Work and the Dot Product
Dot Product
A scalar quantity
Magnitude:
rr rr
A " B = A B cos !
The dot product can be positive, zero, or negative
Two types of projections: the dot product is the parallel
component of one vector with respect to the second vecto
Chapter 11 Work and Kinetic Energy
11.1 The Concept of Energy
The transformation of energy is a powerful concept that enables us to describe a vast number of processes: Falling water releases stored gravitational potential energy, which can become the kin
Work and Kinetic Energy
Concept Questions
Question 1 Work and Kinetic Energy
Compared to the amount of energy required to accelerate a car from rest to 10 miles per
hour, the amount of energy required to accelerate the same car from 10 mph to 20 mph is
1.
Module 15: Simple Harmonic Motion
15.1 Introduction: Periodic Motion
There are two basic ways to measure time: by duration or periodic motion. Early clocks
measured duration by calibrating the burning of incense or wax, or the flow of water or
sand from a
Potential Energy and
Conservation of Energy
Conservative Forces
Definition: Conservative Force If the work done by
a force in moving an object from an initial point to a
final point is independent of the path (A or B),
B
rr
Wc ! # Fc " dr
A
(path independ
Potential Energy Diagrams
Challenge Problems
Problem 1
A particle moves along the x -axis under the influence of a conservative force with a
potential energy U ( x ) . A plot of U ( x ) vs. x is shown in the figure above. The figure
shops several alternat
Simple Harmonic Motion
Concept Questions
Question 1 Which of the following functions x(t) has a second derivative which is proportional
to the negative of the function
d 2x
! "x ?
dt 2
1. x(t ) =
12
at
2
2. x(t ) = Aet / T
3. x(t ) = Ae ! t / T
" 2!
4. x(
Conservation of Mechanical
Energy
8.01
Non-Conservative Forces
Work done on the object by the force depends
on the path taken by the object
Example: friction on an object moving on a
level surface
Ffriction = k N
Wfriction = ! Ffriction "x = ! k N "x < 0
Conservation of Energy
Concept Questions
Question 1: A block of inertia m is attached to a relaxed spring on an inclined plane. The
block is allowed to slide down the incline, and comes to rest. The coefficient of kinetic
friction of the block on the incl