Transcript Friction and Inclined Planes

Frictional Forces
• Question: how does a highway patrol
officer use skid marks to recreate an
accident?
• What produces skid marks on the road?
• The wheels on a car lock, and rub the
surface of the road
• As this occurs, the car slows down
• Why?
• Frictional forces
Friction: The Force that Slows Us
• http://phet.colorado.edu/new/simulations/si
ms.php?sim=Friction
• On what does this force depend?
• How do we quantify it?
• The frictional coefficient describes the
interaction between two surfaces
• Symbol is m
• The higher the value, the rougher the
surface interaction
Which surface interaction would
have the highest frictional
coefficient?
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Ice rubbing against ice
Wood on a table top
Wood on mouse pad
Water on rock
Teflon on glass
Consider three surface interactions: Rubber
on glass (A), rubber on concrete (B), and
rubber on ice (C). Rank these in order of
decreasing m.
• 1. A, B, C
• 2. B, A, C
• 3. A, C, B
• 4. C, A, B
• 5. B, C, A
Some Values
Other Factors?
• Quick Experiment:
• Slide your textbook across the desk
• Now slide it across the desk while you
push down upon it
• Which produces more friction
• Why?
• We’re increasing the normal force
Frictional Calculations
• Friction Force = m N
• This works for both static and
kinetic friction
A 1000kg car screeches to a halt
on a surface with m = 0.5.
Calculate the frictional force acting
upon the car
Think about pencil sitting at rest on the
top of your text book. As you tilt the
cover of your book, what happens to the
frictional force?
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1. It increases
2. It decreases
3. It stays the same
4. Who cares, the NCAA tournament is 7
weeks away
• Think about why you chose your answer
• Imagine a highway patrol officer, arriving
at the scene of an accident
• He uses something called a drag sled to
determine the amount of friction produced
by the road
• Assuming he applies a 40N force to pull a
5kg drag sled at constant velocity across a
horizontal road way, what is the coefficient
of friction between the road way and drag
sled?
• So if he knows m for the interaction
between roads and tires, how will he figure
out the car’s acceleration?
• Newton’s 2nd law!
• Frictional Force = mN = ma
Another car, mass 2000kg slides across a
slick road with m = 0.2. Calculate the
magnitude of this car’s acceleration
• Bonus Question: How would this
acceleration compare to that of a 4000kg
car?
A 3900kg Hummer has an acceleration of
5.9m/s2 as it slides to a stop. What was the
coefficient of friction between the Hummer’s
tires and the road way?
Friction Types
• Static friction is the force of friction that
keeps an object at rest
• Kinetic friction acts on the object once it is
moving
• Which is larger?
Some Values
The 3900kg Hummer, moving at
20m/s, locks its brakes and
starts skidding on a road with
frictional coefficient 0.75. What
minimum distance does the
Hummer need to stop?
Friction in Multiple Dimensions
• A traveler pulls his rolling bag at constant
velocity across a horizontal surface by
applying a 50N force, directed at an angle
of 45 above the horizontal. Assuming the
bag’s mass is 10kg:
• Find the normal force acting on the bag
• Find the frictional force acting on the bag
• Find the coefficient of friction between the
ground and bag
• If the traveler from the previous problem
pulls his bag with a force of 30N, directed
at 30 above the horizontal, find the bag’s
acceleration across the floor
Inclined Planes and Friction
• The ancient Egyptians used inclined
planes to help build the pyramids
• How did they ensure that the blocks they
were pulling didn’t slide back down the
ramp and kill them?
• Think about a book (m = 1.5kg), lying at
rest on a slanted table (makes an angle of
15 with the horizontal)
• Draw a force diagram for this book
• Find the frictional force acting on the book
• Find the normal force, and the coefficient
of friction between table and book
Hitting the Slopes…
• A snowboarder (m = 95kg) travels down a
hill at an angle of 25 above the horizontal
• Assuming the skier travels at constant
velocity, find the frictional force acting on
the skier, and mk
• Force = 400N
• Coefficient = 0.47
• Now we all know that snowboarders speed
up as they go down a slope
• Assuming the same mountain from before,
with m = 0.2, find the snowboarder’s
acceleration
• Given such a low friction coefficient, how
does the skier slow down (ie, which forces
slow her down)?
• a = 2.4 m/s/s
Building the Pyramids
• Constructed from approximately 25802560 BCE
• The world’s tallest structure (480 ft, now
460ft) for over 3000 years
• The pyramid contains 2 million blocks,
each weighing 1.5 tons
• Some materials were transported over 500
miles to the construction site
• A truly massive undertaking (no pun
intended…)
• http://maps.google.com/
Moving a Block up a Ramp
• Let’s think about moving one block (W =
1.5 tons = 20,000N) up a ramp of unknown
angle
• Assuming the coefficient of static friction
between the ramp and block is 0.6, find
the maximum angle of inclination at which
the block will remain at rest
• Theta = 31 degrees above the horizontal
• Now, assuming the coefficient of kinetic
friction between the block and ramp is 0.5,
find the minimum force necessary to pull
the block up a ramp at an inclination of 15
degrees
• If the block gets pulled with a force of
20kN up the ramp, what is the block’s
acceleration?
Using Pulleys to Help
• Imagine using a pulley system to aid in
your block lifting (although the Egyptians
had not yet thought of pulley-systems)
• In the absence of friction, find the
acceleration of block 1
• Assuming a kinetic frictional coefficient of
0.4, calculate the mass of the hanging
block necessary to make the second block
slide up the ramp at constant velocity