I. Mechanics
C. Newton’s Laws & Forces
AP Physics
Intro to Forces
Why do objects move?
Force: a push or pull on an object
Forces cause objects to accelerate
(speed up, slow down, change
direction)
Forces are VECTORS!
Force Diagrams
• A book rests on a table. Draw the
forces on the book:
Force Diagrams vs. Free Body
Diagrams
Diagram Practice
• Draw a force diagram and a free
body diagram for a monkey hanging
by one arm from a tree branch:
Newton’s Laws of Motion
• A long, long time ago, this philosopher/ scientist
guy Aristotle noticed that moving things around
him would eventually come to rest.
He believed that the
natural state was at
rest, and that forces
were needed to
keep things moving.
Newton’s Laws of Motion
Eventually, this
other scientist
guy, Galileo,
decided that
things in motion
(like the moon)
remained in
motion, and if
there was no
friction, then
everything else
would remain in
motion, too!
2. Newton’s First Law of Motion
(aka the Law of Inertia):
Every object continues in its
state of rest, or of uniform
velocity in a straight line, as
long as no net force acts on it.
Newton’s Laws of Motion
a. So, an object keeps doing what it’s
doing until a force is applied.
b. Inertia: the tendency of an object to
maintain its state of rest or uniform
motion; laziness
c. Mass: (kg) the quantity of matter in an
object, or the measure of inertia of an
object
d. Weight: the gravitational force on an
object
Newton’s 1st Law Practice
• A robot is accidentally fired out of a
spaceship . Diagram the forces acting
on the robot after he has been
launched from the ship.
• Describe the motion of the robot after
he has been launched.
Net Force
• Net force is the SUM
of the forces on an
object
• If the net force is
zero, the forces are
balanced and the
object does not
accelerate.
3. Newton’s Second Law of
Motion
a. What if an object’s velocity does change?
b. Acceleration is affected by Force on
the object and the object’s mass
OR:
Force is measured in Newtons, mass in
kilograms, and acceleration in m/s2
Working 2nd Law Problems
1. Identify the system being accelerated
2. Define a coordinate system
3. Identify forces by drawing a force or free
body diagram
4. Explicitly write ΣF=ma
5. Replace ΣF with the actual forces in your
diagram (separate eqns for x and y
motion)
6. Solve for unknowns, substitute, & calculate
Newton’s Second Law
Practice
1. Moe, Larry, and Curly
push on a 752-kg
boat that floats next
to a dock. They each
exert an 80.5-N force
parallel to the dock.
What is the
acceleration of the
boat if they all push in
the same direction?
2. What is the
acceleration of the
boat if Larry and
Curly push in the
opposite direction of
Moe’s push?
More Practice
3. In a grocery store, you push a 14.5 kg
cart with a force of 12.0 N. If the cart
starts at rest, how far does it move in
3.00 seconds?
Types of Forces: Gravity
a. Acceleration from gravity = g
b. Force of gravity:
Normal Force
a. Normal Force – acts perpendicular to
surface in contact with the object
b. The normal force is only as large as
the force of the object on the surface
Normal Force
• Derive an expression for the normal
force of a box on a flat table
Normal Force
• Derive an expression for the normal
force of a box sitting on a ramp
Normal Force
• Derive the normal force for the box in
the picture below. Ignore friction.
Friction
• Frictional forces oppose motion
Friction
Sliding friction/Kinetic friction:
a)
b) K = coefficient of kinetic friction (depends on
the surface – p. 90)
FN = normal force
Static friction:
a) Greater than kinetic friction
b)
Friction Practice
1. A 10-kg box rests on a ramp that is lying flat.
The coefficient of static friction is 0.50 and
the coefficient of kinetic friction is 0.30.
a. What is the maximum horizontal force that can
be applied to the box before it begins to slide?
b. What force is necessary to keep the box sliding
at constant velocity?
More Forces
Tension: a pulling
force from
ropes/strings;
assume they
have a mass of 0
kg
Tension Practice
• A 1,500 kg crate hangs from a crane cable.
– What is the tension in the cable when the crate is
motionless? (assume the cable has zero mass)
– Suppose the crane accelerates the crate
upward at 1.2 m/s/s. What is the tension in the
cable now?
Spring Forces (Hooke’s Law)
• The force exerted by a
spring is proportional to
how far the spring is
stretched
• F = -kx
F: force exerted by the spring
(N)
k: force constant of the spring
(N/m or N/cm)
x: displacement from
equilibrium (unstretched)
position (m or cm)
Hooke’s Law Practice
• A 1.50 kg object hangs motionless from a spring with
a force constant of k = 250 N/m. How far is the
spring stretched from its equilibrium length?
4. Newton’s Third Law of Motion
a. Where do forces come from?
b. For every action force, there is an equal
and opposite reaction force.
Forces act on different objects
Practice
• You rest an empty
glass on a table
a. Identify the forces on
the glass with an FBD
b. Are the forces equal
and opposite?
c. Are the forces an
action-reaction pair?
Why/why not?
Practice Problem
• A force of
magnitude 7.50 N
pushes three boxes
as shown. Find the
acceleration of the
system.
Practice Part 2
• A force of
magnitude 7.50 N
pushes three boxes
as shown. Find the
force that box 2
exerts on box 3.
Connected Objects
• A 5.0 kg object is
connected to a
10.0 kg object by a
string. If a pulling
force of 20 N is
applied to the 5.0
kg object:
• Assume a frictionless surface
a. What is the
acceleration of
the system?
b. What is the tension
in the connecting
string?
Pulleys
• Pulleys bend
the line of
action of the
force of
gravity
without
affecting
tension
• Pulleys are MAGIC!!!
• Pulleys have no mass,
no friction, and no
effect on tension
Pulley Practice
• Derive an
expression for the
acceleration due to
gravity of the
system, AND for the
tension in the string
Inclines
a. To resolve forces on an object on an incline,
choose the simplest frame of reference – tilt
axes with incline!
b. Gravity always directed toward center of
Earth
c. Normal force always perpendicular to
surface
Sample Problem
• How long will it take a 1.0 kg block
initially at rest to slide down a
frictionless 20.0 m long ramp that is at
a 15 degree angle with the horizontal?
• (hint: use forces to find acceleration!)
Friction and Inclines
• A 10-kg box rests on a ramp that is lying flat.
The coefficient of static friction is 0.50 and
the coefficient of kinetic friction is 0.30.
What is the friction force between the box
and the ramp if:
a. The ramp is at a 25 degree angle?
b. The ramp is at a 45 degree angle?