Transcript Chapter 4 notes

Chapter 4
Dynamics:
Forces Notes
Anything in red is extra
examples and information
necessary for
understanding concepts,
but not necessary to write
4-1 Force
A force is a push or pull. An
object at rest needs a force
to get it moving; a moving
object needs a force to
change its velocity.
Force is a vector.
Measured in Newtons (N)
1 N = 1 kgm/s2
Forces are always at work, even on stationary objects.
• Fields existing in space can be used to explain all interactions
• Forces are interactions between objects that don’t actually touch
• All forces are determined by the 3 fundamental forces
– Gravitational
– Electroweak (formerly electromagnetic and nuclear weak) – essentially
forces existing between charges
– Strong – force that holds a nucleus together
• Forces act through “contact” or at a distance.
• Contact force: result from actual physical contact with
objects (no real such thing - electroweak)
• Examples?
• Field force or long-range:
no contact occurs
but the force exists
• Examples?
• Forces associated with solids
– Normal (N, Fn)
The force between two solids in contact that prevents them
from occupying the same space. The normal force is directed
perpendicular to the surface. A "normal" in mathematics is a
line perpendicular to a planar curve or surface; thus the name
"normal force".
– Friction (ƒ, Fƒ)
The force between solids in contact that resists their sliding
across one another. Friction is directed opposite the direction
of relative motion or the intended direction of motion of
either of the surfaces.
– Tension (T, Ft)
The force exerted by an
Tension
object being pulled
upon from opposite
ends like a string, rope,
Tension
cable, chain, etc.
Tension is directed
along the axis of the object.
– Elasticity (Fe, Fs)
The force exerted by an object under deformation (typically
tension or compression) that will return to its original shape
when released like a spring or rubber band. Elasticity, like
tension, is directed along an axis (although there are
exceptions to this rule).
– Centripetal – a net force that makes an object travel in a
circular or curved path (typically due to
tension from a
central axis)
• Forces associated with fluids. Fluids include
liquids (like water) and gases (like air).
– Buoyancy (B, Fb)
The force exerted on an object immersed in a
fluid. Buoyancy is usually directed up
(although there are exceptions to this rule).
– Drag (R, D, Fd)
Friction in a fluid.
– Lift (L, Fl)
The force that a moving fluid exerts as it flows around an
object; typically a wing or wing-like structure, but also golf
balls and baseballs. Lift is generally directed perpendicular to
the direction of fluid flow (although there are exceptions to
this rule).
– Thrust (T, Ft)
The force that a fluid exerts when
expelled by a propeller, turbine,
rocket, squid, clam, etc. Thrust is
directed
opposite the direction the fluid is
expelled.
• Forces associated with physical phenomena.
– Gravity or Weight (Fg, W)
– Electrostatic Force (FE)
The attraction or repulsion between charged bodies.
Experienced in everyday life through static cling and as the
explanation behind much of basic chemistry.
– Magnetic Force (FB)
The attraction or repulsion between charged bodies in motion.
Experienced in everyday life through magnets
and as the explanation behind why
a compass needle points north.
• Fictitious forces. Apparent forces objects experience in an
accelerating coordinate system (i.e. accelerating car, airplane,
spaceship, elevator, rides). Fictitious forces are a consequence of
trying to keep up with an accelerating environment and are not
exerted by another object like real forces.
– Centrifugal Force
The force experienced by all objects in a rotating coordinate
system that seems to pull them away from the center of
rotation.
– Coriolis Force
The force experienced by moving objects in a rotating
coordinate system that seems to deflect them at right
angles to their direction of motion.
– "G Force"
Not really a fictitious force but rather gravity-like
sensation experienced by objects in an accelerating coordinate system.
Wind
direction
Wind flows into area of low pressure and
deflected to the right in N. Hemisphere –
counterclockwise rotation of hurricanes
• Force Diagram: shows all forces (as vectors) acting
in a situation.
N
• Free Body Diagram: shows the forces (as vectors)
that act on one object of interest.
Net force
• The net force is the sum of all the forces
• Equilibrium: ∑F = 0
– Static equilibrium vs. Dynamic equilibrium
• Objects will accelerate in the direction of a nonzero net
force
• Finding net force: resolve all forces into vector
components and add the vectors as normal
4-7 Solving Problems with Newton’s Laws—
Diagrams
1. Draw a sketch.
2. For one object, draw a free-body
diagram, showing all the forces
acting on the object. Make the
magnitudes and directions as
accurate as you can. Label each
force. If there are multiple objects,
draw a separate diagram for each.
© 2014 Pearson Education, Inc.
Free-Body
Newton’s Laws Notes
Anything in red is extra
examples and information
necessary for
understanding concepts,
but not necessary to write
18 Nov.
Newton’s First Law of Motion
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.
Inertial reference frames:
• An inertial reference frame is one in which Newton’s first law is valid.
• Rotating and accelerating frames are NOT inertial.
• Relativity Principle: the basic laws of physics are the same in all
inertial reference frames, no one reference frame is better than another
when viewed
from train
when viewed
from ground
• Fictitious forces appear in accelerating reference frames.
• Example: Earth is rotating, so not inertial
• Example: An accelerating elevator
• Example: An accelerating car
The Theory of Relativity
• Special theory of relativity – inertial reference frames
– Relativity principle - there is no way for an observer to
determine if a given reference frame is at rest or moving at
constant velocity in a straight line
• General theory of relativity – accelerating reference frames and gravity
– Equivalence principle – no observer can determine by experiment whether
he or she is accelerating or in a gravitational field
Conceptual Practice Problems
1. An astronaut is always tethered to
the space shuttle when outside of
the shuttle. Why?
