3.1 Spring Scales
New ideas for today
• Weight vs. Mass
• Springs
• Scales
http://www.youtube.com/watch?v=MFXLhN3YNmg
Springs, torsion spring
Observations
• Lots of useful and fun things have springs
in them
• Different types of materials act as springs
• Springs always seem to exert a force on
you
• Scales measure your weight…sometimes
How is all of this related?
A Free Spring
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•
•
•
A free spring adopts a certain length
Its ends experience zero net force
Its ends are in equilibrium
The spring is at its equilibrium length
Hooke’s Law
A Distorted Spring
• If you distort a spring, forces act on its ends
• These forces
– act to restore the spring to equilibrium
length
– are called “restoring forces”
– are proportional to the distortion
Hooke’s Law
The restoring force on the end of a spring is
equal to a spring constant times the
distance the spring is distorted. That force
is directed opposite the distortion.
Restoring Force = – Spring constant
x Distortion
Spring compression
F = -k x
“+”
F = -k x = -k 0 = 0
F = -1 N/cm· 1 cm = -1 N
F = -1 N/cm· 2 cm = -2 N
F = -1 N/cm· (-1) cm = 1 N
Springs
Metal sheet
Always produce a force that opposes the
distorting force
Clicker question
The figure shows a strobed photograph of a small ball being shot
upward by a spring. The spring, with the ball on top of it, was initially
compressed to P (its equilibrium position is Q). The ball left the spring
at point Q and flew up to point R. Neglect air resistance. Which is a true
statement?
A. The spring force at P is
less than the force of
gravity on the ball.
B. The spring force at P is
greater than the force of
gravity on the ball.
C. The spring force at P is
equal to the force of
gravity on the ball.
Follow the money work.
What is the difference between the FLYBAR
and a normal POGO stick?
How do diving boards and trampolines allow
you to jump higher?
Why can you jump higher on the FLYBAR?
Scale
Spring Scales
Use a spring to
measure weight
Equilibrium
• An object in equilibrium
– experiences zero net force
– is not accelerating
• At equilibrium,
– individual forces balance one another
perfectly
– an object at rest remains at rest
– an object in motion coasts
Clicker Question
Scale on skates
A scale sits on a skate. A mass hangs over a pulley on one
end, and the other end is attached to a pole (fixed).
Read the scale.
Now, remove the fixed end and attach it to an identical
mass hung over a pulley. Compared to the first case,
does the scale read:
A) Twice
B) Half
C) The same
Scale on spring
Spring Scales and Acceleration
• Weight measurement requires equilibrium
• Without equilibrium,
– spring force doesn’t balance weight
– “measurement” is meaningless and
inaccurate
• You must not bounce on a scale!
(wait for the scale to settle before reading)
Clicker question:
If her weight is 500 Newtons, what does the
scale read (in Newtons)?
A) 500
B) 1000
C) 550
D) 450
Mass=
50 kg
Two scales
Total Weight = sum of all four measurements
Balance
A balance measures MASS
The international
mass standard is the
only “old school”
standard left
There’s a big effort
to redefine the
kilogram:
•Watt balance
•Extremely round
silicon sphere