Transcript external forces. - Mahidol University

Chapter 4 : Laws of Motion
Weerachai Siripunvaraporn
Department of Physics, Faculty of Science
Mahidol University
email&FB : [email protected]
What is in this chapter?
Force is the causes of motion.
Force
In previous chapter, we described motion in terms of position, velocity,
and acceleration. But we have not considered the causes of motion.
Here, we begin our investigation of the causes of motion.
Definition:
1. a force is a push or a pull that causes an object to move.
2. a force is something that causes an object to accelerate.
Forces have both magnitude and direction,
so forces are vector quantities.
Contact and Field Forces
No physical
contact is
required
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Fundamental Forces
Gravitational

force
Between objects
Electromagnetic

Between electric charges
Nuclear

force
Between subatomic particles
Weak

forces
forces
Arise in certain radioactive decay processes
Note:
These are all field forces.
Section 5.1
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∑F = F1 + F2
Net Force
F
F1
F2
∑F = F1+ F2
Net Force
Each force and net force can be divided
into components.
Sir Isaac Newton
1642
– 1727
Formulated
basic laws of
mechanics
Discovered Law of
Universal Gravitation
Invented form of calculus
Many observations dealing
with light and optics
Section 5.1
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Inertial frames are frames of reference that are not accelerating (i.e.
not moving or moving at constant velocity)
A reference frame that moves with constant velocity
relative to the distant stars is the best approximation of
an inertial frame, and for our purposes we can consider
the Earth as being such a frame.
The Earth is not really an inertial frame because of its
orbital motion around the Sun and its rotational motion
about its own axis, both of which result in centripetal
accelerations. However, these accelerations are small
compared with g and can often be neglected. For this
reason, we assume that the Earth is an inertial frame, as
is any other frame attached to it.
If there is no force
acting on it, it remains
the same.
Newton’s First Law – Alternative
Statement
In
the absence of external forces, when viewed from an
inertial reference frame, an object at rest remains at rest
and an object in motion continues in motion with a
constant velocity.



Newton’s First Law describes what happens in the absence of
a force.
 Does not describe zero net force
Also tells us that when no force acts on an object, the
acceleration of the object is zero
Can conclude that any isolated object is either at rest or
moving at a constant velocity
Section 5.2
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Applications of Newton’s first law
Applications of Newton’s first law
Which is easier to pull, a shredder or a fire truck?
A fire truck is more resistant to changes in its velocity than the shredder.
How can we quantify this concept?
• Mass is that property of an object that specifies how much
resistance an object exhibits to changes in its velocity.
• The SI unit of mass is the kilogram (kg).
• The greater the mass of an object, the less that object accelerates
under the action of a given applied force.
More About Mass
Mass
is an inherent property of an object.
Mass is independent of the object’s surroundings.
Mass is independent of the method used to measure it.
Mass is a scalar quantity.
 Obeys the rules of ordinary arithmetic
The SI unit of mass is kg.
Mass and weight are two different quantities.
Section 5.3
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Force is the cause of changes in motion, as measured by the
acceleration.
• Remember, an object can have motion in the absence of forces.
• Do not interpret force as the cause of motion.
Notice that the acceleration is in the same
direction as the resultant force.
Newton’s Second Law

F

is the net “external” force
This is the vector sum of all the forces acting on the object.

May also be called the total force, resultant force, or the unbalanced force.
Newton’s
Second Law can be expressed in terms of components:
Remember

The

that ma is not a force.
The sum of the forces is equated to this product of the mass of the
object and its acceleration.
SI unit of force is the newton (N).
1 N = 1 kg·m / s2
Section 5.4
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action force
reaction force
reaction force
action force
reaction force
action force
Free Body Diagrams and the Particle Model
The
particle model is used by representing the object as a dot in the
free body diagram.
The forces that act on the object are shown as being applied to the dot.
The free body helps isolate only those forces acting on the object and
eliminate the other forces from the analysis.
Section 5.6
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External and Internal Forces and
System
We only care about the
external forces.
To tell which forces are
external forces, we
must define system of
interest first.
If dog is system,
External force …
External and Internal Forces
F1’
F
F2’
m1
m2
Force F acting on m1 and m2, there is internal force between m1 and m2.
If m1 and m2 are our system of interest,
F is external force and F1’ and F2’ are internal forces.
If m1 is our system of interest,
F and F2’ are external force.
If m2 is our system of interest,
F1’ is external force.
130 N
Forces in every day
Gravitational force and weight
 Normal force
 Tension force
 Friction

