Newton’s Second Law of
Motion – Force and
Acceleration
Chapter 6
Objectives
• State the relationship between acceleration and net
force.
• State the relationship between acceleration and mass.
• State and explain Newton’s 2nd law of motion.
• List the factors that affect the force of friction between
surfaces.
• Distinguish between force and pressure.
• Explain why the acceleration of an object in free fall
does not depend upon the mass of the object.
• List the factors that affect the air resistance force on an
object.
6.1 Force Causes Acceleration
• At rest, a hockey puck is in
equilibrium – gravity and the
support force are balanced.
• If a player exerts an
unbalanced force on the puck
(pushes it), it accelerates.
• When the puck is no longer
being pushed, there is no
longer an unbalanced force
acting on it. The puck does not
accelerate but moves at
constant velocity.
* Unbalanced forces acting
on an object cause the
object to accelerate.
6.1 Force Causes Acceleration
• Since one force is usually not the only force
acting on an object, we must amend our
statement: Acceleration depends on net force.
• In fact, an object’s acceleration is directly
proportional to the net force acting on it.
o If you double the force, the acceleration doubles.
o If you increase the force by a factor of ten, the
acceleration increases by a factor of ten.
• We can write: acceleration ~ net force
(The symbol ~ stands for “is directly proportional to”).
6.2 Mass Resists Acceleration
100 N
100 N
0.1
•Review the diagrams to the left.
•The car of greater mass will
accelerate less than the car of
smaller mass with the same
applied force.
•Therefore, acceleration depends on
the size of the mass being pushed.
•In fact, acceleration is inversely
proportional to the mass.
•If mass is doubled (see diagram), then
the acceleration is halved.
•Acceleration ~ 1
mass
•This means the 2 values change in
opposite directions. If mass increases,
acceleration must decrease.
6.3 Newton’s Second Law
• Newton realized acceleration depends not only
on the force of a push but also on an object’s
mass.
* The acceleration produced by a net force on
an object is directly proportional to the
magnitude of the net force, is in the same
direction as the net force, and is inversely
proportional to the mass of the object.
6.3 Newton’s Second Law
• This means: acceleration ~ net force
mass
• When force is in newtons (N), mass is in
kilograms (kg) and acceleration is in meters per
second squared (m/s2), we get the equation:
acceleration = net force
mass
a = F/m or F = am
What is the acceleration due to gravity of these 2 objects?
Recall: Force due to gravity = weight and W = mg
Practice
• A car has a mass of 1250 kg. What is the
acceleration produced by a force of 2250 N?
• What is the acceleration if the force is doubled?
• What is the acceleration if the mass is doubled?
• How much force is needed to accelerate a
35,000 kg plane by 1.2 m/s2?
• If a car can accelerate at 5 m/s2, what
acceleration can it attain if it tows another car
that has a mass equal to its own?
Practice
• Suppose a plane is flying at a constant 900
km/hr and the thrust (force) of the engines is a
constant 80,000 N. What is the acceleration of
the plane?
• What is the force of air resistance that acts on
the plane’s outside surface?
6.4 Friction
PUSH
FRICTION
• Recall (from Ch. 2 & 3)
that friction acts on
materials that are in
contact with one another.
• It always acts in a direction
opposite to the relative
motion.
• Friction is due to
irregularities in the 2
surfaces. It requires force
for a surface to overcome
the “bumps” in another
surface.
6.4 Friction
• More specifically, the force of friction depends
on the KINDS of material that are in contact
and HOW MUCH the surfaces are pressed
together.
٠ For example, rubber against concrete produces more
friction that steel against steel.
• Friction occurs between solids, liquids, gases, or
any combination of the states of matter.
Types of Friction Force
• Static friction: the resistance force that must be
overcome to start an object in motion.
• Kinetic or sliding friction: the resistance force
between two surfaces already in motion.
• Rolling friction: the resistance force between a
surface and a rolling object.
• Fluid friction: the resistance force of a gas or a
liquid as an object passes through. Air
resistance is a special type of fluid friction.
Friction Force
• Force of sliding
friction =
(coefficient of
friction) (normal
force)
• Ff = µ x Fn
6.4 Friction
• A diagram (like the ones shown
here) in which all the forces acting
on an object are shown is called a
free-body diagram.
• Here, the forces are balanced – the
net force is zero in each case.
Therefore, the objects are not
accelerating but are moving with a
constant velocity.
6.5 Applying Force - Pressure
• If you stand on your
bathroom scale, the force
measured is called your
weight. (Fgrav = W = mg)
• Will the reading change if you
stand on one foot?
• Will the reading change if you
stand on one toe?
• What does change?
6.5 Applying Force - Pressure
• Although the force (your weight) is the same in all 3
cases, the area of contact is different in each case. That
is, the area supporting the weight in each case is
different.
