Foundations of Physical Science Workshop: The Lever

The Lever CPO Science

Key Questions How does a lever work? What is the relationship between force and distance in a simple machine? What factors balance a lever? These are the key questions for our investigation. Key questions challenge students to explore the parts of a lever system and how the lever works. By using the equipment and experimenting, students get a first hand feel for the scientific process as they develop ideas and test their hypothesis.

Overview Describe how a lever works Identify the relationship between force & distance on a lever Apply the concept of mechanical advantage to levers

Introducing… The Lever Anatomy of the lever Fulcrum – point around which the lever rotates Input Force – Force exerted ON the lever Output Force – Force exerted BY the lever The Lever is a simple machine. A simple machine is a device that has an input and output force. The Fulcrum is the point around which the lever rotates, and is pretty much synonymous with levers. It was Aristotle that said “ Give me a lever and a fulcrum and I shall move the Earth.” The lever pictured is only one kind of lever. There are a total of 3 “classes” of levers. This one is of class One, because the fulcrum is in between the input and output forces. We find examples of all three classes of levers everywhere.

Three Classes of Levers First Class - fulcrum between Input and output Second Class – output between fulcrum and input Examples of three kinds of levers. The pair of pliers is a first class lever because the fulcrum is between the forces. The wheelbarrow is a second class lever because the output force is between the fulcrum and input force. Human arms and legs are all examples of third class levers because the input forces (muscles) are always between the fulcrum (a joint) and the output force (what you accomplish with your feet or hands) Third Class – input between fulcrum and output

CPO Lever – First Class All The Way This is Investigation 4.2. You can use your handout/Investigation Manual to follow along. The CPO lever is a first class lever. The first thing to do is put two weights on the lever to get it to balance. Notice that you can attach the weights at different places on the lever. The weights are easily attached by slipping a loop of yellow string through the hole in the weight and threading one side of the string through the other. Most people will realize quickly that the two weights must be placed equal distances from the fulcrum. Here we have a first class lever The fulcrum is between the input and output Can you get two weights to balance?

A Lever in Equilibrium Hang your weights like shown here Does the lever balance? What variables can be changed to balance a lever First of all, we don’t have equal #s of weights on each side. Second of all they are at different distances from the fulcrum. Yet the lever balances, or more scientifically, it is in Equilibrium. How could this be? What factors, or variables could be changed to reach equilibrium?

Variables Involved in Levers Amount of Input Force Amount of Output Force Length of Input Arm Length of Output Arm Initially, the terminology of Input vs. Output can be a bit confusing, but here’s the deal- the side you first put weight on will be the Input side, and the side to which you must add weight to balance the Lever will be the Output side. We’re going to assume each individual weight has the same mass, and therefore weighs the same. Therefore, we can easily refer to the Input and Output forces in terms of the # of weights, like 1, 2, or 3 weights. Since each weight must be hung at a particular hanging spot on the lever, and the distance away from the fulcrum is marked right on the hook, figuring out the lengths of the Input and Output arms is simple. Whatever the number on the hook from which you are hanging weight, that is the length of that particular arm.

Levers Investigation Hang weights from the lever and get it to balance Try 4 trials and record how many weights to hang and where you hang them Investigation 5.1 The Lever - Its easy to balance 2 weights on the lever, that comes natural to us. But what about when there are more than 2? For this investigation we are going to balance 2,3,4 or even 5 weights. We are also going to try to use more than just one location on each side of the fulcrum. Try to use two or even three. From the example in the slide, you can see there are many ways to get the lever to balance. Challenge yourself to find four different balancing situations and record them on the chart. The ones on there now are merely examples and they are not allowed to be used. SORRY!

Mathematical Rule for Balancing the Lever What mathematical relationship can you find that will balance the lever every time? Put your rule in terms of Input and Output and forces and distances What if there is more than one location on either side of the Lever?

What is the Relationship? Input Force x Length of Input Arm= Output Force x Length of Output arm Force x Distance = Force x Distance # of Weights x Distance = # of Weights x Distance

What if there are several groups of weights? Sum of Input = Sum of Output (Force a x Distance a) + (Force b x Distance b) = (Force c x Distance c) + (Force d x Distance d)

Mechanical Advantage Output Force/Input Force We use the same kind of relationship for all simple machines to calculate Mechanical Advantage Output Force/Input Force Length Input Arm/Length Output Arm