http://ssrsbstaff.ednet.ns.ca/nsmart/
Nathan Smart
October 23, 2009
njsmart@nstu.ca
Frictionless
Friction
and
Simply
Simple
Machines
Why are simple machines popular?
Because we’re lazy!
…….…. Or weak.
Are simple machines really all that
and a side of chips?
Well….
Yes!
… and No
Huh?!?!?
It’s a compromise thing
Do you want a job to be
hard, but over quickly?
Force
Or would you rather it be
easy, but take longer?
versus
Work
Is a little force really going
to hurt me?
A little force may not
That depends….
But not all forces are little
Ok, so how about this work thing?
Work = Force x Distance
With work it’s not just about how hard you have to
push, it’s also about how far you have to push.
PREPARE FOR SOME MATH!!!!!!!!!
Example
If I wanted to lift a box with a weight of 1000 Newtons (224 pounds) I
would need to apply a force of 1000 Newtons to get it off the ground.
1000 N
If I lift the box 1 meter off the ground,
then it should take 1000 Joules of work to
accomplish the task.
Force x Distance = Work
(1000 N) x (1 m) = 1000 J
An Alternative Course of Action
If I decide to push the same 1000 Newton box up a ramp, it may
only require a force of 200 Newtons to make it move. I’ll have to
push it farther though, because the ramp is on an angle.
Force x Distance = Work
(200 N) x (5 m) = 1000 J
Now to lift the box 1 meter off the ground I
have to push it 5 meters with a force of 200
Newtons. That’s still 1000 Joules of work.
1m
Wasn’t it supposed to take
more work?
200 N
Friction
Friction is a force that opposes all motion, but it’s not an equal opportunity
force. It depends on the surfaces that are in contact. Air presents very little
resistance, while solid surfaces can be much harder to move over.
When I push the box up the ramp I actually have to push a little harder
because I’m not just working against gravity anymore, I’m also working
against friction.
That means that the 200 Newton force that I thought I would need to push
with should be more like 250 Newtons. Now to push the box up the 5
meter ramp it will take 1250 Joules instead of the 1000 Joules needed to
lift it.
Force x Distance = Work
(250 N) x (5 m) = 1250 J
So what?
We just discovered that using the ramp is less efficient than simply lifting the box.
In other words, I did 250 joules more work pushing the box up the ramp to a
height of 1 meter than I would have done just by lifting it.
That’s the compromise. I get to apply less force when I use a simple machine, but
it comes at the cost of doing more work.
Lifting
(1000 N) x (1 m) = 1000 J
Pushing
(250 N) x (5 m) = 1250 J
Using any simple machine involves this tradeoff. There are times when it’s
necessary (like when you aren’t strong enough to lift the box). There are
also times when you might just be making more work for yourself.
Efficiency = Minimum Work You Could Have Done ÷ Work You Actually Did
Efficiency = 1000 J ÷ 1250J = 80 %
Static and Kinetic Friction
There are actually two types of friction; static and kinetic. Static friction refers to
the force needed to put an object into motion when it’s at rest. Kinetic friction
refers to the force needed to keep an object in motion once it has begun moving.
The force of static friction is almost always larger than the force of kinetic
friction. This explains why it is usually harder to start things moving, but once
they are moving it becomes easier to keep them going.
Measuring the two types of friction requires two different techniques:
To measure static friction you simply record the maximum force that can
be applied to an object before it begins to move.
To measure kinetic friction you must start the object moving and then
keep it moving at a constant speed before you record the force required.
If the object is speeding up or slowing down, the measurement is invalid.
This is easy to achieve with a spring scale by hand, but can be very
tricky when using weights to control the applied force.
What have we learned so far?
1) Force simply refers to how hard one thing is pushing on another.
The push can be caused by contact, like kicking a chair, or without
contact, like how gravity gives you weight.
2) Work measures how much force you apply over a certain distance.
Just remember that if you’re not pushing in the direction of motion, or
if there is no motion, you’re not doing any work.
3) Friction is the resistive force between two surfaces as they rub
against each other. Friction is always present, unless you’re moving
through a complete vacuum (which doesn’t exist). Friction can be
static or kinetic, depending on the situation.
Questions?
How do forces, work and friction
apply to simple machines?
