Transcript Work and Energy

Work and Energy
Conception of Work
For the simplest case, where the force is constant and the
motion takes place in a straight line in the direction of
the force we define the work done on an object by
applied force as a product of the force and the distance
through which the object is moved. In shorter form
Work = force x distance
More generally, work is a product of only the
component of force that acts in the direction of
motion and the distance moved. For example, when a
force acts at right angles to the direction of motion,
with no force component in the direction of motion,
no work is done!
Conceptual Question
Does Earth do work on Moon?
Important: Definition of work
involves both a force and a
distance.
Units of Work
1J=1Nm
Power
Power = work done/time interval
Units of Power
1 W = 1J/s
Mechanical Energy
We can define energy as “the
ability to do work”.
The energy of an object at motion
is called kinetic energy.
Conservation of Kinetic Energy
Question
Are the collisions of billiard balls perfectly elastic?
Conservation of Kinetic Energy:
Example.
The net work done on an object is
equal to the change in its kinetic
energy.
Conceptual Example:Work to Stop a car
An automobile traveling 60 km/h brake to a stop within a
distance of 20 m. If the car is going twice as fast, 120 km/h,
what is its stopping distance? The maximum braking force is
approximately independent of speed.
Questions
Can an object have energy?
Can an object have work?
Potential Energy
Potential energy is the energy
associated with forces that depend
on the position or configuration of
a body (or bodies) and the
surroundings.
PE of Gravity
We will define the potential energy of a
body as the product of gravitational force
mg acting on a body and its height h above
some reference level.
Important: The change in potential energy
between any two points does not depend on
the choice of reference level.
Important: The changes in gravitational
potential energy depend only on the change in
vertical height and not on the path taken.
PE of Elastic Spring
Equation
Fs = - kx
is known as spring equation and
also as Hooke’s law.
Elastic PE =
2
kx /2
Important: Potential energy
belongs to a system, and not to a
single object alone!!!! The
potential energy is a property of a
system as a whole.
Mechanical Energy and its
Conservation
If no frictional (or other dissipative)
forces are involved, the total
mechanical energy of a system
neither increases nor decreases in any
process. It stays constant – it is
conserved.
Total energy cannot be created or
destroyed; it may be transformed
from one form into another, but
the total amount of energy never
changes.
Problem Solving Using Conservation
of Mechanical Energy
If the original height of the stone is y1 = h = 3.0m,
calculate the stone’s speed when it has fallen to 1.0m
above the ground.
Conceptual Example: Speeds on
Two Water Slides
Two water slides at a pool are shaped differently, but have the
same length and start at the same height h. Two riders, Paul
and Kathleen, start from rest at the same time on different
slides.
(a) Which rider, Paul or Kathleen, is traveling faster at the
bottom?
(b) Which rider makes it to the bottom first?
Questions
1. You have been asked to analyze a collision at a traffic
intersection. Will you be better off to begin your analysis
using conservation of momentum or conservation of kinetic
energy? Why?
2. If a system has zero kinetic energy, does it necessarily have
zero momentum? Give an example to illustrate your answer.
3. An object has a velocity toward the south. If a force is
directed toward the north, will the kinetic energy of the
object initially increase, decrease, or stay the same? Explain.
1. In tryouts of the national bobsled team, each competing team
pushes a sled along a level, smooth surface for 5 meters. One
team brings a sled that is much lighter than the others.
Assuming that this team pushes with the same force as the
others, compare the kinetic energy of the light sled to that of
the others after 5 meters . Compare the momentum of the
light sled to that of the others after 5 meters.
2. Suppose the rules were changed in previous question so that
the teams pushed for a fixed time of 5 seconds rather that a
fixed distance of 5 meters. Compare the momentum of the
light sled to that of the others after 5 seconds. Compare the
kinetic energy of the sled to that of the others after 5 seconds.