# Exploring mechanical advantage with simple machines

This lesson is part of the unit "Work, power, and machines." In this lesson, students will conceptually and quantitatively explore ideal and actual mechanical advantage with three simple machines: the lever (second- and third-class), the inclined plane, and the pulley.

**A lesson plan for grades 9–12 Science**

Provided by Kenan Fellows Program

In this lesson, students will conceptually and quantitatively explore ideal and actual mechanical advantage with three simple machines: the lever (second- and third-class), the inclined plane, and the pulley. Students will move throughout stations in the classroom to manipulate and collect data from each machine and then practice calculating mechanical advantage. Students will draw conclusions from their lab experience and data. Most materials required for this lab are standard classroom materials

## Learning outcomes

Students will:

- explore the difference between ideal and actual mechanical advantage by manipulating and measuring components of and forces required to operate three simple machines: the lever, the inclined plane, and the pulley.
- be able to identify necessary variables (effort and resistance position, effort and resistance force) on real simple machines and in word problems for the purpose of calculating ideal and actual mechanical advantage.
- be able to correctly determine when to use each formula based on information provided in word problems.

## Teacher planning

### Time required

One 90-minute block period

### Materials needed

- Simple machines lab sheet — one per student
- Simple machines: Mechanical advantage calculations sheet — one per student
- Work, power, and machines study guide — one per student
- paper
- pencils
- Lab stations already set up with the following materials:
**inclined plane station**(set up two stations, each with the following materials):- one long, flat surface which can be angled as the plane (such as shelves from a bookshelf)
- one stack of books for changing the height of the plane
- one small cart or car to travel on the plane (Hot Wheels cars are too small — try to find a toy car for a child younger than three years old)
- one spring scale to measure forces
- one metric ruler to measure effort and resistance positions

**second-class lever station**(set up two stations, each with the following materials):- one metric ruler (wooden, if possible) attached to a lab bench or table with tape at the 0
*cm*end to act as the fulcrum - one 100 gram mass to act as the load
- one roll of masking tape for attaching the load to the lever
- one spring scale for measuring force

- one metric ruler (wooden, if possible) attached to a lab bench or table with tape at the 0
**third-class lever station**(set up two stations, each with the following materials):- one metric ruler (wooden, if possible) attached to a lab bench or table with tape at the 0
*cm*end to act as the fulcrum - one 100 gram mass attached to the ruler with masking tape as the load at the end of the fulcrum
- one spring scale for measuring force

- one metric ruler (wooden, if possible) attached to a lab bench or table with tape at the 0
**pulley station**(set up one station with the following materials):- interactive white board
- flash-enabled web browser navigated to the online pulley simulation
- the friction for the pulley should be set to 0.15 so that the ideal mechanical advantage does not equal the actual mechanical advantage, and the load should stay at five Newtons.

### Technology resources

- Interactive white board connected to a computer
- Flash-enabled web browser connected to the online pulley simulation

### Handouts

- Simple machines lab sheet
- Students fill out this data sheet while testing out the simple machines at each station.
- Open as PDF (68 KB, 2 pages)

- Simple machines: Mechanical advantage calculations
- Students complete this sheet during the guided practice portion of the lesson. This document contains an answer key.
- Open as PDF (67 KB, 2 pages)

- Work, power, and machines study guide
- Students complete this study guide after completing the the first two lessons in this unit. This document contains an answer key.
- Open as PDF (249 KB, 5 pages)

### Prior knowledge

- The lesson Levers and mechanical advantage should be taught prior to this one to review simple machines, introduce the concepts of ideal and actual mechanical advantage, introduce the experimental set-up for levers, and familiarize students with the use of a spring scale.
- Prior to this lesson, students will need to know about 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

Students will be using an internet-based pulley simulation for this lab. Demonstrate for students how to change the type of pulley system and make the pulley work, and demonstrate how to count the number of rope strands, which will determine the ideal mechanical advantage. Point out where they can read the effort force used to make the pulley work, and make sure to enforce that they should not change any other settings on the pulley other than the type.

## Activities

- Hand out the “Simple machines lab sheet” to each student.
- Explain the directions for the lab activity. You might say:

In the previous lesson, we learned and practiced calculating ideal and actual mechanical advantage with first-class levers. In this lesson, we’re going to explore mechanical advantage in other simple machines: second- and third-class levers, inclined planes (ramps), and pulleys. As you move to stations throughout the room, you are going to modify each machine in two ways so that you can observe how the mechanical advantage changes. For example: at the second-class lever station, you will change the load position; at the third-class lever station, you will change the effort position; at the inclined plane station, you will change the height of the plane; and at the pulley station, you will change the type of pulley system, which will change the number of wheels and therefore rope strands. You must sketch the experimental set-up for both trials and record the data for each machine on your data sheet so that you can calculate mechanical advantage when you return to your seat. Before we begin, you are going to make some hypotheses.

