Physics 106 Lesson #1
Mass and Weight
Dr. Andrew Tomasch
2405 Randall Lab
atomasch@umich.edu
Mechanics: The Big Picture
 Kinematics: How
objects move
 Dynamics: Why
objects move
 Energy and
momentum
 Fluids (Resting and
moving)
 Oscillations and
Waves
 How does the
mechanical world
work?
Galileo Galiliei
Johannes Kepler
Isaac Newton
Units for Physics
• How to describe motion?
– Measurements →
Physical Quantities
– Requires units →
• Système International (SI)
units:
SI units are also called MKS units
for Meters, Kilograms and Seconds
Prefix
Fact.
Symb.
Common
name
Giga-
109
G
Billion
Mega-
106
M
Million
Kilo-
103
k
Thousand
Centi-
10-2
c
Hundredth
SI
CGS
BE
Length
meter (m)
centimeter (cm)
foot (ft)
Milli-
10-3
m
Thousandth
Mass
kilogram (kg)
gram (g)
slug (sl)
Micro-
10-6
m
Millionth
Time
second (s)
second (s)
second (s)
Nano-
10-9
n
Billionth
Two Quantities: Scalars & Vectors
• Scalars: magnitude only (ex: radius R =10 cm)
• Vectors: magnitude and direction
– Arrow length ≡ magnitude of the vector
– Arrow direction ≡ vector direction
Example:
d
Displacement ≡
1m
d
d
= 1 m to the right
magnitude
direction
Mass and Weight
• Mass (or inertia) is an intrinsic property of matter. Mass
is a scalar.
• Weight is an attractive force exerted by the Earth on an
object in accordance with Newton’s Universal Law of
Gravitation. Weight is a vector with a magnitude equal
to the product of mass and the acceleration of gravity
(mg) directed toward the Earth’s Center, a direction we
perceive as “downward” toward the Earth’s surface.
• Weight depends on the properties of the gravitating
body (radius and mass) and is therefore different on
different planets. On Earth the acceleration of gravity
has a value of g = 9.8 m/s2. On the moon the acceleration
approximately 1/6 that at the Earth’s Surface
Spring Scales
• Springs can be used to make simple scales
• Spring scales measure weight by means of Hooke’s
Law which states that the force required to stretch a
spring is proportional to the distance the spring
stretches. The constant of proportionality between the
applied force and the distance the spring stretches is
called the spring constant or force constant of the
spring.
• Attaching a pointer to a spring and observing the
amount the spring stretches with a weight hanging on it
provides a direct measure of the weight (force) acting
on the spring.
• Since weight near the Earth’s surface is proportional to
the mass of an object (W = mg), scales can also be
calibrated in units of mass (grams, kilograms) rather
than in units of force (Newtons, pounds)
Hooke’s Law for Springs
• An applied force
stretches a spring:
Fapplied  kx
x  Distance spring has been
stretched from equilibrium
Fapplied
Robert Hooke
1635-1703
spring constant or force
constant units: N/m
“The force required
to stretch a spring is
proportional to the
distance the spring
stretches” Equivalently, the
Hooke’s Law works for
compressed springs too
amount a spring
stretches is
proportional to the
applied force: x = F/k
The Free Body Diagram (FBD)
• A “cartoon” used to
understand the forces
acting on an object
• Only the object and the
forces acting on it are
shown
• A powerful conceptual
tool for understanding the
net (total) force acting on
an object, which in turn
determines its motion
• Because the washer is at
rest the net (total) force
on it is zero
Spring Force
Fs= kx
Washer
Weight
W = mg