Transcript Dynamics: Interactions of Forces

Dynamics: Interactions of Forces
How do we represent
interactions of forces within
a system?
What is a Force?
 The word “force” is used in physics for a physical
quantity that characterizes the interaction of two
objects.
 A single object does not have a force by default, as
the force is defined through the interaction of two
objects.
 Remember that all physical quantities are measured
in units.
 The unit of force is called the Newton (N), where
1 N = (1 kg)(1 m/s2).
What is a force diagram?
 Force diagrams are used to represent the forces
exerted on an object of interest (system) by other
objects.
 A system is an object or group of objects that we
are interested in analyzing.
 Everything outside the system is called the
environment and consists of objects that might
interact with and affect the system object’s
motion. These are external interactions.
 When we draw force diagrams, we only consider
the forces exerted on the system object(s).
•In the example below, the first image is a picture of a climber on the
side of a cliff.
•The second image shows just the object of interest (the climber) and
has vectors drawn representing the different forces on the climber,
which are labeled with everyday language.
•The third image is a force diagram; the object of interest is simply
represented by a dot, and the vectors are labeled by the type of force,
the object exerting the force, and the object receiving that force.
Did you know?
 When the forces exerted on an object of interest are
balanced, we say that the object is in EQUILIBRIUM
(equilibrium does not necessarily mean rest).
 For example: Let’s take the situation of a puppy
curled up in your lap.
 We can write the total force exerted on the puppy by
your legs and Earth as:
 F legs on dog + F
Earth on dog =
0.
 Does it matter whether you chose up as (+) or down?
 How does it change your equation above?
How do we ADD vectors?
 Suppose we want to add the two vectors A and B. To
add them graphically, we redraw A and place the tail
of B at the head of A.
 While we can move vectors from one place to
another for addition, we cannot change the magnitude
or direction of a vector while moving it.
How do we SUBTRACT vectors?
 You are familiar with subtraction a little bit already –
this is what we do when we find the ∆v vector on
motion diagrams.
 Basically, to find the vector which is equal to A-B, you
need to find the vector that you need to add to B to
get A.
 Or simply ADD the negative
vector (-B), which has the
same magnitude opposite
sign (direction).
What is an Inertial Reference Frame?
 Inertial reference frame: Inertia is the phenomenon
when an object continues moving at constant velocity
if no other objects interact with it or if the sum of all
these interactions is zero.
 Reference frames in which we can observe this
phenomenon are called inertial reference frames.
 If the sum of all forces exerted on the object is zero,
then in an inertial reference frame, the object’s
velocity remains constant.
Let’s Look at an Example
 You are driving in a car and you have a cup of coffee on the
dashboard.
 The car in front of you stops so you slam on the brakes, from
your frame of reference, what would happen to the cup of
coffee?
 Now look at from the frame of reference of a pedestrian on
the street watching the car and the coffee cup, what would
they see?
 Which person is in the inertial frame of reference?
Newton’s 1st Law
 Newton’s first law of motion: We choose a
particular object as the object of interest—the
system.
 If no other objects interact with the system object or if
the sum of all the external forces exerted on the
system object is zero (forces in the y direction are
balanced and forces in the x direction are balanced),
 then the system object continues moving at constant
velocity (including remaining at rest) as seen by
observers in the inertial reference frames.
Newton’s 2nd Law
Newton’s 2nd Law
 Mass: Mass (m) characterizes the amount of matter in an object
and the ability of the object to change velocity in response to
interactions with other objects
 The unit of mass is called a kilogram (kg). Mass is a scalar
quantity, and masses add as scalars.
 Gravitational force: The magnitude of the gravitational
force that Earth exerts on any object near its surface
equals the product of the object’s mass m and the
gravitational constant g:
F E on O = m g
 where g = 9.8 m/s2 = 9.8 N/kg on or near the earth’s
surface. The force points toward the center of Earth.
Newton’s 3rd Law
 Newton’s Third Law of Motion: When two
objects interact, object 1 exerts a force on object
2. Object 2 in turn exerts an equal-magnitude,
oppositely directed force on object 1: