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Forces and Motion
Chapters 11-12
Frame of reference
• A system of objects that are not moving with
respect to one another
– To describe motion accurately and completely, a
frame of reference is necessary.
Relative Motion
• Movement in relation to a frame of reference.
Distance v. Displacement
Distance
• The length of the path between two points
– Scalar quantity
– SI unit = meter (m)
– Ex. 100 meters
Displacement
• The direction from the starting point and the length of a
straight line from the starting point to the ending point.
– Vector Quantity
– SI unit = meter (m)
– Ex. 100 meters East
Combining Displacements
• Vector
– A quantity that has magnitude and direction
• Magnitude can be size, length, or amount
– Vectors are represented by arrows
• Length of the arrow shows magnitude
• The way the arrow is pointing shows direction
• Displacements are combined using vector
addition
– Vector addition is the combining of vector magnitudes
and directions
Combining Displacements (cont.)
• Vectors that have the same direction are
added together.
• Vectors that are in different directions are
subtracted
Combining Displacements (cont.)
•When two or more displacement vectors have
different directions, they are combined by
graphing.
Combining Displacements (cont.)
• The vector in red is called the resultant vector
– A resultant vector is the SUM of two or more
vectors
– The resultant vector WILL ALWAYS point from the
starting point to the ending point
Instantaneous v. Average Speed
• Average speed is for the entire time of the trip
• Instantaneous speed is the speed at a
particular instant
NOTE: both are scalar quantities!!!
Speed
• Average Speed
– The total distance traveled, d, divided by the time,
t, it takes to travel that distance
– SI unit is meter per second (m/s)
Problems
While traveling on vacation, you measure the
times and distances traveled. You travel 35
kilometers in 0.4 hour, followed by 53
kilometers in 0.6 hour. What is your average
speed?
Problems
A person jogs 4.0 kilometers in 32 minutes,
then 2.0 kilometers in 22 minutes, and finally
1.0 kilometer in 16 minutes. What is the
jogger’s average speed in kilometers per
minute?
Problems
A train travels 190 kilometers in 3.0 hours, and
then 120 kilometers in 2.0 hours. What is its
average speed?
Speed (cont.)
• Instantaneous speed
– V, is the rate at which an object is moving at a
given moment in time
– Si unit is meter per second (m/s)
Graphing Motion
• To graph speed, you place time (independent
variable) on the x-axis, and distance
(dependent variable) on the y-axis
– These graphs are called distance v. time graphs
– The slope on the graph equals the speed
• A positive slope shows positive direction
• A negative slope shows opposite direction
• A horizontal slope shows standing still
– The steeper the slope is, the higher the speed
Velocity
• Velocity is both speed and direction
– Therefore velocity is a?????
Vector Quantity!
• A long vector shows a faster speed
• A short vector shows a slower speed
• Velocities are added using vector addition
• SI unit is meter per second (m/s)
• Average velocity = displacement/time ( Δx / t )
– Displacement = vector quantity from starting point to
ending point
Are distance and displacement the same???
Problems
A kayak is moving across a stream that is
flowing downstream at a velocity of 4 km/h.
The kayak’s velocity is 3 km/h. What is the
magnitude of the kayak’s velocity relative to
the river bank?
Acceleration
• Acceleration, a, is the rate at which velocity
changes
– Acceleration = ANY CHANGE IN velocity
• Magnitude
• Direction
– Increase in velocity = positive acceleration
– Decrease in velocity = negative acceleration
– SI derived unit is meters per second squared (m/s2)
– Acceleration is a vector quantity!
Note: “change in” = delta (Δ)
Constant Acceleration
• Constant acceleration is a steady change in
velocity
– Ex. Taking off in an airplane or stopping at a red
light. Both are constant acceleration.
• Which one is positive and which is negative?
Calculating Acceleration
• If change in velocity is positive than
acceleration is positive
• If change in velocity is negative, than
acceleration is negative
Problems
An airplane travels down a runway for 4.0
seconds with an acceleration of 9.0 m/s2.
What is its change in velocity during this time?
Problems
A car traveling at 10 m/s starts to decelerate
steadily. It comes to a complete stop in 20
seconds. What is its acceleration?
Problems
A ball rolls down a ramp, starting from rest.
After 2 seconds, its velocity is 6 meters per
second. What is the acceleration of the ball?
Graphing Acceleration
• Acceleration is graphed by putting time
(independent variable) on the x axis, and
velocity or speed (dependent variable) on the
y axis.
• The slope of the graph is equal to the
acceleration
– Positive slope = positive acceleration
– Negative slope = negative acceleration
Graphing Acceleration (cont.)
• Constant acceleration is
represented by a
straight line on a speed
v. time graph.
– Constant acceleration is
ALWAYS linear on a
speed v. time graph
• Constant acceleration is
represented by a curved
line on a distance v.
time graph
Instantaneous Acceleration
• Instantaneous acceleration is how fast a velocity is
changing at a specific instant
–Acceleration is rarely constant, and motion is rarely in a
straight line.
–Acceleration involves a change in velocity or direction or
both, so the vector of acceleration can point in any direction.
–The vector’s length depends on how fast velocity is
changing.
–For an object that is standing still, the acceleration vector is
zero.
Force
• Force is a push or pull that acts on an object
• Forces cause:
– A resting object to move
– A moving object to accelerate
Measuring Force
• A Unit of Force
– Newton (N)
• 1 kilogram to accelerate at a rate of 1 meter per second
each second
• 1 N = 1 kg·m/s2
Combining Forces
• The net force is the overall force acting on an
object after all of the forces are combined.
