MECHANICAL ENERGY
KINETIC ENERGY
When an object is in motion it has kinetic energy.
1/2 x m x v^2
m = mass in kilograms
v = velocity in meters per second
inverse formulas
v = √k.e./(1/2(m))
m = k.e./(1/2(v^2))
POTENTIAL ENERGY
It is the energy stored in a body due to its position or its configuration
It is called potential energy because because the objects have the potential of doing work.
work = force x displacement
If there is a position or change in configuration of the object involved, it has storing energy waiting to be released, so it has potential energy.
two different categories
gravitational
elastic
the energy stored in an object due to the Earth's gravity
the energy stored in an object due to its default state
objects kept at a height store this kind of energy
objects that have a change in configuration store this kind of energy
SI unit: joule
objects can store energy thanks to the work done on them
work = change in energy
formula
m x g x h
m = mass
g = acceleration due to gravity
h = height
Height usually is not the actual height, but the height taken from a reference.
The potential energy does not depend on the path taken, but only on the height
CONSERVATION OF ENERGY
law of conservation of energy
energy can neither be created nor destroyed, but it changes from one form to another form
When a moving toy car goes into the loop of a roller coaster toy, it has both potential and kinetic energy, because the car is at a height from the table surface and it is also in motion.
potential + kinetic energy = mechanical energy
This also happens when the car reaches the top of the loop.
During the track (frictionless) of the car, the amount of energy is conserved; the energy only changes from one form to another.
What should be the minimum speed of the car at the start to complete the loop?
energy at the start = energy at the top of the loop
start
top
k.e. = 1/2 x m x (v1)^2
p.e. = m x g x (h2)
k.e. = 1/2 x m x (v2)^2
1/2m(v1)^2 = mg(h2) + 1/2m(v2)^2
1/2(v1)^2 = g(h2) + 1/2(v2)^2
v1 = minimum speed at the start
g = 9.8 m/s^2
h2 = height of the loop = 24 cm = 0.24 m
v2 = ?
When the car goes around the loop, it is in circular motion, for which centripetal force is needed
(mv^2)/R
m = mass
v = velocity
R = radius of the circle
centripetal force = weight of the car
(m(v2)^2)/R = mg
(v2)^2 = gR
v2 = √gR
1/2(v1)^2 = g(h2) + 1/2(gR)