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CHAPTER 7: CONSERVATION OF ENERGY, NUR ADIBAH BINTI ROZAINI - Coggle…
CHAPTER 7: CONSERVATION OF ENERGY
7.3 - MECHANICAL ENERGY AND ITS CONSERVATION
If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero - the kinetic and potential energy changes are equal but opposite in sign.
Total mechanical energy:
E = K + U
And its conservation:
K2 + U2 = K1 + U1
The principle of conservation of mechanical energy:
If only conservative forces are doing work, the total mechanical energy of a system neither increases nor decreases in any process. It stays constant and it is conserved
7.5 - THE LAW OF CONSERVATION OF ENERGY
Nonconservative, or dissipative, forces:
a) Friction
b) Heat
c) Electrical energy
d) Chemical energy
do not conserve mechanical energy
. However, when these forces are taken into account, the total energy is still conserved:
∆K + ∆U + [change in all other forms of energy] = 0
The law of conservation of energy is one of the most important principles in physics.
The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant
7.4 - PROBLEM SOLVING USING CONSERVATION OF MECHANICAL ENERGY
Total mechanical energy at any point is:
E = K + U
= 1/2 mv^2 + mgy
a) Which to use for solving problems
b) Newton's laws: best when forces are constant
c) Work and energy: good when forces are constant; also may succeed when forces are not constant
7.1 - CONSERVATIVE AND NONCONSERVATIVE FORCES
A force is conservative if:
The work done by the force on an object moving from one point to another depends only on the initial and final positions of the object, and is indipendent of the particular path taken.
The net work done by the force on an object moving around any closed path is zero.
If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force.
Potential energy can only be defined for conservative forces
7.9 - POTENTIAL ENERGY DIAGRAMS; STABLE AND UNSTABLE EQUILIBRIUM
7.7 - GRAVITATIONAL POTENTIAL ENERGY AND ESCAPE VELOCITY
Far from the surface of the Earth, the force of gravity is not constant:
F = -GmM/r^2
Work done
W= GmM/r2 - GmM/r1
Gravitational potential energy
U(r) = -GmM/r
If an object's intial kinetic energy is equal to the potential energy at the Earth's surface, its total energy will be zero. The velocity at which this is true is called the escape velocity; for Earth:
Vesc = √ 2GM/r
7.8 - POWER
Power is at the rate at which work is done.
Average power:
P = W/t
Instantaneous power:
P = dW/dt
In SI system, the units of power are watts:
1W = 1J/s
Power can also be described as the rate at which energy is transformed:
P = dE/dt
In the British system, the basic unit for power is the foot-pound per second, but more often horsepower is used:
1hp = 550 ft.lb/s = 746 W
Power is also needed for acceleration and for moving against the force of friction.
The power can be written in terms of the net force and the velocity:
P= dW/dt = F . dl/dt = F.v
7.2 - POTENTIAL ENERGY
An object can have potential energy by virtue of its surroundings.
Familiar examples of potential energy:
a) A wound-up
spring
b) A stretched
elastic band
c) An object at some
height
above the ground
This potential energy can become kinetic energy if the object is dropped.
Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces)
FORMULA:
Work done by external force
a) Wext = Fext ✕ d
Gravitational potential energy
b) Ugrav = mgy
c) ∆U = U2 - U1 = -W
Conservative force
d) ∆U = -Wg
Force exerted by spring
e) Fs = -kx
Potential energy
f) ∆U = 1/2 kx^2
A spring has potential energy, called elastic potential energy, when it's compressed.
7.6 - ENERGY CONSERVATION WITH DISSIPATIVE FORCES : SOLVING PROBLEMS
Problem solving:
Draw
a picture.
Determine the
system
for which energy will be conserved.
Figure out what you are looking for, and decide on the
initial
and
final
positions.
Choose a
logical
reference frame.
Apply
conservation
of energy.
Solve
.
NUR ADIBAH BINTI ROZAINI
