# 1 Levers and mechanical advantage

Provided by Kenan Fellows Program.

In this lesson, students will be introduced to the basic principles of all machines and review the six simple machines. They will use a first class lever to explore the relationship between fulcrum position and effort force required to operate the lever. Students will analyze their experimental data both quantitatively (by calculating ideal and actual mechanical advantage) and qualitatively (by summarizing their results).

## Learning outcomes

Students will:

- calculate mechanical advantage of levers of their own construction by measuring effort and resistance distances and by measuring force.
- generate their own procedure for collecting experimental data.
- be able to calculate mechanical advantage and ideal fulcrum position for lever scenarios in word problems.
- be able to determine effort and resistance distances for levers in order to calculate mechanical advantage.

## Teacher planning

### Time required

One 90-minute block period

### Materials needed

- Levers data sheet — one per student
- Levers: Mechanical advantage calculations sheet — one per student
- paper
- pencils
- materials for each pair of students at lab stations:
- one twelve inch ruler (wood works best)
- one large Crayola-type marker
- two strips of masking tape (one for taping down the marker to the lab bench and one for taping the mass to the ruler
- one 100 gram mass (can use slightly less or slightly more, if needed)
- one spring scale

### Technology resources

- Levers PowerPoint presentation
- PowerPoint software
- multimedia projector and computer
- calculators — one per student

### Handouts/Resources

- Levers data sheet
- Students fill out this data sheet while testing out their levers.
- Open as PDF (112 KB, 2 pages)

- Levers: Mechanical advantage calculations
- Students complete this sheet during the guided practice portion of the lesson. This document contains an answer key.
- Open as PDF (155 KB, 2 pages)

### Prior knowledge

This lesson on levers is designed to be incorporated into a unit on work, power, and machines. Immediately prior to this lesson, students should have been instructed on mechanical work and power, the relationship between the two, and calculations involving both quantities. Students should also know that friction reduces efficiency in all systems. Students need to know the concept of force, how to calculate it, and the units in which it is measured. Have a brief class discussion to review these key points.

## Pre-activities

- Using the PowerPoint presentation (see Technology resources above), instruct students on the six types of simple machines.
- Teach them the basic parts and functions of machines and how to determine those on a lever.
- Have students take notes during the presentation.

## Activities

- Give each study a copy of the “Levers data sheet” handout.
- Put students in groups of two, and have each pair go to their lab station with data sheets and pencils.
- Each lab station should already be equipped with the appropriate materials (see Materials needed above).
- Guide the students in constructing a uniform first-class lever according to the photo and these directions:
- Tape a marker on the edge of a table or lab bench as a fulcrum.
- Place the lever (ruler) on top of the fulcrum with the small numbers resting on the table and the large numbers oriented off the table.
- Place the 100 gram mass (the load) on the edge of the ruler resting on the table.
- Use the ruler edge that is off the table to connect the spring scale for applying and measuring the effort force.

- Students will explore the relationship between the effort force and the resistance distance by modifying their lever in three ways of their choosing. Before beginning, have students predict what they will observe about this relationship on the hypothesis section of their data sheet.
- Have students use a spring scale to measure the force required to lift the 100 gram load to the height of the marker without using a lever. They will record and label this as the resistance force on their data sheets.
- For the first fulcrum position, students should pick a location on the ruler (noted by the
*cm*or*mm*marking) to position the fulcrum and record the location on their data sheets in the experimental setup section and in the caption for the first data table. - They must record the effort and resistance distances in data table one on their data sheets. The effort distance is the length from the end of the ruler where the effort was applied to the fulcrum (total length of the ruler — fulcrum position).
- The resistance length is the distance from the beginning of the ruler to the fulcrum (equal to the fulcrum position). Students will then record the effort force needed to level the ruler over three trials (level is measured by the height of the load to the height of the marker). They will then average this force for the three trials.
- This process will be repeated with two additional fulcrum positions (for a total of three positions with three trials each).
- While students are working, rotate throughout the room from group to group:
- Assist and explain when needed.
- Listen to student discussions to gauge understanding and address misconceptions.
- Redirect off-topic conversations.
- Glance at the data sheets from time to time to make sure students are accurately and precisely recording data. If it is ensured that data is collected properly to begin with, it will prevent frustration later when students are working on their calculations.
- Finally, give students a reasonable time limit for each activity and set a timer. If students know they have a limited amount of time to complete the assignment, they will work more efficiently.

