PHYS 1410A
II.1
Forces: what makes objects move
Newton I:
objects with constant mass
not acted upon by forces conserve ~
v
Newton II: law stating how the net force affects ~
v
Four fundamental forces in nature:
gravity, electromagnetism, [strong, weak].
They act over some range (non-contact).
Manifestations of electrostatic (and magnetic) forces:
friction, bonding, drag, restoring spring force,
tension force (rope), normal force (‘solid’ surfaces), ...
These are typically contact forces.
PHYS 1410A
II.2
Forces in Classical Mechanics
The box is moved by the tension force
Idealize the box as a point mass
(centre of mass to be defined later = CM)
Move the tail of the force vector to the CM
Orientation of rope: → force vector
A compressed spring pushes(!) the box
Well-defined contact between spring and box:
force vector has horizontal orientation
(what could happen if the spring applied at top?)
Objects near earth’s surface experience weight
Box is a rigid body (no tidal forces)
Weight is a force (m ~
g ), mass m is a scalar.
This is a simplified view of gravity which
follows an inverse distance squared force law.
Distance between CM of box and CM of earth!
PHYS 1410A
II.3
Superposition of Forces
Suppose the box is pulled by two ropes
with forces of equal magnitude,
but different orientation.
Equivalent to pulling with
a single force ?
Net force:
~net =
F
N
X
~i
F
i =1
~i to CM,
Move tails of F
and use vector addition
PHYS 1410A
II.4
Tension Force
Note how the upward orientation
~ helps to move over bumps.
of T
~
The horizontal component of T
moves the sled forward!
How is force transmitted
by the rope ?
What would happen if there was
no weight pulling the sled down?
We would observe motion in the
~!
direction of T
Chemical bond =
net effect of electrostatic forces
between valence electrons
and ionic cores
(microscopic model)
Rope doesn’t stretch:
Tension force is just transmitted
(idealization; why?)
PHYS 1410A
II.5
Normal Force
Weight of the brick is
compensated by a response
from the table
Two forces apply at the CM:
~ (downward), ~
w
n (upward);
Net force vanishes!
normal = perpendicular
~
n applies at the contact
~ applies at the CM
w
will tilt occur at some point?
look at translation only (for now) !
PHYS 1410A
II.6
Static Friction
Real surfaces: objects tend to stick
microscopically:
electrostatic forces → bonding
Why doesn’t the frog move ?
~ =w
~∥ +w
~⊥ ; w
~ ⊥ = −~
Weight: w
n
~ ∥ | = mg sin θ.
The parallel component has magnitude |w
Why doesn’t the frog move ?
~ ∥.
Static friction ~
f s adjusts itself such as to compensate w
~ ∥ always be achieved?
Can ~
f s = −w
No, there is a limit; depends on object/surface materials
|~
f s | ≤ µs |~
n |. Here µs is the static friction coefficient.