Download Ch 5 Forces

Ch 5 Forces
Questions: 3, 7, 11
Problems: 1, 7, 15, 19, 24, 27, 35, 45,
51, 55, 58, 59, 76
Force – What causes an object to accelerate.
Forces are not objects. They are actions.
examples:
car running into a telephone pole
The telephone pole is just a telephone pole. When
the car comes into contact with the pole, the pole
acts on the car, causing the car to stop.
Ball falling to Earth
The Earth’s pull on the ball is what accelerates
a dropped ball.
Newtonian Mechanics
Newtonian mechanics is a set of rules that govern
how forces accelerate objects. Newtonian
mechanics are not always valid.
If the speed of an object is a noticeable fraction of
the speed of light, we replace Newtonian
mechanics with Einstein’s theory of relativity.
If the interacting objects are very small, we replace
Newtonian mechanics with quantum mechanics.
Newton’s First Law
Before Newton, people thought that an object at rest was
in its natural state. It would take some outside force to
keep an object moving at constant velocity.
However in the absence of frictional and drag forces, an
object with a set velocity will keep that velocity
indefinitely.
Newton’s 1st law of motion. If no net force acts on an
object, the object’s velocity cannot change.
“Objects at rest, stay at rest. Objects in motion, continues
the same motion, as long as there are no net forces.”
Unit of Force (Newton)
1 N is defined as the force needed to give a 1 kg object,
an acceleration of 1 m/s2.
A force can be assumed to be in the direction of the
acceleration it produces.
We can prove by experiment that forces have
magnitudes and directions, thus they are vectors.
Do this by balancing out some non-parallel forces with
another force.
Since forces are vectors, we can combine 2 or
more forces to find the resultant force, or net
force.
The net force is a single force that has the
same effect as the individual forces combined.
Newton’s 1st law states that if there is no net force,
there is no acceleration. There can be forces, they
just have to have a vector sum of zero for there to be
no acceleration.
Note on frames of reference
An inertial frame of reference is one where Newton’s Law
are held true.
In noninertial reference frames, Newton’s laws of motion
are not true. These reference frames are themselves
accelerating.
examples:
taking into account, the rotation of the Earth
performing an experiment in an acceleration elevator
We the rotation of the Earth needs to be considered
when a projectile is launched and covers a large
distance.
For smaller distances, the effects are negligible.
We will ignore the rotation of the Earth for the most
part and assume it is an inertial reference frame.
If you wanted to launch a missile across the ocean,
you would need to consider the rotation of the Earth.
Mass
Common definition: Mass has to do with the amount of
matter that an object has.
Quite often confused with weight and size.
Book definition: “Mass is the characteristic that relates a
force on a body to the resulting acceleration.”
mass = force/acceleration
Newton’s 2nd Law. The net force on an object is equal to
the product of the mass and the resulting acceleration.


Fnet ma
Mass is a scalar quantity that relates acceleration to force.
Related units of force, mass, and acceleration
SI
CGS
British
Force
Mass
Newton (N)
dyne
pound (lb)
kilogram (kg) m/s2
gram (g)
cm/s2
slug
ft/s2
1 N = kg m/s2
1 dyne = 1 g cm/s2
1 pound = 1 slug ft/s2
Acceleration
Force and acceleration are vector quantities.
Can write Newton’s 2nd Law in components.
Fnet, x = m ax
Fnet, y = m ay
Fnet, z = m az
Forces only affect the components of motion
that they are parallel to.
For example the force of gravity, only affects
the vertical motion.
Internal Forces
Sometimes when we are studying systems of masses, the
individual particles interact with each other.
The internal forces do not create an acceleration on the
system as a whole. They cancel each other out.
It is the net external force that accelerates a system of
particles.
Pretend you pull on a toy locomotive that is connected to
some train cars. The internal forces between train cars
cancel each other out and only the pull that you supply,
accelerates the train.
Newton’s 3rd Law
Forces always act in pairs.
“For every action, there is an equal and opposite reaction.”
Your standing on the Earth. You are exerting a force on the
Earth, while the Earth exerts an equal and opposite force
on you.


Remember vectors that are opposites, A and - A. They
have the same magnitudes, but are in opposite directions.
Examples of forces
Gravitational force – The force that one object exerts
by pulling on the other object. (One of the objects is
Fg
usually
the Earth)
When the Earth is the source of the gravitational
force, that force is the amount that the Earth pulls
the other object down towards its center.
The gravitational force is always directed towards
the center of the object in question. So for objects
on/near the Earth, the direction is downwards.
The gravitational force is related to the acceleration due to
gravity.
Thus the magnitude will be: |Fg| = m g, g = 9.8 m/s2
If up is positive, then in vector form:



2ˆ
ˆ
g
9
.
8
m
s
j
where
Fg
mgj mg
Gravitation
There is a chapter on gravitation later. In it we
will see that the acceleration due to gravity is
not always g = 9.8 m/s2.
The value of 9.8 m/s2 will work well enough
when particles are not experiencing huge
changes in elevation, so we will assume it is
constant for the next few chapters.
Weight
Weight is defined as the magnitude of the net
force required to prevent an object from
experiencing free fall.
Hold an rock in the air. The gravitational force
pulls the rock down. You push the rock up.
In an inertial frame of reference, the weight is
equal to the gravitational force.
W = Fg
W = mg
Weight is different from mass.
The mass of a body is an intrinsic property and
does not change.
The weight can be different.
A 7.2 kg bowling ball has a weight of 71 N on
the Earth.
The same ball has a weight of 12 on the moon.
Weight of Object on Inclined Plane
Fn
w
Fn
Fn
w
• Fn is the adjacent component of the weight.
• What about the opposite component?
opp
FN
FP
FN
FP
FN
w
w
FP, is the opposite (parallel) component of the
weight vector. It is parallel to the inclined plane.
This is the component of the weight that causes
the object to slide down the plane.
FP = W sin = mg sin
What happens when we increase from 0 to 90
degrees? Let mass = 50 kg.
FP = (50 kg)(9.8m/s2) sin
FP = (50 kg)(9.8m/s2) sin
FP = (50 kg)(9.8m/s2) sin
FP = (50 kg)(9.8m/s2) sin
FP = (50 kg)(9.8m/s2) sin
FP = (50 kg)(9.8m/s2) sin
FN
FP
FN
w
Normal Force
When a body is pressed against a surface, the
surface deforms and pushes back on the body with
a normal force, that is perpendicular to the surface.
Put a block that weighs 20 N on a table. The table
exerts a 20 N force up onto the block. If it wasn’t
for this force the block would accelerate through
the table.
F
N
Fg
Normal Forces
Normal forces are always perpendicular to the
surface, and object is pressed against.
Fn
Fn
Normal Forces
The Red block has mass, m
Fn = mg cos 0 = mg
Fn
Fn = mg cos
Fn
Trig trick
Fn
w
Fn
Fn
w
• Fn is the adjacent component of the weight
Normal Forces
Let the mass of the block
be 50 kg.
Fn
w = (50 kg)(9.8m/s2) = 490 N
Fn = (50 kg)(9.8m/s2) cos 30 = 424 N
Normal Forces
What happens when we increase from 0 to
90 degrees?
Fn = (50 kg)(9.8m/s2) cos
Fn = (50 kg)(9.8m/s2) cos 0 = 490 N
Fn = (50 kg)(9.8m/s2) cos 10 = 483 N
Fn = (50 kg)(9.8m/s2) cos 30 = 424 N
Fn = (50 kg)(9.8m/s2) cos 45 = 346 N
Fn = (50 kg)(9.8m/s2) cos 60 = 245 N
Fn = (50 kg)(9.8m/s2) cos 90 = 0 N
Fn
Friction – Will cover in chapter 6. Involves one
surface sliding, or attempting to slide, over
another surface. Friction is always in the
direction opposite to the intended motion.
Tension – a force that occurs whenever a rope,
chain, or other object such as a bone, is
attached to an object held pulled tight.
Typically the rope is considered massless and
unstretchable. Tensions always pull on both
ends (objects) with the same magnitude.
Applying Newton’s Laws
Goal when studying forces is to find quantities
such as individual forces, net forces, and
accelerations. These results can often then be
applied to kinematic problems.
Example: If a truck is sliding down a sloped
gravel road, you can find the acceleration and
then find how fast it is moving after a certain
time or how far it slides before it stops.
Free Body Diagrams
Free body diagrams are very useful tool that when
used correctly will lead you to the equations of
motion.
Free body diagram consists of the object (usually
drawn as a point particle) and all of the forces that
are exerted on the object.
Also can add the acceleration vector off to the side.
Example
Mass 1 is sitting on a rough table. It is tied to mass 2,
which is dangling over the edge.
N
1
1
Ff
2
T
Fg
2
T
Fg
Mass 1 is assumed to stay on the table and will
move horizontally (right +)
Mass 2 can move vertically (up +)
Mass 1
Mass 2
T – Ff = m1a1
T – m2g = - m2a2
A 80 kg climber is dangling over a cliff via a rope
tied to a 100 kg rock. If the rock is 10 meters
from the edge, how long before the rock reaches
the edge? Assume no friction between the rock
and the ground.
mR = 100 kg
mC = 80 kg
First find the acceleration of the climber and
the rock.
T
Fn
Mass R
T
WR
Mass C
WC
Newton 2nd Law (F = ma)
Rock:
T = mRa
Climber:
T – WC = -mCa
T = WC – mCa
m
g
(
80
kg
)
g
2
C
a=
4.4 m / s
mC mR 80 kg 100 kg
Now that we know the rock is accelerating at
4.4 m/s2, we can calculate the time before the
rock reaches the edge.
Use: x = v0t + ½ at2
10m = ½ (4.4m/s2)t2
10m = 2.1 s
Problems: 6, 12, 20, 26, 54, 60