- Have students return to their seats with their data sheets.
- Introduce the concept of mechanical advantage and show equations for calculating ideal and actual mechanical advantage.
- Have students analyze their own experimental data by calculating ideal mechanical advantage (IMA) and actual mechanical advantage (AMA) on their data sheets. Each fulcrum will have an IMA and an AMA.
- Next, have students summarize their findings of the relationship between the effort force and the resistance distance in paragraph form on their data sheets. In this summary, students should include information on their data and calculations, as well as the validity of the hypothesis.
- Have students turn in their data sheets for review.
- Conduct a whole-class discussion on the overall findings and the relationship between the effort force and the resistance distance. The consensus should be that the shorter the resistance distance, the less effort force is needed to raise the load. Students should observe that a lever has the most mechanical advantage when the fulcrum is closest to the load.

### Guided practice

Students will practice determining ideal and actual mechanical advantage in word problems.

- Hand out the “Levers: Mechanical advantage calculations” sheet to each student.
- Review the following process for solving these problems:
- Determine what the problem is asking and identify that variable
- Identify the other variables given in the problem
- Determine the correct formula to use to guide their calculations
- Plug in all values and calculate the final answer

- After completing the next lesson in this unit, students will complete a study guide for unit review.

## Assessment

- The teacher should observe student pairs as they conduct the lab portion of this activity.
- Students’ data sheets and guided practice handouts may be assessed for accuracy.
- At the end of this unit, you may choose to have students participate in the “Around the world” review game and take a final test.

## Modifications

The PowerPoint slides may be printed out and given to students for whom this would benefit.

## Critical vocabulary

- actual mechanical advantage
- the experimental mechanical advantage determined by forces involved in use of a simple machine; calculated by AMA =
^{F}_{R}/^{R}_{E}, where F_{R}is resistance (output) force and F_{E}is effort (input) force - effort
- the force applied to a simple machine to move a load
- effort distance
- the length of a lever between the fulcrum and where the effort is applied
- effort force
- the force applied to a lever to move the load
- first-class lever
- a lever with the fulcrum between the effort and load; the effort is applied down and the load moves up; the less effort required, the greater the distance the effort must be applied
- force
- a push or pull which acts on an object and is dependent upon mass and acceleration; calculated by F = m × a, where
*F*is*force*measured in Newtons,*m*is*mass*measured in grams, and*a*is*acceleration*measured in^{m}/_{s}^{2} - ideal mechanical advantage
- the expected mechanical advantage produced by a simple machine; calculated by IMA =
^{d}_{E}/^{d}_{R}, where d_{E}is the effort (input) distance and d_{R}is resistance (output) distance - load
- the mass being moved by a lever
- mechanical power
- the rate of work; calculated by P =
^{W}/_{t}, where*P*is*power*measured in Watts,*W*is*work*measured in Joules, and*t*is*time*measured in seconds - mechanical work
- the measure of force applied over a distance; calculated by W = F × d, where
*W*is*work*measured in Joules,*F*is*force*measured in Newtons, and*d*is*distance*measured in meters - resistance distance
- the length of a lever between the fulcrum and where the load rests
- resistance force
- the weight (force of gravity) of the load being lifted by a lever
- weight
- a measure of the force of gravity acting on the mass of an object; calculated by F
_{g}= m × g, where*F*is_{g}*weight*measured in Newtons,*m*is*mass*measured in grams, and*g*is*acceleration*due to gravity measured in^{m}/_{s}^{2}(9.8^{m}/_{s}^{2}on Earth)

## Comments

This lesson was written using the most basic lab materials possible to maximize the number of students able to have hands-on interaction with the lesson, minimize the cost to instructors, and minimize the preparation time involved to implement the lesson.

## Supplemental information

- The three classes of levers
- This site contains some background information on the three classes of levers.
- Math and Science Activity Center
- This site contains information on calculating mechanical advantage.
- Physics: A first course — skill and practice worksheets
- These practice worksheets come from CPO Science.
- Physical science: Concepts in action
- This textbook was used as a resource to compose this lesson.

- North Carolina Essential Standards
- Science (2010)
#### Physical Science

- PSc.3.1 Understand the types of energy, conservation of energy and energy transfer. PSc.3.1.1 Explain thermal energy and its transfer. PSc.3.1.2 Explain the Law of Conservation of Energy in a mechanical system in terms of kinetic energy, potential energy and...

#### Physics

- Phy.2.1 Understand the concepts of work, energy, and power, as well as the relationship among them. Phy.2.1.1 Interpret data on work and energy presented graphically and numerically. Phy.2.1.2 Compare the concepts of potential and kinetic energy and conservation...

## North Carolina curriculum alignment

### Science (2005)

#### Grade 9–12 — Physical Science

**Goal 3**: The learner will analyze energy and its conservation.**Objective 3.02**: Investigate and analyze transfer of energy by work:- Force.
- Distance.

#### Grade 9–12 — Physics

**Goal 6**: The learner will develop an understanding of energy as the ability to cause change.**Objective 6.03**: Analyze, evaluate, and measure the transfer of energy by a force.- Work.
- Power.

**Objective 6.04**: Design and conduct investigations of:- Mechanical energy.
- Power.