Transcript Gravitational Potential Energy (PE)

Ch.5 Energy
Energy comes in various forms:
When you apply a Force to an object and it moves a
displacement (x), then you get
done.
i.e.
where:
(Weight is now w, not W)
is the displacement,
is the component of Force that is in the
same direction as the displacement.
is a scalar quantity with units of


Work can be
if the Force applied is in the
to the displacement.
i.e. the Work done by
.(
removes
system)
e.g. Applying the brakes to stop a car.
W=
W is
(θ =
)
because Cos(
o)
from a
=
E.g. Calculate the Work done by pushing a 20kg shopping cart
that’s at rest ,15m with a 120N Force at 30o below the
horizontal. How fast will the cart be going after the 15m
assuming a frictionless floor.

m = 20kg
x = 15m
F = 120N
θ = 30o
W=?
vf = ?
When you push an object on a frictionless surface causing it to
accelerate, you do
to achieve this. When you
release the object of
, it moves with a constant
. The object now has Energy of Motion known as:
and is calculated by:
(measured in Joules)
So, the Net Work done is the change in the object’s Kinetic
Energy.
E.g. A 250g ball at the top of a frictionless incline is pushed with
an initial velocity of 2m/s. When it reaches the bottom of the
5m incline, it’s speed is now 10m/s. What Force (by Gravity)
was needed to achieve this?
Gravitational Potential Energy (PE)
- is the Energy of an object due to its
- It is stored energy that can be used to do
e.g. holding a ball above the ground. The ball has the “potential” to
fall to the ground. The higher the ball, the greater the potential.
Remember:
&
so
(in x direction)
Now switch to y direction:
Substitute
and
, and we get:
Wg = Work done by gravity on an object.
(please note that it is Initial – Final
because the Force of Gravity points
downward.)
So, if an object falls, the work done by
gravity is +ve.
When an external Force is increasing the height
of an object, e.g. lifting something, then this is
considered Working
Gravity.
And so Work is required to increase the object’s Potential
Energy. Therefore:
The Reference Level is arbitarily set. We usually choose
the
as the reference position for
.
This is not essential because we are only interested in
Reference Level
At pt.A, the reference
level is the
At pt.B, the reference
level is the
At pt.C, the reference
level is the
They all have a value of
zero for Potential
Energy. (PE = 0)
N.B. that Work, PE & KE are
.
As stated before, we are interested in the
difference between height
and height
, no matter what the path is.
The
is the same in each case
because (yi – yf) is 3m, even though they each came
down a different way.
Conservation of Mechanical Energy
When an object is in motion, it can possess both
.
Energy in a system can transfer from
to
, and vicey versi, with no loss of
Energy from the system.
i.e. Total Energy (E)
(Assuming Conservative Forces only)
So,
E=
Or we can say
Total Energy before = Total Energy after.
Ei = Ef
The Diver
At the top, the diver only has Energy due
to his position (height).
As he falls, his
is being
converted into
and so
he gains speed.
At the bottom, all his
has been converted to
.
During the whole time, Total Energy has
remained
.
ET =
Example:
Using the Conservation of E:
a.) Calculate the diver’s speed when
he reaches the 5m mark.
b.) Calculate the diver’s speed when
he hits the water.
(Is it twice as fast as in part a?)
c.) Calculate the diver’s speed when
he hits the water, but this time
using a Kinematic equation.
The Pendulum
A 50g pendulum bob hangs on the end of a
string 1.5m long. It is then lifted such that the
bob & string make a 60o angle to the vertical.
Calculate:
a.) the change in it’s Potential Energy, and
b.) the bob’s velocity at its lowest point.
Conservative Forces:
A Force is considered conservative if
the Work done by that Force is
of the path it takes.
i.e. only interested in the initial & final
positions.
E.g.
is a conservative Force
because the Work done by
is
independent of the path.
Non Conservative Forces
A Force is considered Non Conservative
if the Work done by that Force
depend on the path it takes.
e.g.
Conservation of Energy “Violated”
Recap that
WNett = KE = ½ mvf2 – ½ mvi2
Factoring in a Non Conservative Force like friction, then
WNett = Wc + Wnc
where
so
Wc = -PE
(Work done by Gravity)
Realise that
will be a –ve number
reflecting that Energy has been removed from the system.
Example
Power
Remember: Work is a Force applied over a
distance.
does not matter.
e.g. If a 10N Force is applied over 5m, then
the Work done is 50J. Whether it was
done in
or
, the
Work is still the same for both situations.
To distinguish the difference between these
2 situations, we introduce the term
.
is defined as the rate at which
Work is done.
i.e.
Units: J/s = Watts (W)
Substitute
so
or
& for the Petrol Heads!
1 horsepower (hp) = 746 W
and in horsepower, must the motor operate at to lift the elevator up
at a constant rate of 3.00 m/s?