Superposition of
Waves
PC1141 Lecture 24
Linear Wave Equation
Consider an
element of a string
under tension T.
Remarks on Linear Wave
Equation
The term linear refers to the fact that the
equation is only a function of the first
power of y.
If y1(x, t) and
PC1141: Lecture 03-05
Vectors and Kinematics
in 2 & 3 D
Summary of Last Lecture
l
l
l
Quantities and units
l Unit prefixes
l Scientific notation
l Significant figures
l Dimensional analysis
Kinematics in 1D
l Displacement & distance
l Velocity & speed
l A
PC1141 Lecture 07 - 08
Applications of
Newtons Laws of Motion
Newtons Laws of Motion (Book)
I.
II.
III.
A body acted on by no net force moves with
constant velocity (which may be zero) and zero
acceleration,
If a net external force acts on a body, the bod
Work & Kinetic Energy
PC1141 Lecture 09
Motivation : Motion in vertical circle
We have earlier analyzed the motion of a particle in a vertical circle. By
resolving forces into tangential and radial components:
Qn: Can we write down the speed of m, at
any
PC1141 Lecture 06
Newtons Laws of Motion
Newtons Laws of Motion
Describes the relationship between
the motion of a body (kinematics) and
the mass and forces acting on it.
Classical mechanics deals only with
objects:
large compared with atomic
dimensions
PC1141: Lecture 02
Measurements & 1D
Kinematics
Quantities and Units
Experiments require measurements of
physical quantities.
Every measurement give a number with a
unit.
SI (metric) vs Imperial (British)
(Costly mistake : Mars Climate Orbiter 1999)
Stand
Laboratory Information
Laboratory organization
For safety concern, you must wear shoes (no sandals) and long pants when attending your laboratory sessions else you are prohibited from entering the laboratory. No
negotiation and no make up laboratory sess
Measurements and Data Analysis
1
Introduction
The central point in experimental physical science is the measurement of physical quantities.
Experience has shown that all measurements, no matter how carefully made, have some degree of uncertainty that may
Example 1: Thickness of a metal plate
Thickness
d0.001 (mm)
Manual Calculations
(di dmean)2
d1
3.087
Mean
mm
d2
3.156
Std. deviation
mm
d3
3.095
Std error
mm
d4
3.209
d5
3.131
d6
3.052
d7
3.034
d8
3.115
d9
3.044
AVERAGE()
mm
d10
3.080
STDEV()
mm
Sum
Excel
Linear Momentum
& Collisions
PC1141 Lectures 11
Linear Momentum
Linear momentum tells us both something about the object
and something about its motion.
The linear momentum of a particle of mass m moving with
velocity v is defined to be:
Components (recta
Potential Energy
PC1141 Lecture 10
Gravitational Potential Energy
Consider an object moving downwards from y1 to y2.
Work done by gravitational force is given by:
If m is moving upward from
y1 to y2, the work done is
given by the same formula
(value is of
PC1141 Lecture 23
Sound
Waves
Sound Waves
Longitudinal waves
that travels through a
material medium
when the medium is
disturbed.
Described by
changes in pressure
or displacement of
medium elements.
If disturbance
(source) is
Speed of Waves
Transverse
wav
Oscillations:
Simple Harmonic Motion
Damped & Forced Oscillations
PC1141 Lecture 21
Examples of Oscillatory Motion
Mass on a spring
Pendulum (e.g., simple,
physical, torsion)
Vibrations of a stringed
musical instrument
Electromagnetic waves (light,
radio,
Wave Motion
PC1141 Lecture 22
Introduction
Many types of wave motion are encountered in physical
world.
Main types : mechanical waves & electromagnetic waves.
n
n
n
Water waves
Waves on strings, drums
Sound waves, etc
n
n
n
radio waves, TV waves
Infra-red
PC1141Lectures1920
Newtons Law of Gravitation
&
Planetary Motion
Newtons Law of Universal
Gravitation
Every particle in the Universe attracts every other
particle with a force that is directly proportional to the
product of their masses and inversely prop
Fluid
Mechanics
PC1141 Lecture 18
Pressure (Recall)
Fluid - Substance that flows liquids and
gases.
Force exerted by fluid on objects always
perpendicular to surface.
Pressure P defined as:
Pressure is a scalar - proportional to
magnitude of force.
Unit f
Static Equilibrium &
Elastic Property of Matter
PC1141 Lectures 17
Equilibrium & Static Equilibrium
Equilibrium means that an object is at rest or its center of
mass moves with constant velocity.
Static equilibrium refers to the former situation (object a
Rotation&
MomentofInertia
PC1141 Lecture 13
Rigid Body Rotation
Rotation of an extended object - different
parts of an object have different linear
velocities & accelerations.
Assumption that extended object is rigid
(non-deformable, internal motion negle
Angular
momentum
PC1141 Lecture 16
Torque: A cross-product
Remember that the torque of a force was earlier defined as:
This is just the magnitude of torque
vector about O:
F
Direction of vector is normal to the
plane formed by r and F.
Angular Momentum
Th
Rotational
Dynamics &
Rolling Motion
PC1141 Lecture 14-15
Definition of Torque
Torque (moment) is a measure of the tendency of a force to
rotate an object about some axis.
The line of action of a
force is an imaginary
line extending out both
ends of the v
Centre of Mass &
System of particles
PC1141 Lecture 12
Centre of Mass
A mechanical system moves as if all its mass were
concentrated at its centre of mass (CM).
If an external force F acts on this system of total mass M,
the CM accelerates at a = F/M.
Thi
Measurements and Data Analysis
Example 1: Thickness of a metal plate
A student measured the thickness of a metal plate and obtained the results as follow:
d 0.001 mm
3.087
3.156
3.095
3.209
3.131
3.052
3.034
3.115
3.044
3.080
Determine the best estimate f
PC1141 Physics I
Sonometer
1
Objective
Demonstrate formation of standing waves on a string from the interference of travelling
waves travelling in opposite directions.
Investigate standing wave patterns formed on a string for several resonant frequencie
Tutorial 5
_
Week 11
1. Two friends are carrying a 200-kg crate up a flight of stairs.
The crate is 1.25 m long and 0.50 m high, its center of gravity
is its center. The stairs make a 45 angle with respect to the
floor. The crate is also carried at a 45 a
Tutorial 4
_
Week 9
Please attempt the following questions before attending the tutorial.
1. a) Show that the moment of inertia of a cube of mass m and side 2a about one of the edges
is given by 8 ma 2 .
3
HINTS:
Calculate the moment of inertia by perform
Tutorial 3
_
Week 7
Please attempt the following questions before attending the tutorial.
1. A 1.8-kg duck flies at a height of 15 m above the ground and a rate of 5.0 m/s in an easterly direction.
A golf ball of mass 50 g launched from the ground at an a
Tutorial 2 - Solutions
_
Week 5
NOTE: While practicing, try to work-out the problems using the HINTS, before checking the solutions.
1. Block A weighs 8.0 N and block B weighs 16.0 N. The coefficient of sliding friction between all surfaces
is 0.25. Find
Tutorial 1
_
Week 3
Please attempt the following questions before attending the tutorial.
1. Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van
155 m ahead travelling at 5.00 m/s. Sue applies her brakes but can