Simple Machines Simulations
Objectives
- Investigate levers, ramps, and pulleys.
- Measure the mechanical advantage of simple machines.
- Apply the principles of static equilibrium.
Simple machines are devices that change the direction or magnitude of an applied force. Renaissance scholars identified six such machines. We will explore three today: the pulley, the ramp, and the lever.1 Unlike early Renaissance scholars, we have classical mechanics to aid us! We will attempt to analyze these devices using forces, work, and energy.
This lab consists of three major parts
- Investigate a pulley system.
- Investigate an inclined plane.
- Investigate three different classes of levers.
You will investigate three different simulations today. Keep detailed notes. Record your setup, procedure, data, and observations in your lab notes. Data will include tables and plots. In your memo, summarize your findings and discuss any conclusions you draw from your data.
Mechanical Advantage
A simple machine is a device for redirecting or multiplying a force. We often think of such machines in terms of the applied force and the load. The applied force is the force you put into the machine. The load is the force the machine applies to something else. In this lab, it will be the weight you lift.
The mechanical advantage of a machine is the ratio of the load to the applied force:
load
mechanical advantage = -------------
applied forceFor example, if you apply a force of \(\Quantity{100}{lbs}\) and you are able to lift a load of \(\Quantity{200}{lbs}\), the system has a mechanical advantage of 2: It doubles your applied force. In principle, the mechanical advantage is a constant for a particular machine. Thus, if we measure and plot the load as a function of applied force, the mechanical advantage will be the slope of this line.
Note, however, that conservation of energy implies that the work done by each force be equal in magnitude. When a system is in equilibrium, the net work for any small displacement of the system must be zero. This is known as the principle of virtual work.
Pulleys
In a simple pulley system, a mass hangs on one side of the pulley (the load) and you apply a force by pulling on a string on the other side of the pulley (the applied force). We can also combine multiple pulleys. The mechanical advantage of the pulley system is the ratio of the load to the applied force.
Open the Pulley Lab from Physics Aviary. Play with this simulation to see how it works. When you are comfortable with the controls, carry out the following investigations.
Predict. Consider the following questions before you make any measurements.
- How do you think the mechanical advantage will change with the number of pulleys — if at all? I.e., for a given load, how will the applied force you need to lift that load depend on the number of pulleys?
Measure.
- For a fixed mass, measure the applied force for all six pulley combinations. The load is the weight of the hanging mass (\(W=mg\)), and the applied force is the reading on the force sensor. What is the mechanical advantage of each pulley system?
Reflect. Were your predictions correct? Can you explain your findings? In your memo, discuss useful applications for a simple pulley, in light of your measurements.
Inclined Plane
An inclined plane can be used to raise a weight gradually instead of lifting it directly. We can use a pulley to apply a force to a string (applied force) and pull a cart (load) up the ramp.
Open the Atwood's Machine and Inclined Plane with Friction simulation from oPhysics. Play with the simulation to see how it works. You can adjust the two masses, the angle of the ramp, and the coefficient of friction.
Predict. Consider the following questions before you start collecting data.
- How will the angle of the ramp affect its mechanical advantage?
- How can you lift the largest weight using the smallest force with a ramp?
Measure. In this simulation, the weight of \(m_1\) is the applied force and the weight of \(m_2\) is the load. The ratio \(m_2 / m_1\) when the acceleration is zero gives the mechanical advantage.
- Determine the angle required to achieve the mechanical advantages in the table below. Record the mass combinations you used in your notes. Set the coefficient of friction to zero before you collect data.
| Mechanical Advantage | Mass 1 [kg] |
Mass 2 [kg] |
Required Angle |
|---|---|---|---|
| 1 | |||
| 1.5 | |||
| 2 | |||
| 3 | |||
| 5 | |||
| 10 |
Reflect. Were your predictions correct? Can you explain your findings? In your memo, discuss useful applications for an inclined plane, in light of your measurements.
Balance
A lever uses a beam and a fulcrum (a pivot point) to multiply an applied force. It may also redirect the applied force. A Class 1 lever places the load and applied force on opposite sides of the fulcrum — like a teeter-totter or a balance. In this portion of the lab, we will investigate the relation between forces and distance from the fulcrum in a Class 1 Lever.
Open the Balancing Act from PhET. Select the “Balance Lab” simulation. Play around with the simulation to figure out how it works.
Predict. Consider the following questions before you make any measurements.
- Will two equal masses on either side of the lever always balance?
- Can you arrange the system to balance an \(80\,\mathsf{kg}\) man and a \(20\,\mathsf{kg}\) child?
Measure. Attempt all three of the following investigations.
- Mass and Distance. Record the locations at which two masses balance in a table like the one below. Investigate at least 5 different mass combinations. Only one combination should include equal masses.
| Trial | Mass 1 [kg] |
Distance 1 [m] |
Mass 2 [kg] |
Distance 2 [m] |
|---|---|---|---|---|
| 1 | 10 | 10 | ||
| 2 | 20 | 80 | ||
| 3 | ||||
| 4 | ||||
| 5 |
Mystery Objects.
- Balance Mystery Object B and Mystery Object G. Record their locations.
- Determine the mass of Mystery Object B, using objects of known mass.
- Determine the mass of Mystery Object G, using objects of known mass.
Game. Click on the “Game” tab at the bottom of the simulation. Work through “Level 2”. Describe the problems you work through and how you solved them. Send a screen shot of your final score with your lab. (It won’t affect your grade. Dr. Kinder just wants to see that you worked all the way through it.)
Analyze.
- What patterns do you notice in your data from the first investigation, “Mass and Distance”?
- How do the masses and locations of the mystery objects in the second investigation compare?
Reflect. Can you explain your findings? In your memo, discuss useful applications for a balance.
Further Exploration
The following activities are not required. If you have the time and the inclination, you may carry out these investigations for extra credit. You are also free to use any of the materials available in the lab to carry out your own investigations. You need to keep a record of your work (setup, procedure, data, analysis) to get credit for your efforts.
Gravity on Other Planets: Use the Pulley Lab on Physics Aviary to measure the acceleration due to gravity on the Jupiter and on the asteroid Vesta by comparing measurements on these planets with measurements on Earth.
Theoretical Analysis — Pulley: Apply Newton’s Laws to the systems of 1 and 2 pulleys that you investigated. Show — by using free body diagrams, Newton’s Second Law, and Newton’s Third Law — that the mechanical advantage of these two systems should be the same. (The simulation ignores the mass of the pulleys. You can, too.)
Game — Balance: Complete the Level 3 or Level 4 games on the Balancing Act simulation from PhET. One point each, as long as you keep good notes and describe your progress through each level.
Footnotes
The other three are the wheel and axle, the wedge, and the screw.↩︎