2. A school bus comes to a sudden stop, and all of the
backpacks on the floor start to slide forward. What force
causes them to do that? Explain the situation and draw a
free-body diagram.
Newton’s Second Law of Motion
Acceleration is proportional to force and inversely proportional to mass.
*slightly different on equation sheet
Inertial Mass
Mass is the measure of inertia of an object. In the SI system, mass is
measured in kilograms.
Mass is not weight:
• Mass is a property of an object. Weight is the force exerted on that object
by gravity. Weight = mass x gravity
• Pounds are a unit of Force, not mass
• If you go to the moon, whose gravitational acceleration is about 1/6 g,
you will weigh much less. Your mass will be the same.
• Gravitational mass = when one body attracts another (universal law of
gravitation)
Weight and Normal Force
Weight is the force exerted on an object by gravity. Close to the surface of
the Earth, where the gravitational force is nearly constant, the weight is:
The force exerted
perpendicular to a surface
is called the normal force.
It is exactly as large as
needed to balance the force
from the object (if the
required force gets too big,
something breaks!)
(4-3)
Newton’s Third Law of Motion
• Whenever one object exerts a force on a
second object, the second exerts an equal
force in the opposite direction on the first.
• The forces are acting on DIFFERENT objects
Solving Problems with Newton’s Laws
1. Draw a sketch and/or freebody diagram, showing all
the forces acting on the
object.
Make the magnitudes and
directions as accurate as you
can. Label each force. If there
are multiple objects, draw a
separate diagram for each.
3. Resolve vectors into components.
4. Apply Newton’s second law to
each component.
5. Solve.
Practice Problems
4-3. What net force is required to bring a 1500kg car to rest from a speed of
100km/h (28m/s) within a distance of 55m?
4-6. A 10.0kg box is resting on a frictionless horizontal surface. A)
Determine the weight and normal force. B)Your friend pushes down on it
with a force of 40.0N. Again determine the weight and normal force. C) If
your friend now pulls up with a force of 40.0N, what is the normal force?
4-7. What happens when a person pulls upward with a force of 100.0N on a
10.0kg box?
4-11. Now your friend pulls on the 10.0kg box with a force of 40.0N but at
an angle of 30.0°. Calculate the a) Acceleration of the box, and b) the
normal force (ignore friction).
4-12. Two boxes are connected by a lightweight cord and are resting on a
table. The boxes have masses of 12.0kg and 10.0kg. A horizontal FP of
40.0N is applied by a person to the 10.0kg box. Find the a) acceleration of
each box and b)tension in the cord between the two boxes.
4-13. Masses suspended over pulleys are known as an
Atwood’s Machine . Consider an elevator (m1=850kg)
and its counterweight (m2=1000kg). When 4 passengers
are in the elevator m1=1150kg. Calculate the acceleration
of the elevator with the passengers and the tension in the
cable.
Finding her car stuck in the mud, a bright physics student ties a strong rope
to the back bumper of the car and the other end to a tree. She pushes the
midpoint of the rope with her maximum effort which she estimates to be
Fp=300N. The car just begins to budge with the rope at an angle θ which
she estimates to be 5°. With war force is the rope pulling on the car?
Neglect the mass of the rope.
Chapter 4
4 Dec.
Dynamics:
Friction and Inclined Plane Notes
Assignment 2:
• Misconception questions
• Q9,10,20
• P9,12,17,20,21,24, 25,46,49
Kinetic Friction
Kinetic—sliding—friction:
μk is the coefficient of kinetic friction, and is different
for every pair of surfaces.
*slightly different on equation sheet
This table lists the measured values of some coefficients of friction. Note
that the coefficient depends on both surfaces.
© 2014 Pearson Education, Inc.
Static friction is the frictional force between two surfaces that are not
moving along each other. Static friction keeps objects on inclines from
sliding, and keeps objects from moving when a force is first applied.
*slightly different on equation sheet
The static frictional force increases as the applied
force increases, until it reaches its maximum.
Then the object starts to move, and the kinetic
frictional force takes over.
Inclined Planes
An object sliding down an incline has three forces acting on it:
the normal force, gravity, and the frictional force.
• The normal force is always perpendicular to the surface.
• The friction force is parallel to it.
• The gravitational force
points down.
If the object is at rest, the forces are
the same except that we use the static
frictional force, and the sum of the
forces is zero.
Practice Problems
4-16. A 10.0kg box rests on a horizontal floor. The coefficient of static
friction is µs = 0.40 and the coefficient of kinetic friction is µk = 0.30.
Determine the force of friction Ff, acting on the box if a horizontal external
applied for of FA is exerted on it of magnitude a) 0N, b)10N, c)20N, d)38N,
and e)40N. Under which applied force(s) does the box accelerate and by
how much?
4-19. Your little sister wants a ride on her sled. If you are on flat ground,
will you exert less force if you push her or pull her? Assume the same angle
in each case. Explain.
4-20. Two boxes are connected by a cord running over a pulley. The µk =
between box I and the table is 0.20. Find acceleration of the system which
will have the same magnitude for both boxes assuming the cord doesn’t
stretch. As box II moves down, box I moves to the right.
5.0kg
2.0kg
4-21. A skier has just begun descending a 30 degree slope. Assuming the
µk = 0.10, a) draw a free body diagram, then b) calculate her acceleration
and c) the speed she will reach after 4.0s.