Download Section 3.5 - Edvantage Science

3.5 The Law of Conservation of Mechanical
Energy
Conservation of Mechanical Energy
A frictionless pendulum would swing from its high point to its
lowest point. The potential energy at the top of its position would
be converted to kinetic energy at the bottom of its swing.
Ek = Ep
Ep
The total work done remains constant through out the
pendulums motion.
Total mechanical energy
Ek
=
Ek = Ep = constant
½ mv12 + mgh1 = ½ mv22 + mgh2
Of course in the real world there is always friction and some energy lost as heat would have to
be included in the formula stated above.
Energy can be transformed from one form to another, but it is never created and it is never
destroyed. Total energy remains constant.
p. 106
3.5 The Law of Conservation of Mechanical
Energy
Categorizing Force in a System
A force is conservative if the work done by it in moving the object is
independent of the object’s path. In this case only the initial and final
position of the object are used the determine the amount of work done on
the object.
A force is non-conservative if the work done by it in moving an
object depends on the objects path. Friction is an example of a nonconservative force. The longer the path the more force of friction is
used and the more heat energy is generated.
p. 108
3.5 The Law of Conservation of Mechanical
Energy
Types of Collisions in a system
Elastic Collisions
In this type of collisions the total kinetic energy of the system is conserved.
Energy can be transferred from one object to another, but no energy is
transferred to the surrounding.
Inelastic Collisions
In this type of collisions the total kinetic energy of the system is not
conserved. Some (or all) of the kinetic energy is transferred to other forms
(such as sound, elastic, deformation, and heat energy). Eventually all forms
of energy become low grade heat energy.
Regardless of the type of collision momentum is always conserved which is due to the
vector nature of momentum.
p. 108
3.5 The Law of Conservation of Mechanical
Energy
Applying the Law of Conservation of Energy: A ballistic Pendulum
A ballistic pendulum is used to measure the
speed of bullet and uses both the law
conservation of momentum and law of
conservation of mechanical energy in its
solution.
m +M
vb
mb
h
The bullet is shot into a block of
wood or clay causing the bullet-block
to swing up to some height, h.
M
From this height, mass of both block and bullet, the initial speed of the bullet can
be determined.
p. 109
3.5 The Law of Conservation of Mechanical
Energy
The bullet entering the block transfers its momentum to the block:
mbvb = (m + M)v
(Law of Conservation of momentum)
The impact cause the bullet and block combination to move. The combination
bullet and block gains kinetic energy:
Ek = ½ (mb + M)v2
Since the block is connected to a string, it will swing upwards reaching a maximum
height, h. The kinetic energy is converted to potential energy.
Ek = ½ (mb + M)v2 = (mb + M)gh = Ep
(Law of Conservation of
Mechanical Energy.)
p. 109
3.5 The Law of Conservation of Mechanical
Energy
If there is very little energy lost as heat due to friction then:
½ (mb + M)v2 = (mb + M)gh
v2 = 2gh
(Where v is the initial speed of the
block and bullet after impact.)
v = √2gh
Going back to the through the original momentum equation:
mbvb
= v =
(m + M)
vb =
(m + M)
mb
x
mbvb = (m + M)v
√ 2gh
√ 2gh
By placing in this equation all the
know values, the speed of the bullet
just before it hit the block can be
determined
p. 109
3.5 The Law of Conservation of Mechanical Energy
In this section, you should understand how to solve the following key questions.
Page #107 - Practice Problems 3.5.1 Conservation Of Mechanical Energy #1– 3
Page#110
Quick Check #1 – 3
Page #111 – 112
3.5 Review Questions #1 – 7
To be sure you understand the concepts presented in the entire chapter on Energy:
Page #113 – 116
Chapter 3 Review Questions #1 – 21