Transcript 2.Newtons_Laws

Dynamics
• Galileo
–An object will stay in motion unless friction is present.
–Friction acts between surfaces of objects slowing them
down.
• Inertia means “resistance to being accelerated”.
• Forces:
–pushes and pulls exerted on objects by other objects.
–Measured in pounds (lbs) or “S.I.” units of newtons (N)
– 1N is about equal to ¼ pound.
Newton’s First Law of Motion
(“Law of Inertia”)
• An object at rest or at some velocity will remain
at rest or at that velocity unless acted upon by an
external net force.
• An object is in static equilibrium if
– It is at rest.
– It is acted upon by no net external force.
• Forces are vectors
– I can pull 40 newtons east (or west)
– we add them the same way we added the
displacement vectors.
External Force vs. Internal Force
• External Forces on an object are forces applied
from outside the object.
• Internal forces are applied from within the
object.
– For example, If I pull on a book, the molecules I’m
touching are pulling in turn on molecules behind
them. These “intermolecular pulls” are “internal
forces”.
Mass and Weight
• Mass is a measure of the amount of material
in an object. (a “chemical” definition.)
– S.I. unit is kilograms (kg)
• The weight (w) of an object is the gravitational
force (Fg) exerted by the Earth on that object.
– Units of weight are newtons (N) (it’s a force)
– Near the Earth’s surface: w = Fg = mg,
• where m = object’s mass (kg)
• g = 10 (m/s)/s = 10 m/s2
• Please don’t confuse MASS with WEIGHT.
– It’s a very common error.
Calculations with Mass and Weight
• What is the weight of a block with a mass of 1 kg?
w = mg = (1 kg) (10 m/s2) = 10 N = 2.2 pounds.
(So: 1 kilogram weighs 10 newtons or 2.2 pounds)
• What is the force of gravity on this block due to the Earth?
Fg = w = 10 N = 2.2 pounds.
Remember:
• The force of gravity on an object and the object’s
weight are the same thing.
• The mass of an object and the object’s weight are
different things.
Which of the following are examples
of Static Equilibrium?
• A ball at its highest point after being tossed
in the air?
– No. The ball is stopped but it has a net force on it
equal to its weight.
• A book at rest on a table?
– Yes. The Earth pulls down on it, but the table
pushes back up on it. The net force on it is zero.
• A pendulum at the top of its swing?
– No. It has a nonzero net force due to its weight
and the tension in the string.
What is the Net Force on These Objects?
North
East
1.
10 N
5N
FNET = 5N West
5N
FNET = 5N East + 5N South
3N
8N
10 N
An Object Held up by a String
(example 1)
The object has a mass (m)
Suppose m = 1 kg.
1.
2.
3.
4.
5.
How many Forces are acting on the object?
What is the Net Force on the object?
What is the Force due to gravity on the object?
What is the Tension in the string?
Let’s go through the steps needed to solve this
problem.
Free Body Diagram
• The Free Body Diagram is a drawing to help us
visualize all of the forces acting on an object.
• You will use the Free Body Diagram throughout
your career in physics.
• To draw an FBD:
– Draw the object as a point
– Draw each force on the object as a vector starting from
the object.
T
– Example:
Fg = mg
Steps for solving a problem.
1. Draw the FBD
2. Sum up the forces as vectors to find FNET.
3. If the object is in Equilibrium, then set FNET
equal to zero (Applying Newton’s First Law).
4. Solve for the unknown (for example, the
tension in the string.)
Let’s apply these steps to the above problem.
Another Problem
(example 2)
• Suppose the same mass (m=1kg) is
suspended by two strings. What is the
tension in each string?
Apply the steps from the last slide.
Another Problem
(example 3)
• Suppose the object is suspended by two strings,
but they are each at an angle (θ = 45o).
• Does the tension change? If so, how?
θ
How do we find the
tension in the strings?
Newton’s Second Law
• Suppose FNET is not zero. What will happen to the object?