– Same direction – add
– Opposite direction – subtract
• When the net force = zero
– Forces are balanced
• When the net force ≠ zero
– Forces are unbalanced
– Forces add up to resultant force
Friction
• Friction is a force that opposes the motion of objects
that touch
• Static friction
– Acts on objects that are at rest
– Acts in opposite direction of applied force
• Dynamic (sliding) Friction
– Acts on moving objects as they slide over a surface
– Dynamic friction < static friction
• Coefficient of Friction
– The ratio of the frictional force compared to the normal
force (force due to gravity)
– μ = Ff/FN
Gravity
• Gravity is a force that acts between any two
masses
– Attractive force
– Causes objects to accelerate as they are pulled
toward center of mass
• Terminal velocity – force of air resistance = force of
gravity
– Can act over large distances
Free Fall
• Free fall is the movement
of an object toward Earth
due to the pull of gravity
– For every second of fall
time, the object’s velocity
increases by 9.8 m/s
– Therefore, acceleration due
to gravity, g, is 9.8m/s2
t=0s
v = 0 m/s
t=1s
v = 9.8 m/s
t=1s
v = 9.8 m/s
t=1s
v = 9.8 m/s
Problems
A child drops a ball from a bridge. The ball
strikes the water under the bridge 2.0 seconds
later. What is the velocity of the ball when it
strikes the water?
Problems
A boy throws a rock straight up into the air. It
reaches the highest point of its flight after 2.5
seconds. How fast was the rock going when it
left the boy’s hand?
Projectile Motion
• Projectile motion is the motion of a falling
object (projectile) after it is given an initial
forward velocity
– Only two forces act on a projectile
• Air resistance
• Gravity
Famous Men In Physics
• Aristotle
– Incorrectly proposed that a force is required to keep
an object moving at a constant speed
• Galileo
– Studied how gravity produces constant accleleration
• Rolled balls down ramps yo!
• Concluded that moving objects not subject to friction or any
other force would continue to move forever
• Newton
– First defined mass and force
– Introduced three laws of motion
Newton’s Laws of Motion
• First Law of Motion
– An object in motion stays in motion and an object at rest
stays at rest unless acted upon it by another object
• Inertia – the tendency of an object to resist a change in motion
– Second Law of Motion
• The acceleration of an object is directly proportional to the net
force acting on it and the mass of the object
• Mass is a measure of the inertia of an object
• ΣF=ma; ΣF – net force, m – mass, a – acceleration
• Third Law of motion
– For every action there is an opposite but equal reaction
Problems
An automobile with a mass of 1000 kilograms
accelerates when the traffic light turns green.
If the net force on the car is 4000 newtons,
what is the car’s acceleration?
Problems
A boy pushes forward a cart of groceries with
a total mass of 40.0 kg. What is the
acceleration of the cart if the net force on the
cart is 60.0 N?
Problems
What is the upward acceleration of a
helicopter with a mass of 5000 kg if a force of
10,000 N acts on it in an upward direction?
Problems
An automobile with a mass of 1200 kg
accelerates at a rate of 3.0 m/s2 in the forward
direction. What is the net force acting on the
automobile? (Hint: Solve the acceleration
formula for force.)
Problems
A 25-N force accelerates a boy in a wheelchair
at 0.5 m/s2. What is the mass of the boy and
the wheelchair? (Hint: Solve Newton’s second
law for mass.)
Weight and Mass
• Mass
– Measure of inertia
– Amount of material an object contains
• Weight
– The force of gravity on the mass of an object
– Weight = mass times acceleration due to gravity
Problems
If an astronaut has a mass of 112 kilograms,
what is his weight on Earth where the
acceleration due to gravity is 9.8 m/s2?
Momentum
• Momentum is the product of an object’s mass
and its velocity
– Objects with large momentums are harder to stop
than those with smaller momentums
– All objects at rest have zero momentum
– Mass is in kg; velocity is in m/s
– SI unit for momentum is kg∙m/s
Problems
Which has more momentum, a 0.046-kilogram
golf ball with a speed of 60.0 meters per
second, or a 7.0-kilogram bowling ball with a
speed of 6.0 meters per second?
Conservation of Momentum
In a closed system, the loss of momentum of
one object equals the gain in momentum of
another object— momentum is conserved.
• A closed system means other objects and forces
cannot enter or leave a system
– Objects within a closed system can exert forces on one
another
– According to the law of conservation of momentum,
if no net force acts on a system, then the total
momentum of the system does not change
Universal Forces
There are four fundamental forces in the
universe
•
•
•
•
Electromagnetic
Strong Nuclear
Weak Nuclear
Gravitational
Electromagnetic Force
• Electric and magnetic force are two different
aspects of the electromagnetic force
– Electric force and magnetic force are the only
forces that can both attract and repel
• Opposite charges attract
• Like charges repel
• Electromagnetic force is associated with
charged particles
Nuclear Forces
• Strong Nuclear Force
– Holds a nucleus of an atom together
– Strong force that acts on the protons and
neutrons
• Weak Nuclear Force
– An attractive force found in certain types of
radioactive processes
– Is found inside protons and neutrons
Gravity
• Gravitational force acts between any two
masses
– Force is dependant on mass and distance
– Force decreases and distance between objects
increases
– The weakest of the universal forces