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Forces
Chapter 6.1
What You Already Learned
• Velocity is the ratio of the change in
position of an object over a period of
time.
• Acceleration describes a change in
velocity of an object.
Acceleration
• What may cause an object to
experience a change in velocity?
– Force
• Forces are often described as a push or pull.
• A force may cause an object to speed up.
– Acceleration (positive)
• A force may cause an object to slow down.
– Acceleration (negative) or deceleration
• A force may also cause an object to change
direction.
Acceleration
• Force
• Force is a vector
– It has magnitude
– It has direction
• A force may also cause an object to change
direction.
– This may or may not include a change in magnitude
Types of Forces
• Gravitational
• Electromagnetic
• Normal
• Frictional
• Tension
Force
• Force is a vector quantity, therefore it
has both magnitude and direction.
Force
• In the English system, we start with
pounds and derive a unit of mass (the
slug) – 1 pound accelerates 1 slug at a
rate of 1ft/sec2
• In the metric system we start with mass
– what is the force that accelerates 1 kg
at a rate of 1m/sec2?
Force
• The SI unit for force is the Newton.
– 1 Newton is the amount of force required
to accelerate a 1 kg mass 1 m/s2.
– The Newton is a derived unit where:
1N = 1kg•m/s2
• Kg, m, second are fundamental units
Force
• 1 Newton is the amount of force
required to accelerate a 1 kg mass 1
m/s2.
– So 1N causes a mass to change its velocity
at a rate of 1m/sec.
– Example: A 1kg object is accelerated by a
1N force. If it starts with Vi = 0, what is Vf
after one second? Two? Four?
• Hint: a = 1m/sec2
The System and Environment
• The object of interest is called the
System.
• The area around the object is called the
Environment.
FN
System
Environment
Fg
Contact vs. Long Range
• Some forces act over distances while
others act only when two objects are in
contact with one another.
– Contact forces exist when two objects
are in contact with one another.
– Long-range forces act over distances
without a need for direct contact.
Electromagnetic forces and gravity are
long-range forces.
Free Body Diagram
FN
FN = Force of
Desk on Book
System
=
Fg
Fg = Force of
Gravity on Book
Free-Body diagrams provide a means by which all the external forces
acting on a system can be summarized and accounted for, and the
resultant vectors determined.
Free Body Diagrams
FN
FN = Force of
Desk on Book
System
=
5
kg
Fg
Is the book accelerating?
Fw = Force of
hanging mass
on Book
Fg = Force of
Gravity on Book
Newton’s 2nd Law
• Newton determined that the
acceleration of an object is directly
proportional to the force applied to
move it and inversely proportional to
the mass of the object.
• a = Fnet/m
Where F = Force in Newtons
m = mass of the object
a = acceleration of the object
Newton’s 2nd Law and Force vs.
Acceleration
• How does acceleration relate to force?
– As the force on an object increases, the
rate of acceleration will increase.
m2
m1
Acceleration
m2 > m1
Note: The slope of
the line in a F vs. a
graph will equal the
mass of the object.
The greater the
slope, the greater
the mass
Newton’s 2nd Law and
velocity vs. time (constant force)
• Newton’s 2nd Law indicates that a constant
force applied to an object will cause the
speed to change at a constant rate.
Note: Remember from
kinematics that the slope
of the line is equal to a.
Time
Newton’s 2nd Law
Force Constant / Increasing Mass
• If the applied force to a system is held constant and
the mass is increased from m1 to m2, what would a
velocity vs. time graph look like?
m1
m2
m2 > m 1
Time
As the mass increases, the rate of acceleration will decrease.
Newton’s 2nd Law
Mass Constant / Increasing Force
• If the mass is held constant and the force applied to
a system is increased from F1 to F2, what would a
velocity vs. time graph look like?
F2
F1
F2 > F1
Time
As the force increases, the rate of acceleration will increase.
Example: What is the rate of
acceleration?
• Two people are pushing a stalled car. The mass of
the car is 1850 kg. One person applies a 275 N force
while the other applies a 395 N force. A third force
of 560 N acts in in the opposite direction compared
to the two people. What is the acceleration of the
car?
Diagram the problem
Fnet = Fperson 1 + Fperson 2 – Fopposing force
State the Known and Unknowns
• What is known?
– Mass (m) = 1850 kg
– Force of person #1 (N) = 275 N
– Force of person#2 (N) = 395 N
– Opposing Force (N) = 560 N
• What is not known?
– Acceleration (a) = ?
Perform Calculations
• Fnet = Fperson 1 + Fperson 2 - Fopposing
Where:
o Fnet = ma
• Substitute for Fnet and solve for a:
o ma = Fperson 1 + Fperson 2
- Fopposing
o a = (Fperson 1 + Fperson 2
- Fopposing)/m
o a = (275 N + 395 N – 560 N)/1850 kg
o a = 0.059 m/s2
o If there was no opposing force, how would the rate
of acceleration change? It would increase.
o What do you think is the source of the opposing
force? Friction.
Key Ideas
• Force is a vector quantity that is a measure of the
magnitude of a push or pull in Newtons.
• Forces exist as contact or long range.
• Use free body diagrams to represent forces when
problem solving.
• Newton’s 2nd Law of Motion states that the rate of
acceleration of an object is proportion to the force
applied and inversely proportional to its mass.
– A constant force applied to an object will cause it to accelerate
at a uniform rate.
– As force increases, acceleration increases.
– As mass increases, acceleration decreases.