Download Forces and Newton`s Laws

Forces and Newton’s Laws
Announcements:
•  CAPA due today at 10pm – we
postponed the due date, so you would
have the opportunity to go to the
helproom.
•  Next CAPA Assignment is available!
•  Beginning Material in Chap. 5 on Forces
and Newton’s Laws
Web page:
http://www.colorado.edu/physics/phys1110/phys1110_sp12/
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Last Wed Example
Set frequency to BA
Q. An object is dropped from an airplane flying at uniform
velocity (constant speed in a straight line). Neglecting air
resistance, the object will:
Since the plane is traveling at uniform
velocity, it is not accelerating. The
object only experiences acceleration
from gravity which is vertical so it will
stay under the plane.
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Clicker question 1
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Q. Who won the Superbowl yesterday?
A.  Denver Broncos
B.  New York Giants
C.  Colorado Avalanche
D.  New England Patriots
E.  Who cares?
21-17 Giants over Patriots
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Force
Force is a vector!
Because force is a vector the principle
called superposition of forces is true.
Superposition of forces
Suppose there are a bunch of forces acting on an
object. The vector sum of these forces is the net
force. Applying just this net force is the same as
applying all of the forces that add up to the net force.
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Analysis of force
What forces act on the weight?
We model weight as a simple block
The rope is a force in the negative x direction
Gravity is a force in the negative y direction
Rope
Friction is a force in the positive x direction
The normal force is the force of the ground on
the weight. It is perpendicular to the surface.
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Normal
Friction
Gravity
This drawing is called a free body diagram which
we use to show the forces acting on a body
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Analysis of force
Net force:
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Often separate vectors into
perpendicular components:
So in this case we have a net force of
Assume the weight is not moving. What is
the net force on the weight? 0. There is no net force.
and
so
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Newton’s first law
Although we might all agree that a stationary body has no
net force acting on it, this is also true for a body traveling at
constant velocity (magnitude and direction are constant).
Formulations of Newton’s first law
A body acted on by no net force
maintains the same velocity (can be 0)
A body moving at constant velocity
has no net force acting on it
A body in motion tends to stay in motion;
a body at rest tends to stay at rest
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Newton’s first law
But how can you say there is no net
force operating on the weight when it
is moving at constant velocity?
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It is true that the person exerts a force on the
weight through the tension in the rope. But if the
weight is moving at constant velocity, this force is
canceled by friction so there is no net force.
If you imagine the weight on ice it would sail along once
you got it started. It would require force to slow it down.
The tendency to keep moving is called inertia.
Sometimes Newton’s first law is called the law of inertia.
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Clicker question 2
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Q. A sailboat is being blown
across the sea at a constant
velocity. What is the direction
of the net force on the boat?
A.  Left ←
B.  Right →
C.  Net force is zero Boat is traveling at constant
velocity so the net force is 0.
D.  Down ↓
There are individual forces
E.  Up ↑
from gravity, wind, etc. but they
all add up (vectorially) to 0.
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Clicker question 3
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How large is the force of friction
on Skinney's feet compared to
the force of friction on Fatty's
feet?
A) FS > FF
B) FS = FF
C) FS < FF
FS
FRope on S
Skinney
FRope on F
FF
Fatty
FS = FR on S , FF = FR on F ,
 FS = FF
FR on S = FR on F

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Inertial reference frames
The person on the sailboat watching the shore go by and
the person on the shore watching the sailboat go by are in
two different reference frames. Neither one is preferred.
Newton’s first law implies there is no real difference
between zero velocity and constant (non-zero) velocity.
Reference frames which move at constant velocity
(including 0) are called inertial reference frames.
Newton’s laws work the same
in all inertial reference frames
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Inertial reference frames
Is the inside of a car an inertial reference frame?
When traveling at a constant speed in a straight line,
everything at rest will stay at rest so yes in this case.
