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WORK
WORK is done when a FORCE is applied to an object
and it moves. You can push all day on an object and if it
hasn't moved from it's starting spot then by definition no work
has been done. The equation is W = F x d. W = work (units
are Newton-meters Nm or Joule), F = force (unit is
Newton), d = distance (unit is meters).
SIMPLE MACHINES
Simple machines can be divided into 2 main categories, the
lever types and the ramp types. A lever comes in 3
classes, determined by the arrangement of the Effort, Fulcrum and
Resistance. A 1st Class lever has the Fulcrum in the middle, 2nd
class has the Resistance in the middle and 3rd class has the Effort
in the middle.The amount of work ( F x d ) that you put into a simple
machine is always less than you get out (due to frictional losses).
The advantage of a simple machine is that it can amplify forces
or distances. To amplify force, distance is sacrificed and to
amplify distance, force is sacrificed.
Neglecting friction, the 6 types of simple machines follow
this equation:
Win = Wout
Fe x de = Fr x dr
Now, including friction we can evaluate the
efficiency (Eff) and mechanical advantage (MA) of
a simple machine. Efficiency is just a ratio of the work the machine
puts out to the work you put in. Ideally, the maximum efficiency
would be 1 (100%), but is usually less than one because of frictional
losses..
i.e. Eff = Wout / Win = Fr x dr / Fe x de
Mechanical advantage is a ratio which defines the factor by
which the force has been amplified. Any factor less than 1 amplifies
the output distance dr, greater than 1 amplifies the output
force Fr.
Click Here for
See-Saw Lever DEMO!
Put several masses on a see-saw in an effort to balance the
system.
Click Here
for Inclined Plane DEMO!
This lets you alter the initial velocity, mass, and angle of
a frictionless inclined plane.
ENERGY (KINETIC/POTENTIAL)
The units for both potential energy (PE) and kinetic energy
(KE) are Joules or Newton-meters (just like Work).
Potential energy (PE) is how much work a system is CAPABLE OF DOING.
This stored energy is held in gravitational, electrical or magnetic
fields (subatomic nuclear forces also). A stretched rubber band
or spring, a firecracker, a rock on the edge of a cliff are just
a few examples of potential energy.
Kinetic energy (KE) is how much work a system IS DOING.
This action energy occurs when potential energy is released
to do work. Mass moving (large or small) with a velocity characterizes
kinetic energy.
Work (F x d) can be applied to a mass giving it Kinetic Energy or
stored as Potential Energy.
| Kinetic Energy (Action) |
Potential Energy (Stored) |
Using:
W= F x d, F = m x a,
a = v / t, v = d / t
W = F x d
W = m x a x d
W = m x (v/t) x d
W = m x v x (d/t)
W = m x v x v
Since the velocity changes linearly because the Force is constant
and if we can assume that the initial velocity is zero...then
the average velocity is 1/2 the final velocity.
We can generate several other useful equations by assuming
that Kinetic Energy and Potential Energy convert freely back
and forth, e.g the Potential Energy in a rock on a cliff completely
converts to Kinetic Energy just before impact. By setting
PE = KE you can find the velocity the falling rock would have
at impact.
KE = PE
½mv² = mgd
½v² = gd , m's cancel
v² = 2gd
v = (2gd)^½ , or the square root of 2gd!
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When a force (F = mg)
raises a mass vertically, potential energy (PE) is stored
in the gravitational field.
W = F x d
W = m x g x d = PE
Click
Here for a Freefall Lab
Terminal Velocity Did you ever think of all the physics involved
when you drop a ball (or an expensive plate)?
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