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Forces
What is a Force?
• A force is any push or pull on an object
• A force does NOT always require
contact
– Gravity
– Electrostatic
– Magnetism
Force: A vector quantity
• The direction of the force is the direction of the
push or the pull.
– More specifically, the direction of a particular force is
the direction in which the object would accelerate if
the force was the only one acting on the object.
• The magnitude, or strength, of the force is
measured in the Newton.
kg  m
1 Newton = 1
2
s
The Newton
• A 1 Newton force has the strength to cause a
1 kg object to accelerate at 1m/s2 for as long as
the force is applied.
kg  m
1 Newton = 1
2
s
• A 2 Newton force can cause a 1 kg object to
accelerate at a rate of 2 m/s2, or could cause a 2
kg object to accelerate at a rate of 1 m/s2
The sum of all Forces
• When multiple forces are acting on an object
at the same time, the sum of the forces is
called the net force, ΣF
• Example:
FN
ΣF = FN + FG
FG
Newton’s First Law of Motion:
Inertia
• Every object in a state of uniform motion
tends to remain in that state of motion
unless an NET external force is applied to
it.
FN
ΣF = FN + FG
ΣF = 0 N
FG
Since the cup is in a uniform state
of motion (rest), there must not be
a net force applied to the cup.
FN + FG = 0 N
FN = - FG
The table must be pushing up on
the cup with the same strength
that gravity is pulling down on
the cup.
Newton’s Second Law of Motion:
• II. A net force, ΣF, will cause a mass, m, to
accelerate, a. This relationship can be
quantified by the equation:
ΣF = ma
Try this:
ΣF = ma
• What is the magnitude (strength) of the net
force required to accelerate a 10 kg object
at a rate of 6 m/s2?
Givens:
m = 10 kg
a = 6 m/s2
ΣF = ?
ΣF = ma
ΣF = 10 kg * 6 m/s2
ΣF = 60
kg  m
s2
= 60 N
Try this:
ΣF = ma
• If a total force of 450 N is applied to a 30 kg
object, what will be the object’s acceleration?
Givens:
ΣF = ma
ΣF = 450 N
kg  m
450 2

F
m = 30 kg
F 450 N
m
s
a 
a

 15 2
a=?
m
30kg
30kg
s
m
Try this:
ΣF = ma
• A net force of 200 N is acting upon an box of things. If
the box accelerates at a rate of 4 m/s2, what is the
combined mass of the box and the things?
Givens:
ΣF = ma
ΣF = 200 N
kg  m
200 2

F
a = 4 m/s2
F 200 N
s
m
m


 50kg
m=?
m
a a4m
4 2
2
s
s
A few forces to get us started
•
•
•
•
Force of Gravity
Normal Force
Force of Friction
Applied forces
There are MANY other forces, these are
just a few to get us started.
The Force of Gravity:
•
•
•
•
a.k.a: an object’s weight
A non-contact force
FG or Fw
The force that gravity exerts on an object is
proportional to the object’s mass.
• Specifically, FG=mg,
– g is gravitational acceleration
– g = -9.8 m/s2 on earth
• The direction of the force of gravity is towards
the center of the earth.
The Normal Force, FN
• Normal force is the force exerted by a rigid surface when
an object comes in contact with it.
• The Normal force is usually equal and opposite the force
exerted by the object on the surface.
• Normal means perpendicular to a plane
• It is called the “Normal” force because it is always
exerted perpendicular to the surface of contact.
Force of Friction
• A retarding, contact force
• Friction acts to oppose motion between
two surfaces in contact
• FF
FF
Applied Forces
• An applied force is a name given to a
variety of forces that might act on an
object
– Man pushing on a box
– Child pulling a rope attached to a sled
– Mother pushing a swing
• These forces are almost always
specifically stated in a problem.
Free-Body Diagrams
• A free-body diagram is a picture where all
forces acting on an object are drawn from
the center of the object.
FN
FN
FF
FG
FA
FG
Subtleties of Forces
• The direction of the net force, ΣF, always
indicates the direction of the acceleration,
but not necessarily the direction of motion.
– Example: A projectile
FG
FG
FG
FG
FG
FG
Subtleties of Forces
• The direction of the net force, ΣF, always indicates the direction of
the acceleration, but not necessarily the direction of motion.
• A force that acts in two dimensions is
typically separated into its components
Fx = │F│cos ϴ
Fy = │F│sin ϴ
FThrust
FThrust-y
FThrust-x
Subtleties of Forces
• The direction of the net force, ΣF, always indicates the direction of
the acceleration, but not necessarily the direction of motion.
• A force that acts in two dimensions is typically separated into it’s
components.
• Newton’s second law is most often applied
in each dimension separately.
ΣFx = max
ΣFy = may
Subtleties of Forces
• The direction of the net force, ΣF, always indicates the direction of
the acceleration, but not necessarily the direction of motion.
• A force that acts in two dimensions is typically separated into it’s
components.
• Newton’s second law is most often applied in each dimension
separately.
• Mass and weight are NOT the same thing.
– Mass is a scalar measurement of how much matter
an object is made of. An object’s mass does not
change because it’s location has changed.
– Weight is a vector measurement of the force gravity
exerts on an object. If you take an object from the
surface of the earth to the surface of the moon, it’s
weight will change, but it’s mass will not.