Engr. Kristelle Ann V. Ginez, MECE
Potential Energy
Conservative Force
- A measure of the amount of work
-a force that generates work that
is independent of the path
(depends only on initial and final
position)
- A force that does no work on a
closed path
- Work depends not on the
velocity or acceleration
that a conservative force will do as
a particle changes position.
- It is denoted by letter V. Potential
energy is a scalar quantity and its
S.I. units are Newton-metre (N.m)
or Joule (J).
Example of a Conservative Force
Example of a Non-Conservative
Force
- Spring Force
- Gravity
- Friction ( it depends on the
path)
When an elastic spring is elongated or compressed a
distance s from its unstretched position, elastic
potential energy Ve can be stored in the spring. This
energy is
Ve is always positive since, in the deformed position,
the force of the spring has the capacity or
"potential" for always doing positive work on the
particle when the spring is returned to its unstretched
position,
If a particle is located a distance y above an arbitrarily
selected datum, the particle's weight W has positive
gravitational potential energy, Vg , since W has the
capacity of doing positive work when the particle is
moved back down to the datum. Likewise, if the
particle is located a distance y below the datum, Vg is
negative since the weight does negative work when
the particle is moved back up to the datum. At the
datum Vg = O.
if a particle is subjected to both
gravitational and elastic forces, the
particle's potential energy can be
expressed as a potential function:
V= Vg + Ve
When a particle is acted upon by a system of
both conservative and nonconservative forces,
the portion of the work done by the conservative
forces can be written in terms of the difference
in their potential energies
If only conservative forces do work then we
have:
T1 + V1 = T2 + V2
If a system of particles is subjected only to
When determining the kinetic energy, T =mv²,
remember that the particle's speed v must be
measured from an inertial reference frame.
conservative forces then:
∑T1 + ∑ V1 = ∑ T2 + ∑ V2
The first thing you need to do is to
establish a datum. In this problem, the
datum is at pt C.
Since Point A and point B are below the
datum, then both points are negative
Using the conservation of energy
equation, just substitute the values for
VA and VB. (Potential energy due to
gravitation)
V1=0 because it is where the datum is
located, so vg=0.
T1=0, the kinetic energy is zero since the ram
starts at rest.
V2 both have Ve and Vg
T2=0, the velocity = 0 at point 2 since the
downward motion of the ram is needed to
stop
Vg = weight of the ram multiply by the
(initial height + the compressed
deformation of the springs when the ram
stops)
Ve deformation for spring A = sA while the
deformation of spring B = sA -0 .1 since
spring A’s length = 0.40, while that of spring
B = 0.30. It was assumed kasi na both spring
A and spring B will both have the same
length after being compressed by the ram.
Ta=0 because it starts from rest
Va = 0, since the datum is at A (walang
distance ang gravity, spring is unstretched)
cb = √0.75² + 1² = 1.25 (length of the stretch
spring)
Scb = 1.25 – 0.75 = 0.50 (deformed length
of spring)
a)
b) Since my velocity na at point A, you can
add the kinetic energy at pt A in the
computation.
At pt 1 since the stretch length of the
spring is 48” then
s1 = 48”(stretch) -24” (original length)
=24”
Length at 2 = √24² + 24²
= 24√2
S2 = 24√2 – 24 (then just convert it to ft
nalang)
Take note that the datum is at pt 1 kaya
negative ang gravity ng v2 at o ang v1
Since an external force is given that
pulls the cable, then you need to
compute the work done by the force
, the distance of the 250 N to the
right kapag nasa pt C na ang slider
is 0.60,
AB = √1.2² + 0.9²
=1.50
Distance of Force travelled to the right
= 1.50 -0.90 = 0.60
Va= spring only because it was
establish as a datum kaya walang
gravity, since deformed na dati ang
spring ng 0.60, sa=0.60
Vc = the spring is stretch again ng 1.20
so the deformed sb = 1.20 + 0.60 = 1.80
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