- On their own sheets of paper, have students make predictions of how mechanical advantage will change for each station. Specifically, have them predict when the mechanical advantage will be highest and lowest based on how they will modify the machine:
- For the second-class lever station:
*Where should the load be positioned for highest mechanical advantage? For lowest mechanical advantage?* - For the third-class lever station:
*Where should the effort be positioned?* - For the inclined plane station:
*At what height should the plane be positioned?* - For the pulley station:
*How many components should the pulley have?*

- For the second-class lever station:
- Have a brief class discussion to let students share their hypotheses, but do not confirm accuracy.
- Put students in groups of two or three, and have each group go to a lab station with their lab sheets and pencils.
- In their groups, students will determine how to manipulate each simple machine based on their hypotheses. On their data sheets, they will sketch the experimental set-up for two different variations of each machine and then record the relevant data (effort and resistance distance and force) for IMA and AMA calculations.
- Have the groups rotate to different stations approximately every five minutes.
- 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.

- After collecting data at all stations, students will return to their seats and use the data to calculate IMA and AMA. They will compare the two calculated quantities across the two trials for each machine. They should write at least one summary sentence and one sentence confirming or refuting their hypotheses based on the results for each machine type. This should be done on the same paper as their hypotheses.
- Students will also answer the following summary questions:
- For the second-class lever station:
*Based on your data, where is the ideal position for the load when using a second-class lever?*(Qualitative answers should say something along the lines of “closer to the fulcrum is best.” Quantitative answers should state the shortest resistance distance, which should be closest to the value zero.) - For the third-class lever station:
*Why do you think the mechanical advantage is less than one for this type of lever? What would be an advantage to using this type of lever?*(The mechanical advantage is always less than one because the resistance distance is always greater than the effort distance. As many students may experience, this type of lever accelerates forward quite easily past a certain point — the usefulness of a third-class lever is in acting like a catapult, which increases the output velocity.) - For the inclined plane station:
*What causes the difference in the ideal and actual mechanical advantage for this machine?*(Friction and the angle of force applied will both cause a difference in the mechanical advantages.) - For pulley station:
*What is the relationship between the effort distance and effort force as components are added to the pulley?*(As components are added, the effort distance increases while the effort force decreases. This is an inverse relationship.)

- For the second-class lever station:
- Students should turn in their lab sheets and hypothesis/summary sheets so that you can check for understanding.
- Upon completion of the lesson, engage students in a classroom discussion of their results. Encourage students to discuss their observations and conclusions and any connections they might see to the world at large (e.g. the usefulness of simple machines).

### Guided practice

Students will complete six practice calculations at the end of class using ideal mechanical advantage and actual mechanical advantage.

- Hand out the “Simple machines: Mechanical advantage calculations” sheet.
- In these six problems, students should:
- determine what the problem is asking for and identify that variable.
- identify the other variables given in the problem.
- plug in all values and calculate the final answer.

- Give each student a copy of the “Work, power, and machines study guide,” and have them complete it on their own.

## Assessment

- The teacher should observe student groups as they conduct the lab portion of this activity.
- Students’ lab 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

- This lesson may be conducted over two class periods, if necessary.
- Instead of the interactive white board being used for the pulley activity, a desktop or laptop computer will work. If a pulley kit is available with compound pulley parts and different weights, this will also work.

## Critical vocabulary

- actual mechanical advantage
- the experimental mechanical advantage determined by forces involved in use of a simple machine; calculated by AMA =
^{F}_{R}/^{F}_{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 the path across which the effort or input is applied to a simple machine; one levers, this is the length of the lever from the fulcrum to the pint at which the effort is applied
- effort force
- the force applied to a simple machine 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} - fulcrum
- the fixed point about which a lever moves
- 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 - inclined plane
- a flat surface elevated at an angle; the base is flat and the other adjacent side is vertical; more or less, a three-dimensional right triangle where the hypotenuse is used as the machine
- load
- the mass being moved by a simple machine
- mechanical advantage
- the number of times the input force is multiplied by use of a simple machine
- 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 - pulley
- a variation on the lever, a pulley includes a cable wrapped around a wheel (circular lever), which causes the wheel to rotate about its fulcrum and thus move the load; fixed pulleys change the direction of force exerted, and the more wheels added, the less force is needed; moveable pulleys simply decrease the force needed to lift a load, and the direction of the load’s movement and applied force are the same
- resistance distance
- the displacement of the load moved by a simple machine; on levers, this is the length of the lever from the fulcrum and to the load
- resistance force
- the weight (force of gravity) of the load being lifted by a simple machine
- second-class lever
- a lever with the load between the fulcrum and the effort; the effort is applied up and the load moves up; the less effort required, the closer the load is to the fulcrum
- third-class lever
- a lever with the effort between the fulcrum and the load; the effort is applied up and the load moves up; there is no mechanical advantage to using a third-class lever, but the distance the load moves is greater than the effort distance; this type of lever can increase power
- 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)

## Supplemental information

- 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.