We’re going to look at three simple machines and how
they work in terms of friction, work and force:
The Ramp
The Pulley
The Lever
Ramps
A ramp, or inclined plane, lets you elevate an object gradually over a
long distance instead of lifting it straight up. It can be very handy,
though it often requires far more work to accomplish the same result.
As the angle of the ramp decreases, the
force needed to overcome gravity also
decreases, but the force of friction (and
thus the work) increases.
gravity
friction
Forces and Friction on Ramps
Pushing something up a ramp is a balance between the benefit of less gravitational
resistance and the hindrance of more frictional resistance.
You can use a pulley to hang weights off of the end of a ramp. By adding weights until
the object on the ramp moves you can gauge the minimum force needed to move the
object. Vary the angle of the ramp to see what the optimum angle for that ramp is.
Work on Ramps
As mentioned earlier, to find the work done when using a ramp you need to
multiply the force used to ascend the ramp by the length of the ramp. You
could use the measurements from the previous friction experiment and simply
multiply the force you found by the length of the ramp. Just make sure that the
ramp always lifts the object to the same height.
Angle
Ramp Length
Force
Work
30o
2.0 m
6.0 N
12 J
45o
1.4 m
8.0 N
11 J
60o
1.2 m
9.0 N
11 J
90o
1m
10 N
10 J
Pulleys
A pulley is a simple machine that redirects forces. When several
pulleys are used together they can also decrease the force required
to lift objects. However, using this tool comes at a price.
weight
weight
These pulleys are allowing each
box to support the other’s weight.
weight weight
weight weight
The weight of the black box is transferred
through the ropes and pulleys to balance out
the weight of the red box and vice versa.
Forces and Pulleys
To use make pulleys really work for you, you’ll need something like the setup
below. The weight of the black boxes hanging from the pulley is shared on both
sides of the hanging pulley. This means that the red box only has to support half
the weight of the black ones because the ceiling is supporting the other half.
force from rope
attached to ceiling
2 X weight
weight
Balanced force means balanced boxes!
Friction in Pulleys
Testing the friction in a pulley can be done by balancing equal weights on a pulley
and adding more weight to one side until it begins to move. The extra weight that
you added before motion began equates to the amount of friction in the pulleys.
Balanced to begin with….
Still balanced, though it shouldn’t be….
Add one more….
It moved!
…Thrilling.
Work and Pulleys
We’ve seen that when a system of pulleys is used to lift things the system can do
some of the lifting for you. However, we know that this must come at some cost.
Since only half the
force is needed to
Before lift the boxes, they After
Lifting can only be lifted Lifting
half as far!
2 X distance raised
distance raised
Work = 2 boxes X 1 distance = 2
Work = 1 box X 2 distances = 2
The Lever
Leavers make our lives easier by allowing us to fiddle with where
certain forces are applied, and thus achieve useful results.
To see forces at work on a lever simply set up a good old-fashioned teetertotter. By moving weights around on the arms you can see how the lever will
multiply or divide the weight of objects by their distance from the pivot point.
Since the leaver rotates about the pivot point when forces are applied, we call
the resulting twisting force torque.
The torque due to any object sitting on the lever is equal
to its weight multiplied by its distance from the pivot point.
Torque = Distance x Weight
distance
weight
Torque and Levers
When 2 boxes are an equal distance from the pivot
their torque will be equal. Nothing will happen.
With different numbers of boxes the torque from
all the boxes on each side must be equal.
Torque = 1 box X 5 divisions = 5 (for both)
Torque = 1 box X 2 divisions = 2 (for both)
Torque = 4 boxes X 1 division = 4
Torque = 1 box X 4 divisions = 4
Friction in Levers
The most obvious sign of friction in levers is when they stick, i.e. they don’t
move even though the torques aren’t balanced.
Clearly, one unit of torque (measured in newton
meters) is unaccounted for in the diagram below. That
missing force must be the result of friction.
By slowly moving one of the boxes, you can find out exactly what
friction’s contribution is by finding the maximum extra distance
that you can sneak the box away from where it should be.
Torque = 1 box X 1 division = 1
Torque = 1 box X 2 divisions = 2
Work and Levers
You can demonstrate work done by a lever when using it to lift a
weight. Without friction, the work you do to one end of the lever
would be equal to the work you get out of the other end.
To lift this box to a certain height, you’ll only have to move the other end
of the lever half the distance, but you’ll need to apply twice the force.
Work = 1 box X 4 divisions = 4
2d
Work = 2 boxes X 2 divisions = 4
d