Download Friction, Springs and Scales

9/4/2011
Friction, Springs and Scales
Summary
Physics 1010: Dr. Eleanor Hodby
Last time
• Net force
- Terminal velocity
• F = ma
- Car crashes
Today
• All about force of friction
- How big is it?
- What causes it
- How to reduce/increase it
Day 6:
Friction
Springs and scales
Reminders:
Homework 3 due Tuesday!
No HW next week – just revision
No new reading
Review lecture Tuesday – email topics to me ASAP
• All about springs
- How is spring force related to extension of spring
- How to make a spring scale
Investigating friction
Investigating friction
+
Force sensor + metal weight
Total weight = 12N
PULL 
Force sensor plus metal weight has mass of 1.2 kg,
It weighs approx. how many N? (How much force needed to lift it?)
b. 12
c. 1.2/2.2
d. (1.2/2.2) x 9.8
Friction between table and force sensor.
Predict graph of force which we must apply by pulling on string in order to
move sensor along table at a constant speed … prediction should include
force from before starting to pull until sensor is moving at constant speed
across the table. (Make guess as to specific value as well as shape.)
Force sensor + metal weight
Applied
Force
?N
time
-? N
Force sensor + metal weight
Total weight = 12N
PULL 
Sliding (kinetic) friction
Force sensor + metal weight
Total weight = 12N
Fpull
Starts moving here
PULL 
FslideF
Force
a. 1.2
0
time
Balancing sliding friction:
How much force is required to keep it moving along table at constant speed if
weight of (force sensor + metal ) = mg = 12 N ?
a. Weight x 0.3, b. Weight x 0.7, c. Weight x 1.5
d. Weight x 5
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Sliding (kinetic) friction
Increase the mass to 5 kg, what is pulling force (approx) needed to keep
moving at a constant speed?
a. 0 N,
b. 4N
c. 17N d. 49N c. 100N
It takes a pulling force of 17N to keep a box moving in a straight line
across the floor at a constant speed of 0.2 m/s.
Now I double the speed to a steady 0.4 m/s. What constant pulling
force is required now?
a.
0N
b. less than 17N
• The atoms from the two surfaces catch and drag against each other
producing a force that opposes motion called friction
d. more than 17N
Friction and heat
Microscopic details of static and sliding friction
• Atoms of same material (color) all hooked together by forces like tiny springs
• Viewed at atomic level surfaces are never perfectly smooth
c. about 17N
Dragging surfaces across each other causes atoms to start vibrating= heat!
Heat energy produced = work done = F friction x distance moved.
Examples:
-Rubbing hands together to keep warm
- Rubbing 2 sticks to start a fire
- Spinning tires on car
block
friction force
on block
opposing motion
block
Motion of block
Motion of block
table
table
Why is maximum static friction force greater
than sliding friction force?
• When stationary, atoms at surfaces can get embedded and stuck more than
when sliding.
 So maximum static friction force bigger than sliding friction force.
What if you increase the weight of an object?
• Frictional force increases proportional to weight
• More force pushing surfaces together
 atoms at surface mesh together more
 more friction
• Size of frictional force also depends on material in each surface
Increased weight force
block
block
table
table
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How does a lubricant affect friction?
A lubricant is:
• A layer of slimy stuff between surfaces
• Doesn’t stick to either surface, flows out of way of surface atoms
• Keeps surfaces apart
• e.g. oil, snow, water
• Reduces friction between the 2 surfaces
Physics that might save your life
Why are you supposed to pump your brakes
when stopping on wet or icy road?
a. to avoid brakes overheating and wearing out faster
b. to keep tires rolling so do not skid and wear out tires
c. to make brake lights flash on and off to get attention
of drivers behind you.
d. to keep tires rolling so will slow down more quickly
Back to wheels and friction
Rolling wheels
Friction allows cars to speed up or slow down.
- Car tires exert frictional force on road
- Road exerts frictional force on tires and hence car which changes velocity
- If rolling, tire in contact with road is stationary  use static friction force
- If skidding tire is moving relative to road  use sliding friction force
 Max static frictional force > sliding friction force.