• The object will accelerate.
• Which will accelerate more under the same FNET :
– A heavy object or a light object?
• A light object.
• Newton’s 2nd Law of Motion:
Net Force = mass * acceleration: FNET = ma
• Can this be a new definition of mass?
• Mass is a measure of an object’s
– resistance to being accelerated or
– “inertia”
• We have just defined “inertial mass”.
Friction
• Force acting between two surfaces in contact.
• Static Friction: Object on surface is not moving.
– Friction acts in the direction opposite to the sum of the
other forces applied parallel to the surface.
• Kinetic Friction: Object is in motion
– Friction acts in the direction opposite to the motion.
– Friction will always act so as to slow down the object.
• Air Resistance:
– Friction between the surface of an object and the air as
the object moves.
– Air resistance increases with increasing speed.
Example
• A crate with a mass of 2 kg is pushed along a
surface with a force of 10N to the east. The
surface exerts a frictional force of 4N on the
object.
–
–
–
–
What is the net force on the crate?
What is the acceleration of the crate?
How fast is the crate moving after 3 seconds?
What distance has the crate been pushed after 3
seconds?
• Always start with a Free Body Diagram.
Recipe for Solving Problems using
Newton’s Second Law
1. Identify known and unknown quantities in the
problem.
2. Draw a free body diagram for each object in the
problem.
3. Using the FBD, write an expression for the net
force on each object.
4. Set the expression for the net force on each
object equal to that object’s mass times its
acceleration: (FNET = ma)
5. Solve for unknowns in the problem.
A More Complicated Example
•
A cart of mass (m1) is on a table attached to
one end of a string running over a pulley.
The other end of the string is attached to a
mass (m2). which hangs out beyond the
table top. (Neglect friction)
a. What is the acceleration of the cart (m1)?
b. What is the acceleration of the mass (m2)?
c. What is the tension (T) in the string?
(Assume we know m1 and m2; we can put
numbers in later.)
• What’s the first thing we do to solve this
problem?
• We must make a Free Body Diagram for
EACH OBJECT in the system.
Pressure
• Pressure = Force applied over an area divided by
the area: P = F/A
• Example:
– Standing on your feet:
• What is the force of gravity acting on you?
• How would you calculate the pressure exerted on the floor?
– Standing on your toes:
• What is the force of gravity acting on you?
• How would you calculate the pressure exerted on the floor?
– Does standing on your feet or on your toes feel any
different?
– Pressure is a measure of the intensity of a force.
Why do All Objects Fall at the Same Rate?
• What is the net force on a free falling object?
FNET = mg
• What do we get if we apply Newton’s Second
Law to such an object?
FNET = ma
• So: mg = ma
• And: g = a
• So the object falls with an acceleration equal to
10 m/s2 regardless of its mass.
Air Resistance and Terminal Velocity
• As an object falls
– What happens to the upward force of air resistance?
• Increases because speed increases.
– What happens to the force due to gravity?
• Remains the same
– What happens when the force due to air resistance equals
the force due to gravity?
• FNET = 0; Object falls at constant (terminal) velocity.
– If you are falling, how can you change your terminal
velocity?
• Expose more area downward to increase air resistance; reduce
terminal velocity.
• Expose less area downward to decrease air resistance; increase
terminal velocity.
Newton’s Third Law
• Forces on objects are exerted by other objects.
• “Whenever an object exerts a force on a second
object, the second object exerts an equal and
opposite force back on the first object.”
– We call these forces “action-reaction pairs”.
• Question: Can these forces cancel out?
– NO. They are acting on different objects.
– Forces can only cancel when acting on the same object.
• Can a Free Body Diagram include both forces in an
action-reaction pair?
– NO. A free body diagram is made for one object and
includes only the forces acting on that object alone.
The “Normal Force”
• When an object is pressed against a surface, the surface
pushes back on the object with a force that is
perpendicular (or “normal”) to the surface. We call this
force the “normal force”.
