Frictionless Friction and Simply Simple Machines Nathan Smart October 23, 2009

Because we’re lazy! …….…. Or weak. Why are simple machines popular?

Well…. Yes! … and No Huh?!?!? Are simple machines really all that and a side of chips?

Or would you rather it be easy, but take longer? Do you want a job to be hard, but over quickly? ForceWork versus It’s a compromise thing

That depends…. A little force may notBut not all forces are little Is a little force really going to hurt me?

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. 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 1000 N

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. 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. Force x Distance = Work (200 N) x (5 m) = 1000 J Wasn’t it supposed to take more work? 5m 1m 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. 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. Lifting(1000 N) x (1 m) = 1000 J Pushing(250 N) x (5 m) = 1250 J 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 Lever The Pulley The Ramp

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 ForceWork 30 o 2.0 m6.0 N12 J 45 o 1.4 m8.0 N11 J 60 o 1.2 m9.0 N11 J 90 o 1 m10 N10 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. These pulleys are allowing each box to support the other’s 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. weight

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. 2 X weight weight force from rope attached to ceiling 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…. It moved! …Thrilling. Add one more….

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. distance raised 2 X distance raised Before Lifting After Lifting Work = 1 box X 2 distances = 2 Work = 2 boxes X 1 distance = 2 Since only half the force is needed to lift the boxes, they can only be lifted half as far!

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 teeter- totter. 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. Torque = 1 box X 5 divisions = 5 (for both) Torque = 1 box X 2 divisions = 2 (for both) With different numbers of boxes the torque from all the boxes on each side must be equal. Torque = 4 boxes X 1 division = 4Torque = 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. Torque = 1 box X 1 division = 1Torque = 1 box X 2 divisions = 2 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.

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. 2d d Work = 2 boxes X 2 divisions = 4Work = 1 box X 4 divisions = 4