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PHYSICS FOR ENGINEERS
We’ll use the book from P.A. Tipler
... and some more resources from the web
1
Dynamics
07 - 2nd week
NEWTON’S LAWS
First law. An object at rest stays at rest unless acted on by an external force.
An object in motion continues to travel with constant velocity unless acted on by an
external force.
act on
influir sobre
Remark: Also called the "law of inertia," Newton's first law states that a body at rest remains
at rest and a body in motion continues to move at a constant velocity unless acted upon by
act upon
influir sobre, afectar
an external force.
Second law. A net force F acting on a body gives it an acceleration a which is in the
direction of the force and has magnitude inversely proportional to the mass m of the

body.

F  ma
Momentum: for a single particle of mass m with velocity v, the momentum is defined as


p  mv
From Newton's second law, a force F produces a change in momentum
Which are the SI units of force and momentum?
 dp
F
dt
stand for
simbolizar, ser las siglas de
agree upon
estar de acuerdo, concertar
2
"SI" stands for "System International" and is the set of physical units agreed upon by international convention
Dynamics
07 - 2nd week
Example. How much horizontal net force is
required to accelerate a 1200 kg car at 2 m·s-2
from the rest on a horizontal plane?
1200 kg
2 m·s-2
F  ma  2400 N
To do yourself: Example 4-1 (5 min)
To do yourself: Example 4-2 (5 min)
strand
varar, dejar desamparado
To do yourself: Example 4-3 (5 min)
For you to read: The Force Due to Gravity: Weight (15 min)
Exemple. A box on a lift
The box is inside a lift
Let W0 be the
weight of the box
The lift accelerates upwards, let a be its acceleration
a
Which is then the apparent weight of the box?
W0  mg
W0
Which is the apparent weight of the box in case the lift
moves up with a constant velocity?
3
Dynamics
07 - 2nd week
Also related with Newton’s second law: impulse.


An impulse is an instantaneous change in momentum dp  mdv
which can be found by integrating a force F over a characteristic time t, giving
 
dp  F dt
t

p 


Fdt
Which S.I. units do we use for impulse?
Can you pose some exemples on impulse?
0
Also related with Newton’s second law: friction forces.
http://www.sc.ehu.es/sbweb/fisica/dinamica/rozamiento/general/rozamiento.htm
Third law. Whenever a body exerts a force on another body, the latter exerts a force of
equal magnitude and opposite direction on the former. This is known as the law of
action and reaction.
A well knowing horse
To do yourself: Exemple 4-11 (5 min)
4
Dynamics
07 - 2nd week
FRICTION FORCES
Static
Kinetic
5
Dynamics
07 - 2nd week
FREE-BODY DIAGRAMS
A diagram that shows schematically all forces acting on a system, is called free-body diagram.
It is called free-body diagram because the body is drawn free from (without) its surroundings.
To do yourself:
Example 4-6 (10 min)
6
Dynamics
MORE PROBLEMS
07 - 2nd week
Find out the acceleration:
Atwood’s Machine
(consider an ideal pulley)
What about the
tension of the rope?
T
To do yourself:
Example 4-9 (10 min)
To do yourself:
Example 4-10 (10 min)
The block m2 has an
inhabitant:it has a
hollow, which is the
home of a bug.
T
T
2m1m2
g
m1  m2
m1
To do yourself:
Example 4-12 (10 min)
m2
m1g
m2g
+)
F1  T  m1 g  m1a
F2  m2 g  T  m2a
m2  m1 g  m1  m2 a
a
m2  m1
g
m1  m2
Let mb be
the mass of
the
bug.
What about
its
weight
when it is at
home?
Try it yourself!
7
Dynamics
07 - 2nd week
SOME MORE QUESTIONS & PROBLEMS
kick
Question:
dar patadas
hurt
hacer daño
An astronaut on Earth kicks a bowling ball and hurts his foot. A year later, the
same astronaut kicks the same bowling ball on the moon with the same force.
His foot hurts... (a)
(b)
(c)
more
less
the same
The masses of both the bowling ball and the
astronaut remain the same, so his foot will feel
the same resistance and hurt the same as before.
Question: Where (the Earth or the Moon) is easier for
the astronaut to pick up the bowling ball from the floor?
The weights of the bowling ball and the astronaut are less
on the Moon...
Thus it would be easier for the astronaut to pick up
the bowling ball on the Moon than on the Earth.
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