Transcript Chapter 11 Forces Laws of Motion

Chapter 11
Forces
Laws of Motion

Force and motion are connected.
– An object will have greater acceleration if
a greater force is applied to it.
– The mass of an object and the force
applied to it affect acceleration.
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Newton’s second law of motion
connects force, mass, and acceleration
in the equation acceleration equals net
force divided by mass
Laws of Motion

Friction—force that opposes motion
between two surfaces that are touching
each other
– Microwelds, areas where surface bumpers stick
together, are the source of friction.
– Friction between two surfaces that are not
moving past each other is called static friction.
– Sliding friction—force that opposes the motion of
two surfaces sliding past each other
– Friction between a rolling object and the surface
it rolls on is called rolling friction.
Laws of Motion

Air resistance that opposes the force
of gravity.
– The amount of air resistance depends on
an object’s shape, size, and speed.
– Terminal velocity—forces on a falling
object are balanced and the object falls
with constant speed
Air Resistance

Air Resistance
– a.k.a. “fluid friction” or “drag”
– force that air exerts on a moving object to
oppose its motion
– depends on:
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speed
surface area
shape
density of fluid
Air Resistance
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Terminal Velocity
– maximum velocity reached by a
falling object
Fair
– reached when…
Fgrav = Fair
– no net force
 no acceleration
 constant velocity
Fgrav
Air Resistance

Falling with air resistance
– heavier objects fall faster because
they accelerate to higher speeds
before reaching terminal velocity
Fgrav = Fair
– larger Fgrav
 need larger Fair
 need higher speed
Animation from “Multimedia Physics Studios.”
Gravity

Weight
– the force of gravity on an object
W = mg
W: weight (N)
m: mass (kg)
g: acceleration due
to gravity (m/s2)
MASS
WEIGHT
always the same
(kg)
depends on gravity
(N)
Gravity

Accel. due to gravity (g)
– In the absence of air resistance, all falling
objects have the same acceleration!
– On Earth: g = 9.8 m/s2
W
g
m
elephant
g
W
m
feather
Animation from “Multimedia Physics Studios.”
Gravity

Law of gravitation—any two masses exert an
attractive force on each other
– Gravity is one of the four basic forces that also
include the electromagnetic force, the strong
nuclear force, and the weak nuclear force.
– Gravity is a long-range force that gives the
universe its structure.
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Due to inertia, all objects fall with the same
acceleration regardless of mass.
Gravity
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Weight—gravitational force exerted on an object
– Weight decreases as an object moves away from Earth.
– Weight results from a force; mass is a measure of how
much matter an object contains.
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Objects in the space shuttle float because they
have no force supporting them.
Projectiles have horizontal and vertical velocities
due to gravity, and follow a curved path.
Acceleration toward the center of a curved path is
called centripetal acceleration; it is caused by
centripetal force, an unbalanced force.
Gravity

Gravity
– force of attraction between any two objects in
the universe
– increases as...
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mass increases
distance decreases
Gravity

Would you weigh more on Earth or
Jupiter?
– Jupiter because...
greater mass
greater gravity
greater weight
Newton’s Third Law

Newton’s third law of motion—to every
action force there is an equal and opposite
reaction force
– Action-reaction forces act on different objects
and differ from balanced forces.
– Rocket propulsion is based on Newton’s third
law of motion.
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Before it was discovered, the existence of
the planet Neptune was predicted based
on gravitational forces and Newton’s laws.
Newton’s Third Law
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Momentum—related to how much force is
needed to change an object’s motion;
momentum equals mass times velocity.
Law of conservation of momentum—
momentum can be transferred between
objects; momentum is not lost or gained in
the transfer.
Momentum

Momentum
– quantity of motion
p = mv
p
m v
p:
m:
v:
momentum (kg ·m/s)
mass (kg)
velocity (m/s)
Momentum

Find the momentum of a bumper car if it has a
total mass of 280 kg and a velocity of 3.2 m/s.
GIVEN:
WORK:
p=?
m = 280 kg
v = 3.2 m/s
p = mv
p = (280 kg)(3.2 m/s)
p
m v
p = 896 kg·m/s
Momentum
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The momentum of a second bumper car is 675
kg·m/s. What is its velocity if its total mass is
300 kg?
GIVEN:
WORK:
p = 675 kg·m/s
m = 300 kg
v=?
v=p÷m
p
m v
v = (675 kg·m/s)÷(300 kg)
v = 2.25 m/s
Conservation of Momentum
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Law of Conservation of Momentum
– The total momentum in a group of objects doesn’t
change unless outside forces act on the objects.
pbefore = pafter
Conservation of Momentum
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Elastic Collision
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Inelastic Collision
– KE is conserved
– KE is not conserved
Conservation of Momentum
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A 5-kg cart traveling at 1.2 m/s strikes a
stationary 2-kg cart and they connect. Find
their speed after the collision.
BEFORE
Cart 1:
p = 21 kg·m/s
m = 5 kg
v = 4.2 m/s
Cart 2 :
m = 2 kg
v = 0 m/s
p=0
pbefore = 21 kg·m/s
AFTER
Cart 1 + 2:
m = 7 kg
v=?
p
m v
v=p÷m
v = (21 kg·m/s) ÷ (7 kg)
v = 3 m/s
pafter = 21 kg·m/s
Conservation of Momentum
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A clown is shot out of a 250 kg cannon at 20
m/s. If the cannon moves backwards at 2 m/s,
how much does the clown weigh?
Given:
Clown:
m=?
v = 20 m/s
Cannon:
m = 250 kg
v = -2 m/s
Conservation of Momentum
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So…now we can solve for velocity.
GIVEN:
WORK:
p = -1000 kg·m/s v = p ÷ m
m = 250 kg
v = (-1000 kg·m/s)÷(250 kg)
v=?
v = - 4 m/s
p
(4 m/s backwards)
m v