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Conservation of Energy
By R. Christoffel
Conservation of Energy
A block of mass 2.5 kg is sliding across a smooth, level
surface at 3.0 m/s when it strikes a stationary spring
bumper, fixed at one at one end as shown, whose force
constant is 3.60 x 102 N/m. By what amount does the
block compress the spring?
Conservation of Energy
The law of conservation of energy states: the sum of the initial energies is equal
to the sum of the final energies.
Another way you can think about this is that if you add up all your sources of
energy; kinetic, potential, spring and work, they should equal the amount
energies in the uses category. Energies can simply change form but their sum
must always add up. Also, energies cannot simply be created nor destroyed.
As a formula, we say this:
Σ Ei = Σ Ef
Conservation of Energy
Energy
Description
Energy
Description
Kinetic
Ek=½mv2
Kinetic energy is the energy
of motion. If a body is
moving, it has kinetic
energy. The energy it
possesses is directly
proportional to its mass and
it’s velocity squared.
Spring
Es=½kx2
Elastic spring energy results from
energy that is stored in some sort
of elastic device. This could be a
metal spring or rubber band or
some other such elastic device.
Ek=kinetic energy
m=mass
v=velocity or speed
Potential
Ep=mgh
Ep=potential energy
m=mass
g=acceleration of
gravity
Es=spring energy
k=spring constant
x=compression or
extension of
spring
If a body is lifted above its
Work
lowest possible position then W=F d
it has gravitational potential W=work
F=force applied
energy. If dropped, it has the d=distance
travelled in the
potential to do some damage direction of
motion.
or hurt something or provide
energy for something.
Work could be done as an energy
input where a motor or force is
adding energy to the system. As an
output, energy might need to be
accounted for as a use such as
friction.
Conservation of Energy
Energy
Questions to ask
Before
After
Kinetic
Is it moving?
✔
✗
Potential Does its height
change?
✗
✗
Spring
Is there a spring
involved?
✗
✔
Work
Is something doing
work on the object?
✗
✗
Conservation of Energy
List all the things you know and the things you are supposed to find.
m = 2.5 kg
vi = 3.0 m/s
g = 9.81 m/s2
k = 3.6 x 102 N/m
μ=0
θincl = 0°
xf = ?
Conservation of Energy
Σ Ei = Σ Ef
Eki + Epi + Esi + Wi = Ekf + Epf + Esf + Wf
This is on a level surface We can now expand each
so there is no gravitationalof the the two energy terms
rewrite
this long
withWe
their
appropriate
potential energy
equation
and
only include
equations.
those energies that will
There isn’t a spring present
actually have relevance in
so no spring energy exists.
this problem.
We now substitute
all of the
Eki = Esf
½mvi2 = ½kxf2
No work is being values in from the given
information.
put into this
system while it is
moving.
f
amount that the
2spring
xfThe
=
√mv
is compressed is the
i x/k
The object stops moving at
the end and therefore has
no kinetic energy.
The height has not changed
so there is no change in
gravitational potential
energy.
value here. We must
x = √(2.5kg)(3.0m/s) /(3.60 x 10 N/m)
xf = 0.25 m
simply solve for2xf
No coefficient
of friction or
2
force of friction is
mentioned, therefore the
energy need not be
included.
Conservation of Energy
Reference:
Martindale, David G., Heath, Robert W., Eastman, Philip C., (1992), Fundamentals of
Physics: A Combined Edition. Canada, Heath Canada Ltd.