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Page 1: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.
Page 2: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Torque

Section 8-1

Page 3: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Recall Equilibrium

In general: Things at restConstant uniform motion

In particular: Equilibrium means that the Sum of forces acting on an object equals zero - there is

No net force = No net acceleration

Page 4: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Up to now, we have had just one type of equilibrium:

For straight line motion:

Translational Equilibrium

ΣForces = 0

Force produces acceleration

Page 5: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Now, we have one for circular motion,

Rotational Equilibrium

ΣTorques = 0

Torque produces rotation

Page 6: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Torque is similar to Work.

Work (W) = Fd cosθ where d = distance

Torque () = Fd sinθ where d = lever arm

Units for both are N·m

BUT, where Work can also use Joules

Torque is just N·m

Page 7: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Lever ArmLever Arm is the distance from where the force is applied (the door knob)

to where rotation takes place (the hinge).

But we only count that part of the force that is perpendicular to the rotating body (sin).

Page 8: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

To maximize the effect of force, it must be applied perpendicular to the lever arm.

Page 9: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Sinθ can be a bit tricky...

This angle

Not this one

Lever arm

You want an angle as close to 90 as possible (perpendicular), sin(90) = 1

Page 10: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Note: In Fd(sinθ),

sinθ is simply multiplied by F and d.

Your text applies it to d

I prefer to apply it to F. For problem solving, it makes no difference.

BUT... use common sense. Make sure you show going DOWN as the angle you apply the force at gets smaller.

Page 11: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

A Practical Example

Both the girl and boy will produce a torque around the fulcrum.

The boy will produce a clockwise torque.

The girl will produce a counter-clockwise torque.

Page 12: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

If the sum of torques in a system = 0, the system is in...

Rotational Equilibrium, which means...

It will not rotate at all, or...It will spin at a constant rate

Important thing is; if torque is 0, just like if force is 0, there will be no change in motion.

No acceleration = Equilibrium.

Page 13: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

How far from the fulcrum must the boy sit to bring this system into rotational equilibrium?

Rotational Equilibrium requires: ccw = cw

(300 N)(4 m) = (400 N)(d)d = ?

d = 3 m

d

Page 14: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Can you play see with no saw?

We know we can, but do we know how?

The trick is to get the board to be the saw

Page 15: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

This is just a shade tricky, so watch closely.

For any object, we can consider that the entire weight of the object

seems to be concentrated in one place called the

Center of Mass (COM)

COM is usually at the center of the object.

Page 16: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

A simple board acts this way.

The entire weight of the board seems to be concentrated at its COM.

Just like any other force, the weight of the board produces a torque.

This torque acts at the COM of the board.

COM

Fw

Page 17: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

If the board is supported at its center,

the effect of this torque is zero because the lever arm (COM to fulcrum) is zero.

COM

Fw

Page 18: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

But, if the board is supported off center,

the weight of the board produces a torque

with a lever arm distance equal to the distance from the fulcrum to the board's center.

COM

Fw

lever arm

Page 19: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

So, can you do this?

ccw = cw

(600 N)(1 m) =(Fw)(3 m)

Weight of Board (Fw) = 200 N

Page 20: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

CW 8 A

Page 21: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

SECTION 8 - 4

Page 22: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Skinner's Simple Law For Survival

Simple Machines

Mechanical Advantage

Efficiency

Page 23: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Skinner's Simple Law for Survival

If you remember nothing else from this course, remember this:

There are no free lunches in theknown universe.

There is a price for everything, but,

everything has a price.

Page 24: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Simple Machines

Wheel & Axel

Pulley

Wedge

Lever

Inclined Plane

Screw

Six Types:

Page 25: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

We use machines:

• To enable us to do work that we could not otherwise do

• To make work easier

Page 26: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Machines CAN:

• Multiple the force we are able to exert

• Change the direction of the force we exert

• Multiple the distance we can move something

Page 27: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Machines CANNOT:

• Multiple energy

• Multiple work

To do either of these two things, would be to violate...

Skinner's Simple Law For Survival.

Page 28: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

How machines do what they CAN do:

Work = Force x distance

To do work, you have to be able to exert enough force to make an object move.

If you cannot exert enough force to make the object move, you cannot do work.

No work = no lunch.

Page 29: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

To calculate the work done,

simply multiply the force you put into the object

by the distance it moves.

Distance is the distance moved AGAINST resistance to applied force.

Page 30: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

FOR ALL PRACTICAL PURPOSES, this is distance against gravity, which means

STRAIGHT UP

You WILL NOT be concerned about any other distance (such as horizontal) unless

Friction is involved.

Page 31: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

an example...

This is a general form for a simple machine showing in and out force and distance.