• Since pressure is defined as force per unit area,
Pressure = force
or P = F
area of application
A
it is the pressure exerted on the surface that changes in
each of our cases
• For a constant force, an INCREASE in area of contact
will cause a DECREASE in the pressure.
Practice
* Note: Pressure is measured in newtons (N) per square
meter (m2) or pascals (Pa).
• What are 2 ways to increase the pressure on something?
• What is the pressure exerted by a 400 N force if its
contact area is
• 4 m2?
• 0.4 m2?
• 0.04 m2?
6.6 Free Fall Explained
• Recall (Ch. 4) that in free fall,
gravity is the only thing that
affects a falling object.
• Galileo showed that falling
objects, regardless of their
mass, accelerate equally.
• Galileo could not explain why
this was true.
6.6 Free Fall Explained
• Recall (Ch. 3) that mass and weight are
proportional to each other.
– A 10 kg. mass weighsabout 10x as much as a 1 kg.
mass.
• In fact, since weight is the force of gravity on an
object, we can use the equation F = ma to
express weight this way: weight (W) = mass (m)
times acceleration due to gravity (g) or W = mg.
6.6 Free Fall Explained
• Therefore, the ratio
of weight (force) to
mass is the same for
any objects.
• All free falling
objects undergo the
same acceleration
at the same place on
Earth.
• This is represented
by g and equals
approximately 10
m/s2.
All freely falling
objects fall with
the same
acceleration
because the net
force on an object
is only its weight,
and the ratio of
weight to mass is
the same for all
objects.
Cartoon from text p. 94
6.7 Falling and Air Resistance
In a vacuum (no air resistance)
In presence of air
6.7 Falling and Air Resistance
• Focus on the feather in the 2nd animation.
• When falling in air, it is obvious that air resistance
(a frictional force) does have an affect on the
NET force of the falling objects – it decreases it.
• The net force is equal to the force or weight of
the object MINUS its air resistance.
• Net Force = Fgrav - Fair
• Therefore, since the Fnet is less, acceleration of a
falling object is less and its resulting velocity is
less.
Speed and Area
• The two most common
factors which have a
direct effect upon the
amount of air resistance present are:
1. The speed of the object: the greater the speed,
the greater the force of air resistance.
2. The frontal area of the object: the greater the
frontal area, the greater the air resistance.
* Air resistance force ~ speed x frontal area
Terminal Velocity
• As a skydiver falls, his velocity continually increases –
he is accelerating due to gravity.
• Since air resistance is proportional to speed, as his
speed increases so does the air resistance he encounters.
• When the magnitude of the air resistance equals
the weight of the skydiver (his force due to gravity),
there is no longer any NET force on the sky diver
Terminal Velocity
Fair
Fgrav
• With no net force on a
falling object, there is no
acceleration and the velocity
remains constant.
• The speed of an object
when its acceleration is zero
(because Fair balances Fgrav)
is called the terminal speed.
• Since we know the direction
(downward), we can call it
the terminal velocity.
• Objects which have a large area relative to their weight will
reach their terminal velocity very quickly.
° The feather pictured above has a large area compared to its weight. It
encounters a lot of air resistance very quickly.
° The elephant has a relatively small area compared to its weight. It will
accelerate for a longer period of time before the force of air resistance equals
the force due to gravity and the terminal velocity is reached.
Terminal Velocity
• Since living things can change their
body orientation, changing their
“area” relative to their weight, they
can somewhat control their terminal
speed.
Terminal Velocity
•Parachutes can also
greatly increase air
resistance.
•Terminal velocity can
be cut from 150-200
km/hr. to 15-25 km/hr.
•Slow terminal speeds
insure a safe landing.
A final note about Galileo . .
• When Galileo dropped objects from the Leaning Tower
of Pisa, the heavier object DID hit the ground first. The
time difference was so small, however, it could not be
detected.
• At low speeds (short distances of fall), air resistance is
negligible.
• At high speeds (long falls where air resistance can “build
up”), the effect of air resistance is more pronounced.
• The effect of air resistance is also more pronounced on
lighter objects. Lighter objects behave more like a
parachute than heavier objects.
Practice
• What is the net force of the
falling object?
• What is the acceleration of the
falling object?
• What will be the acceleration
of the object when it reaches
its terminal velocity?
• Which mass will reach the
ground first – a 10 kg. mass or
a 100 kg. mass? Why?
Fair = 10 N
10 kg.
Fgrav = 100 N
Check your Understanding
• A sky diver jumps from a hot air balloon.
• As she falls faster & faster, does air resistance
increase, decrease, or remain the same?
• Does the net force on her increase, decrease, or
remain the same?
• As she falls faster & faster, does her acceleration
increase, decrease, or remain the same?
• How can she change the air resistance force she
experiences?
Practice
• Draw a series of free body diagrams to represent an 85
kg skydiver undergoing free fall. Show a diagram for the
instances when the Fair is 0 N, 350 N, 700 N and 833 N.
In each instance, determine the Fgrav, Fnet, and the
acceleration.