When the car hits the brakes causing the passenger who is
not wearing a seat belt to hit his head on the dashboard, it
is not an inertial reference frame. The passenger’s head
is staying at rest while the car accelerates.
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Clicker question 4
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Q. Which of the following is an inertial reference frame?
A.  A car traveling at a constant 100 mph down a straight and
level road.
B.  A car in the process of crashing into a concrete barricade.
C.  A car traveling at a constant 20 mph around a curve.
D.  More than one of the above
E.  None of the above
In B and C, the car is accelerating (linear acceleration in B
and centripetal acceleration in C) so they are not inertial
reference frames. Objects inside the car will move relative
to the car with no apparent force applied.
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What does a force do?
Galileo
The concept that a body will
stay in motion if there is no
external force applied is
attributed to Galileo and stated
more explicitly by Newton.
Newton
If a net force is not required to keep a body moving
at constant velocity, then what does it do?
A force is required to change the velocity of a body!
What quantity deals with velocity change?
Acceleration!
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Newton’s second law
So, a net force causes an object to accelerate.
Does the amount of acceleration depend
on the object or just the amount of force?
Acceleration times time gives final velocity which (along
with angle) determines how far a projectile travels.
If you were to throw a gallon milk and a can of soda
(with the same force), which would travel farther?
Longest shot put (16 lb ball): 23 m
Longest baseball throw (1/3 lb ball): 136 m
Acceleration depends on force applied and mass of body.
Newton’s second law:
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Clicker question 5
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Situation 1: A constant force is applied for a short time to a
frictionless cart initially at rest. The cart acquires a final velocity vf.
Situation 2: The same constant force is applied for the same short
time interval to the same frictionless cart initially moving with
velocity v1. The final velocity in this case is v2. The change of
velocity Δv = v2 – v1 compared to the final speed in Situation 1 is…
A.  The same: Δv=vf
B.  Greater: Δv > vf
C.  Less: Δv < vf
D.  Depends on the
signs of v1 and v2
Masses and forces are the same so
acceleration is the same. The time
interval is the same and
is the same:
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Clicker question 6
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An astronaut floating weightlessly in orbit shakes a large iron anvil
rapidly back and forth. She reports back to Earth that
A: the shaking costs her no effort because the anvil has no inertial mass
in space.
B: the shaking costs her some effort but considerably less than on Earth.
C: although weightless, the inertial mass of the anvil is the same as on
Earth.
Just as it says! Mass is the same wherever
you are. It's a measure of inertia
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Clicker question 7
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A constant force is exerted on
a cart (initially at rest) on an
air track. Neglect friction.
The force acts for a short time and gives the cart a certain final speed. To
reach the same final speed with a force that is only half as big, the force
must be exerted on the cart for a time interval
A: four times as long as
B: twice as long as
C: equal to
D: half as long as
... that for the stronger force.
OR E: (Not enough information given)
Force causes acceleration = Δv/ Δt. If you want the
SAME Δv, with HALF the force, it'll take TWICE the
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Δt.
Clicker question 8
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A constant force is exerted for a
short time on a cart (initially at
rest) on an air track. This force
gives the cart a certain final
speed. The same force is exerted for the same length of time on another
cart, also initially at rest, that has twice the mass of the first one. The
final speed of the heavier cart is:
A: one-fourth
B: four times
C: half
D:double
E: the same as
….that of the lighter cart.
F = m Δv/ Δt... If you have the same force, and the same time,
but TWICE the mass, you'll get HALF the change in velocity.
Since we started from rest, it means v(final) is half.
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Force review
Force is a vector so superposition of forces is true (can
combine all forces into one net force using vector addition).
We draw a free body diagram to figure out the effect of
the various forces and to calculate the net force.
Newton’s 1st law: A body will stay at a constant velocity
unless acted upon by a net force.
Newton’s 2nd law:
. Can split:
&
A net force causes an acceleration which is
inversely proportional to the mass of the object
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