 3
Practice Problems
• A 6.0 kg object undergoes an acceleration of 2.0
m/s2.
– What is the magnitude of the net external force acting
on it?
– If this same force is applied to a 4.0 kg object, what
acceleration is produced?
Forces and the Laws of Motion
Section 3
Practice Problems
• A child pulls a wagon with a horizontal force,
causing it to accelerate. Newton’s third law say
that the wagon exerts an equal and opposite
force on the child. How can the wagon
accelerate?
Forces and the Laws of Motion
Section 3
Practice Problems
• Identify the action-reaction pairs in the following
situations:
–
–
–
–
A person takes a step
A baseball player catches a ball
A snowball hits someone in the back
A gust of wind strikes a window
Forces and the Laws of Motion
Section 3
Practice Problems
• The forces acting on a sailboat are 390N north
and 180N east. If the magnitude (including the
crew) has a mass of 270 kg, what are the
magnitude and direction of its acceleration?
Forces and the Laws of Motion
Section 3
Practice Problems
• The forces acting on a sailboat are 390N north
and 180N east. If the magnitude (including the
crew) has a mass of 270 kg, what are the
magnitude and direction of its acceleration?
Forces and the Laws of Motion
Section 3
Practice Problems
• David Purley, a racing driver, survived
deceleration from 173 km/h to 0 km/h over a
distance of 0.660 m when his car crashed.
Assume that Purley’s mass is 70.0 kg. What is
the average force acting on him during the
crash? Compare this force to Purley’s weight.
(Hint: Calculate the average acceleration first.)
Forces and the Laws of Motion
Section 3
Practice Problems
• A giant crane in Washington, D. C. was tested
by lifting a 2.232  106 kg load.
a. Find the magnitude of the force needed to lift
the load with a net acceleration of 0 m/s2.
b. If the same force is applied to pull the load
up a smooth slope that makes a 30.0 angle
with the horizontal, what would be the
acceleration?
Forces and the Laws of Motion
Section 3
Practice Problems
• In 1991, a lobster with a mass of 20.0 kg was caught off
the coast of Nova Scotia, Canada. Imagine this lobster
involved in a friendly tug of war with several smaller
lobsters on a horizontal plane at the bottom of the sea.
Suppose the smaller lobsters are able to drag the large
lobster, so that after the large lobster has been moved
1.55 m its speed is 0.550 m/s. If the lobster is initially at
rest, what is the magnitude of the net force applied to it
by the smaller lobsters? Assume that friction and
resistance due to moving through water are negligible.
Forces and the Laws of Motion
Section 4
What do you think?
• How do the quantities weight and mass differ
from each other?
• Which of the following terms is most closely
related to the term friction?
– Heat, energy, force, velocity
• Explain the relationship.
Forces and the Laws of Motion
Section 4
Weight and Mass
• Mass is the amount of matter in an object.
– Kilograms, slugs
• Weight is a measure of the gravitational force on an
object.
– Newtons, pounds
– Depends on the acceleration of gravity
• Weight = mass  acceleration of gravity
– W = mag where ag = 9.81 m/s2 on Earth
– Depends on location
• ag varies slightly with location on Earth.
• ag is different on other planets.
Forces and the Laws of Motion
Normal Force
• Force on an object
perpendicular to the
surface (Fn)
• It may equal the weight
(Fg), as it does here.
• It does not always equal
the weight (Fg), as in the
second example.
• Fn = mg cos 
Section 4
Forces and the Laws of Motion
Normal Force
• An object placed on a tilted surface will
often slide down the surface.
• The rate at which the object slides down
the surface is dependent upon how tilted
the surface is; the greater the tilt of the
surface, the faster the rate at which the
object will slide down it.
• In physics, a tilted surface is called an
inclined plane.
Section 4
Forces and the Laws of Motion
Normal Force
• As shown in the diagram, there are
always at least two forces acting
upon any object that is positioned on
an inclined plane - the force of
gravity and the normal force.
• The force of gravity (also known as
weight) acts in a downward direction
• The normal force acts in a direction
perpendicular to the surface (in fact,
normal means "perpendicular").
Section 4
Forces and the Laws of Motion
Normal Force
• Up to this point in the course, we
have always seen normal forces
acting in an upward direction,
opposite the direction of the force of
gravity.
• But this is only because the objects
were always on horizontal surfaces
and never upon inclined planes.
• The normal forces is not always
upwards, but rather that it is directed
perpendicular to the surface that the
object is on.
Section 4
Forces and the Laws of Motion
Normal Force
• The force of gravity will be resolved
into two components of force - one
directed parallel to the inclined
surface and the other directed
perpendicular to the inclined
surface.
Section 4
Forces and the Laws of Motion
Normal Force
• The perpendicular component of the
force of gravity is directed opposite
the normal force and as such
balances the normal force
Section 4
Forces and the Laws of Motion
Normal Force
• The parallel component of the force
of gravity is not balanced by any
other force. This object will
subsequently accelerate down the
inclined plane due to the presence
of an unbalanced force
Section 4
Forces and the Laws of Motion
Normal Force
• It is the parallel component of the
force of gravity that causes this
acceleration. The parallel
component of the force of gravity is
the net force.
Section 4
Forces and the Laws of Motion
Section 4
Normal Force
• The task of determining the magnitude of the two
components of the force of gravity is a mere manner of
using the equations. The equations for the parallel and
perpendicular components are:
• .