What's important is to note that YOU do work on the machine. IT does work on the load.

Page 32: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

So...

Suppose you need to move a 50 kg object a distance of 3 m.

W = Fd

F = ma (50 kg)(10 m/s2) = 500 N

So Work = (500 N)(3m) = 1500 J

1500 J (work) is what you will be paid for.

Page 33: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

We need to consider two things:

Amount of Force Required

Amount of Work needed to be done.

NEVER FORGET that while a machine CAN

multiple force

it CAN NOT multiple work

Page 34: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

So, 2 requirements:

• produce 500 N of force

• do 1500 J of work

If force is no problem, just do it.

But if it is a problem, then we need help

Page 35: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

A Simple Machine can help

Because it can multiply force.

We need 500 N, but we can only produce 250 N.

We need a machine that can multiply the force we can produce by how much?

2 times.

Page 36: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

A machine that multiplies force by 2 times is said to have

a Mechanical Advantage (MA) = 2

You will need to know that, as well as

how to compute Mechanical Advantage:

Machine IntoPut You ForceLoad Into Puts Machine Force

MA

Page 37: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

In this example,

Machine Does = 500 N

We Do = 250 N,

so: MA = 500 N/250 N = 2

Machine multiplies our force by 2

Before we choose which simple machine to use, let's complete the math.

Page 38: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Recall that we must do 1500 J of work on the object.

Because of the simple machine, we only have to produce 250 N of force (instead of the 500 N).

The machine will multiply our 250 N by 2 to get the required 500 N.

Page 39: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

That looks like getting something for nothing,

but we know we cannot get something for nothing.

So what else MUST be involved?

Recall that there was a requirement to move the 50 kg object 3 meters.

That requires 1500 J of work

Page 40: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

The machine will do 1500 J of work

ON THE OBJECT

How much work must we do

ON THE MACHINE?

1500 J

And now, the rest of the story...

Page 41: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

ON THE MACHINE, we must do:

1500 J = Fd

1500 J = (250 N)(d)

d = 6 m

Page 42: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

The machine puts OUT 500 N for 3 m

We put IN: 250 N for 6 m

In BOTH cases, 1500 J of work is done.

Page 43: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Instead of moving the object 3 meters,

We move the machine 6 meters.

The machine moves the load the required 3 m.

Page 44: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

We wind up doing exactly the amount of work required,

but without the machine,

we could not have done the job at all.

Getting a job done by a machine that we could not do ourselves may look like a free lunch, but we're not quite done yet...

Page 45: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

In general we have ignored friction in this class.

However, we know it is present even when we can't see or measure it.

When dealing with simple machines, WE MUST consider it.

With friction (which is always present) we will have loses.

Page 46: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Let's Suppose...

That we chose an incline plane to help us do this job.

The situation might look like this:

50 kg object 3 m high loading ramp

Page 47: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

We need to move the object to the top of the loading ramp.

Since the object has a mass of 50 kg, it will require (F = ma) = (50 kg)(10 m/s2) = 500 N

Lifted 3 m (remember – vertically, against gravity)

Page 48: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

But, since we are only able to put 250 N of force into the problem, we use a simple machine with an MA = 2.

And, since we must still do the entire 1500 J of work, we found that we must move the object 6 m.

That would be the distance "up the incline".

That involves friction.

Page 49: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

So, in reality, we will need to produce a little more than 250 N of force

say, 275 N.

So how much work will we really be doing?

W = Fd

W = (275 N)(6 m) = 1650 J

Page 50: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

So, we actually do 1650 J of work,

But we only get paid for 1500 J.

Where did the other 150 J go?

It was consumed by friction between the sliding load and the surface of the plane.

This was converted to heat so it really wasn't lost.

Page 51: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

BUT

There is a net loss of work as far as we and the object are concerned.

This is the price of using a simple machine.

Loss of input work, the essence of

EFFICIENCY

Page 52: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

EFFICIENCY

Another ratio:

in

out

WorkWork

Efficiency

It is VITAL that you remember Skinner's Simple Law of Survival, here.

Because you can't get something for nothing,

Page 53: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

Efficiency:

WILL ALWAYS BE LESS THAN 100%

You will always put in more than you will get out.

In this case, 91% J 1650

J 1500 Efficiency

Like with MA, units cancel out.

Page 54: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

An Aside...

in

out

FF

MA We used the ratio

To calculate Mechanical Advantage. There is another way:

Out DistanceIn Distance

MA In our example, that was the 6 meters we moved the object divided by the 3 meters the machine lifted the object.

Page 55: Torque Section 8-1 Recall Equilibrium In general:Things at rest Constant uniform motion In particular:Equilibrium means that the Sum of forces acting.

CW on Simple Machines