Download lecture 3

Questions to think about
• Which object exerts the force
• Why ramps make is easier to lift objects
• Why is it heavier to ride a bicycle uphill
placing a feather on an orbit
F=m⋅a
Puzzle:
Is a person strong enough to accelerate an object into an orbit
around the earth? Isn’t it just a matter of object’s mass?
Answer:
A light object does not allow a person to apply the required force!
What is pulling what?
F12
F21
Both object equally contribute to the interaction
Newton’s third law of motion:
For every force that one object exerts on the second object,
there is an equal (in magnitude) but oppositely directed
force that the second object exerts on the first object.
Puzzle:
Which pulls stronger (due to gravity): earth on you or you on earth?
fiddler on the roof - support and friction
static frictional force fs
(exerted by the roof)
support force N
(exerted by the roof)
- normal
gravitational force W
(exerted by the earth)
1. When two object are in contact along a rigid
surface, they may exert a support force on each
other. The force is perpendicular to the surface in
contact and adjusts itself to the situation.
2. When two object are in contact along a rigid
surface and do not slide, they may exert a static
frictional force on each other. The force is parallel to
the surface in contact and also adjusts its value.
fiddler on a slippery roof
kinetic
frictional
force
static
frictional
force
f s fk
(exertedbybythe
theroof)
roof)
(exerted
support force N
(exerted by the roof)
net force
gravitational force W
(exerted by the earth)
The magnitude of the static
frictional force is restricted by
fs ≤ µs ⋅ N
When the object slides the kinetic
frictional force has value
fk = µk ⋅ N
and is opposite to sliding direction.
free body diagram includes
•
•
•
•
Only forces exerted on the body.
Only forces exerted by other bodies.
All forces exerted on the body.
Each force counted only once.
missing force
suction force
exerted by
nothing
magic force of
motion
gravitational
force exerted
by earth
net force for double count
just to be sure:
weight of the object
force exerted
by gravity
How strong to push?
When rolling along the ramp,
the person applies a force
much smaller (in magnitude)
than the weight of the object.
When lifting, the person
applies a force equal (in
magnitude) to the weight
of the object.
N1
S
The ramp provides
mechanical advantage
N1
M.A. ≡
N2
N2
W
W
How to get a job done?
The ability of a system to produce motion and structural
rearrangements is called:
E N E R G Y
I have
kinetic energy
I have
potential energy
I have used
the energy
Keeping track of energy
•
•
•
•
The total energy of an isolated system is conserved.
Energy can be transferred from one object to another.
There are two ways of energy transfer: work and heat.
Energy of an object can change its form.
Chemical
(potential)
energy of
the food
Gravitational
potential energy
of the piano
Kinetic energy
of the piano
y
the work
1cm
-1cm
-0.02 N
dW = Fx ⋅ dx + Fy ⋅ dy + Fz ⋅ dz
x
dW = (- 0.02) N ⋅ (- 0.01) m = 0.1 mJ
For a small displacement of an object, the scalar product of a force
applied to the object due to a certain interaction and the
displacement of a selected point of the object in the direction of the
force is called t h e w o r k , done on the point of the object, due
to the interaction.
The work along a path of an object, is equal to the sum of work
done along all small displacements constituting the path.
The SI unit of work is the joule: 1J = 1 N ⋅ 1 m
make a point of the point
Fs>0
c.f.
c.m.
dy<0
Example 1
Determine the work done by the person on the “center of
mass” of the yo-yo (together with the string), over a small
displacement.
dWc.m. = Fs⋅ dy < 0 J
Example 2
Determine the work done by a person on the “center of the
force” exerted on the yo-yo, over a small displacement.
dWc.f. = 0 J
May the Work be with you, too
Work is a measure of cumulative
interaction between objects.
Fs
W
1.
2.
3.
4.
5.
Work is done (performed) on an object,
on a specific point associated with the object,
only by other objects.
Work is done along a path of the object,
and is always due to an interaction.
Example. A person performed work due to friction on the center of mass of
the yo-yo, as it moved from the hand to its lowest point.
Example. The earth performed work due to gravity on the center of mass of
the yo-yo, as it moved from the hand to its lowest point.
Example. The earth performed work due to gravity on the center of gravity
of the yo-yo, as it moved from the hand to its lowest point.
potential energy
For some interactions, the work
does not depend on the path.
These are called conservative
interactions.
Gravity
is
conservative ! 2
Only conservative interactions
result in a potential energy.
h
1
Work Wc done due a conservative
interaction, along a any path
between two locations of the
object, is opposite to the change in
potential energy along this path
∆ U = - Wc
Gravitational Potential Energy
(near the surface of a planet)
Ug = m ⋅ g ⋅ h
work on a ramp
Change in gravitational potential energy: ∆Ug = - Wg = m ⋅ g ⋅ h
Where to get the required energy from?
The same effect is achieved:
LARGE FORCE ⋅ small displacement =
= small force ⋅ LARGE DISPLACEMENT
The mechanical advantage:
S
N1 L
=
N2 h
N1
lifting:
W = N1⋅ h = ∆Ug
on the ramp:
W = N2⋅ L = ∆Ug
N2
L
h
W
W
riding a bicycle
(with constant velocity)
Drag (air resistance) – a frictionlike interaction between a
fluid and a solid object moving in fluid, resulting in
slowing the relative motion. The force depends
on the relative velocity of the object
and the fluid
S
Fs
S
D
Fs
D
W
The energy remains constant (Wg = 0 J)
Ws = - WD and Fs = D
W
The energy is increasing (Wg < 0 J)
Ws > - WD and Fs > D