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 an object equals zero - there is No net force = No net acceleration

Up to now, we have had just one type of equilibrium: For straight line motion: Translational Equilibrium Σ Forces = 0 Force produces acceleration

Now, we have one for circular motion, Rotational Equilibrium Σ Torques = 0 Torque produces rotation

Torque is similar to Work. Work (W) = Fd cosθwhere 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

Lever Arm Lever 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  ).

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

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

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.

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.

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.

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

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

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.

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 FwFw

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 FwFw

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 FwFw lever arm

So, can you do this?  ccw =  cw (600 N)(1 m) =(F w )(3 m) Weight of Board (F w ) = 200 N

CW 8 A

SECTION 8 - 4

Skinner's Simple Law For Survival Simple Machines Mechanical Advantage Efficiency

Skinner's Simple Law for Survival If you remember nothing else from this course, remember this: There are no free lunches in the known universe. There is a price for everything, but, everything has a price.

Simple Machines Wheel & Axel Pulley Wedge Lever Inclined Plane Screw Six Types:

We use machines: To enable us to do work that we could not otherwise do To make work easier

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

Machines CANNOT: Multiple energy Multiple work To do either of these two things, would be to violate... Skinner's Simple Law For Survival.

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.

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.

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.

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.

So... Suppose you need to move a 50 kg object a distance of 3 m. W = Fd F = ma  (50 kg)(10 m/s 2 ) = 500 N So Work = (500 N)(3m) = 1500 J 1500 J (work) is what you will be paid for.

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

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

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.

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:

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.

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.

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

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...

ON THE MACHINE, we must do: 1500 J = Fd 1500 J = (250 N)(d) d = 6 m

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.

Instead of moving the object 3 meters, We move the machine 6 meters. The machine moves the load the required 3 m.

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...

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.

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

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/s 2 ) = 500 N Lifted 3 m (remember – vertically, against gravity)

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.

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

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.

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

Another ratio: It is VITAL that you remember Skinner's Simple Law of Survival, here. Because you can't get something for nothing,

Efficiency: WILL ALWAYS BE LESS THAN 100% You will always put in more than you will get out. In this case, Like with MA, units cancel out.

An Aside... We used the ratio To calculate Mechanical Advantage. There is another way: In our example, that was the 6 meters we moved the object divided by the 3 meters the machine lifted the object.

CW on Simple Machines