 If wheel rolling and using static friction you can acc/decelerate more rapidly
vcar
What is the velocity of the point of the wheel in contact with the ground?
a. 0
b. vcar
c. – vcar
d. something else
Speeding up:
vcar
Force of tire on road
Slowing down:
vcar
Force of road on tire
(and car)
Microscopic picture of rolling wheel
No surfaces sliding across each other
Drive … engine rotates tire.
Tire pushes backwards on road.
Force of road on tire (and car)
Braking – tire rotation slows down
Tire pushes forwards on road
Force of tire on road
Springs – another kind of force
 No work by friction
 No heating
 No wasted energy
If wheel spinning rather than rolling, then LOTs of work by friction
tire
Car motion
road
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Everything you need to know about springs
Relaxed spring
• Hand holding spring at extension x
• Hand pulling to right
• Spring pulling to left
• In equilibrium: Fhand = Fspring
+
x
Identical
stretched
spring
Important note about vectors in diagrams and equations
+
x
In diagrams:
• Always define +ve direction
• Arrow represents direction (sign of vector)
• Letter is the MAGNITUDE so always
represents a POSITIVE number
From experiment we know:
Fspring  x
Extension (m)
Fspring
Fhand
Fspring
Force of spring (N)
Minus sign:
Spring force opposes extension
Vectors in opposite directions
In equations:
Spring constant
Postive number
Units: N/m
• Letter represents a positive number
In equilibirum:
Net force = Fhand – Fspring = 0
Fhand = Fspring
Pull down on spring with
2N of force … measured
by probe
• Arrow in diagram relates to sign infront of
letter in equation (±)
Investigating springs
Investigating springs
Relaxed
Spring
Fhand
Fspring = - kx
Relaxed
Spring
Pull down on spring with
2N of force … measured
by probe
Spring stretches
??? meters.
Spring stretches 0.05m
Force Probe
Force Probe
How much would it stretch if pull down on spring with force of 6 N?
How much would it stretch if we hang a 0.2 kg mass on the spring?
a.
b.
c.
d.
e.
a. same distance as for 2 N force
c. 2 times as far
e. Less than ½ as far
0.02m
0.05m
0.1m
0.15m
0.5m
Scales
• Scales (eg bathroom scales) are just
calibrated springs.
• On scales, mass is stationary and in eqm.
 Net force = 0
 Spring force balances weight force
Scale relates
x to weight (N)
kx
5
Mass
10
Weight (N)
0
+
In equilibrium:
 Fnet = 0
 Fnet = mg – kx = 0
 mg = kx
mg
b. ½ as far
d. more than 2 times as far
Example
I hang a 2 kg mass from a spring and it stretches 2cm.
What is the spring constant (k) of the spring? (assume g = 10m/s 2)
a) 10 N/m
b) 100 N/m
c) 1000N/m
Relaxed
d) 10000 N/m
Stretched
Spring:
e) None of these.
spring
Zero
extension
x
+
x directly related to weight force, mg.
So if you have a spring and measure the value of k (calibrate it), then you can
hang any weight on it, and from x can calculate the weight (mg) and (if on
earth) the mass (m)
kx
mg
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More spring questions
Example
I hang a 2 kg mass from a spring and it stretches 2cm. This implies
that k = 1000N/m.
I remove the first mass and hang a different, unknown mass off the
same spring. It stretches 8cm from its natural length.
What is the second mass in kg?
a) 2 kg
b) 2/3 kg
Relaxed
c) 4kg
Stretched
Spring:
d) 8kg
spring
Zero
e) Not enough information given
extension
Relaxed
Spring
Now hang 0.2 kg mass (2N of force)
off fatter, stiffer spring
X?
Mass
How will spring stretch change?
a. Stretches same distance as before.
b. Stretches further than before.
c. Stretches less than before.
x
kx
mg
More spring questions
X?
Relaxed
Spring
Mass
What about squashing the spring?
When I hand a 0.2 kg mass on the spring it
stretches as amount xhang
How much would it compress if we placed
a 0.2 kg mass on top of it?
a. xsquash smaller than xhang
b. They are about the same
c. xsquash bigger than xhang
kx
X
Springs in ropes … what’s good choice of rope
For climbing, best to use …
a. rope with soft spring
(lots of stretch)
b. rope with stiff spring
(not much stretch)
c. doesn’t matter… any
spring is good.
d. I still haven’t figured out the buttons on
my clicker.
Mass
mg
5