Book resting on a table;
the table pushes
upward, normal to the
table’s surface.
Book on an inclined
surface; the slanted surface
pushes back normal to the
slanted surface.
How many types of Forces have we
seen so far?
•
•
•
•
Applied Force – “pushing/pulling” by hand.
Gravitational Force (or “weight”) = mg
Tension – applied by a rope or string
Frictional force – applied by a surface to an object,
acting parallel to the surface.
• Normal Force applied by a surface to an object,
acting normal to the surface.
What Forces act on a Balloon
Pressed Against a Wall?
What would a Free Body Diagram of the balloon
look like?
People, Scales and Tables
• Suppose I stand on a Scale while pushing upwards
on a table. How will the scale read?
– If I push up on table, it pushes down on me.
– Greater than my weight. Do a Free Body Diagram.
• Suppose I stand on a Scale while pushing down on
a table. How will the scale read?
– If I push down on table, it pushes up on me.
– Less than my weight. Do a Free Body Diagram.
Can the Third Law cause Objects to Move?
• Yes. Examples:
– I can push myself off the wall.
– A balloon forces air out one end; the air forces balloon
forward.
– Car thrusting air one way is propelled the other way.
• How does a car move? Motion is transmitted from:
– Engine to Transmission to Wheels
– Wheels exert a backward force on the road
– The road exerts an equal and opposite forward force
on car, moving it forward.
The Third Law, The Second Law,
and a Couple of Carts.
• A cart hits a stationary cart of the same mass. How
do you expect them to move after the collision?
• A cart hits a heavier stationary cart. How do you
expect them to move after the collision?
• A cart hits a lighter stationary cart. How do you
expect them to move after the collision?
The Horse Cart Problem
The Horse-Cart Problem
(cont’d)
• Let’s look at the forces
– On the Horse ONLY
– On the Cart ONLY
– On the Horse and Cart taken as ONE OBJECT
Forces Involved
• The “Action Forces”:
 Let P = Force by Horse Pulling on Cart (Right)
 Let F = Force by Horse Pushing on Ground (Left)
 Let f = friction by Ground acting on Cart (Left)
• What are the Reaction Forces to these Action Forces?
 P = Force by Cart pulling back on Horse (Left)
 F = Force by Ground pushing back on Horse (Right)
 f= friction force by Cart on Ground (Right)
FBD on Cart
f
FBD on Horse
P
FNET = P – f
= MC a
P
F
FNET = F – P
= MH a
FBD on Horse + Cart
f
F
FNET = F – f
= (MC+MH) a
Forces Involved
FBD on Cart
f
FBD on Horse
P
FNET = P – f
= MC a
P
F
FNET = F – P
= MH a
FBD on Horse + Cart
f
F
FNET = F – f
= (MC+MH) a
• Starting from Rest, to get moving:
– The Horse must __________ on the cart to overcome _________.
– The Horse must ________ on the ground to overcome ________.
• How are the FBD’s on the Cart and Horse equivalent to the
FBD on both?
• Once moving what must the horse do to keep moving at
constant velocity?
Numerical Problem
•
•
•
•
•
Mass of Cart = 800 kg
Mass of Horse = 400 kg
Force of Friction = 1000 N
With what force must the horse pull on the cart?
If the Horse pushes on the ground with a force
of 1600 N what will be the acceleration?
• With what force must the horse push on the
ground to stay at constant speed?
A Closer Look at Friction
• What causes friction between two surfaces?
– Surface Characteristics (Roughness, Stickiness)
– Force with which surfaces are pressed together.
• We specify these properties by:
– μ = measure of surface roughness or stickiness
– N = Normal Force between the surfaces.
• Static Friction (fs): equals sum of other forces
parallel to surface until a threshold is reached where:
fs = μsN.
So we say: fs ≤ μs N
• Kinetic Friction (fk): Once you get moving it’s easier
to stay moving: fk = μk N ;
μk < μs
• μk , μs : “Coefficients of static or kinetic friction.”