Gravitational Force & Weight
The
gravitational force, Fg , is the force
that the earth exerts on an object.
This force is directed toward the center
of the earth.
From Newton’s Second Law:
Fg  mg

Its magnitude is called the weight of
the object.
 Weight = Fg= mg
• Because it is dependent on g, the weight varies with location.
g, and therefore the weight, is less at higher altitudes.
This can be extended to other planets, but the value of g varies from
planet to planet, so the object’s weight will vary from planet to planet.
• Weight has a unit of Newton.
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But g is not constant, decrease with increasing distance
from the surface. Therefore, weight is not constant.
g  1/r2
g near the surface is about 9.8 m/s2 and
vary from point to point.
Mass vs. Weight
Mass
and weight are two different quantities.
Weight is equal to the magnitude of the gravitational force exerted
on the object.
 Weight will vary with location.
Section 5.3
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What is your mass on Earth and on Moon?
What is your weight on Earth and on Moon?
g near Earth’s
surface is about
10 m/s2
g near Moon’s
surface is about
10/6 m/s2
Mass
= 60 kg
Weight = 60 kg x 10 m/s2
= 600 N
Mass = 60 kg
Weight = 60 kg x 10/6 m/s2
= 100 N
Normal Force
N
N
N
Tension Force
String tension is an electromagnetic
force. The molecules in the string are
pulling one another. Each portion of the
string transmits the force undiminished
from end to end.
T1
T1  T2
A light smooth
pulley
T2
If the acceleration of an object
that can be modeled as a
particle is zero, the particle is
in equilibrium.
Fx = max
Fy = may
Problem-Solving Hints – Applying
Newton’s Laws
Conceptualize
Draw a diagram
 Choose a convenient coordinate system for
each object

Categorize

Is the model a particle in equilibrium?


If so, F = 0
Is the model a particle under a net force?

If so, F = m a
Section 5.7
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Problem-Solving Hints – Applying Newton’s
Laws, cont.
Analyze






Draw free-body diagrams for each object
Include only forces acting on the object
Find components along the coordinate axes
Be sure units are consistent
Apply the appropriate equation(s) in component form
Solve for the unknown(s)
Finalize


Check your results for consistency with your free-body
diagram
Check extreme values
Section 5.7
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If we try to drag a box with an increasing force F,
what would happen?
Example
A mass m is attached to a tread and suspended from a
ceiling. A force F pulls the mass sideway such that the
tread is deviated by an angle  from the vertical. Find
the magnitude of F and the tension in the string in terms
of m, g and .

T
T cos
g
F
T sin 
mg
Example
4kg
6kg
10N
a
4kg
T
a
T
6kg
10N
Two bodies of mass 4kg and 6kg
are tied with a string, and put on
a smooth floor. A force 10N pulls
6kg mass to the right. Find the
acceleration of the two bodies
and the string tension.
Example
u = 10 m/s
A body slides on a rough surface
with a kinetic friction constant of
0.4. How far does the body move
before it comes to rest?
a
fk
mg
N
Example

y
a
 T
W
x
A small ball is suspended from a
ceiling of a moving car. The car
moves with a constant acceleration
a. Find the angle  through which
the string is deviated from the
vertical.
Example

A small disc is resting on an inclined
plane making an a small angle  with
the horizontal. The inclination angle 
is then slowly increased. Find the
critical angle c at which the disc
starts to slide down. The static friction
constant is s.
1


tan
s
Ans. c
Example
A force F pushes onto M. Attached to the
front of M is m, which is not glued to M. The
static friction between M and m is s. Find
the minimum magnitude of F that still keeps
m attached to the front of M without slipping
down. The floor is smooth.
F
M
m
s
F

m  M g

s