Machines and Efficiency Lab;

Introduction:

This lab demonstrates the principles of mechanical advantage and efficiency with regard to simple machines. Mechanical advantage is the ratio of output force to input force. Efficiency is the ratio of work output to work input. Studying mechanical advantage and efficiency helps physicists design machines that are most effective at doing their job.

Design an experiment you could construct, that might measure the mechanical advantage and efficiency of a simple machine.

What materials would you use?

What would you measure?

What results would you expect?

What if the results were different; what would that indicate?

Developing a Hypothesis:

In this experiment, you will study and compare the mechanical advantage and efficiency of a pulley with those of an inclined plane.

Create hypotheses of what you think the results of this experiment will be.

Which machine will have the most mechanical advantage?

Which machine will be the most efficient?

You will need to use two different websites for this virtual lab. The inclined plane is found at http://phet.colorado.edu/web-pages/simulations-base.html. After clicking on the given link, click Physics then click Work, Energy, and Power. Then click the lab called The Ramp. Then click the download button and it will download and open on your computer.

The pulley system is found at http://www.walter-fendt.de/ph14e/pulleysystem.htm.

Table 1 – Inclined Plane

Trial Object Mass (kg) ? Force Applied (J) Distance (m) Applied Force Applied Work

Table 2 – Pulley

Trial Number of pulleys Load Weight (N) Pulley Weight (N) Necessary Force (N) ?h string (cm) ?h load (cm)

Inclined Plane

4. Familiarize yourself with The Ramp simulation; follow procedures A–G below. Note that procedure C asks you to record the results in your data tables.

A. The simulation contains an image of a man who can push various items up a ramp. You can make the man apply force to the objects in several ways: by clicking and dragging the item itself, by moving the slider labeled Parallel Force directly to the left of the graph, by clicking the up and down arrows on the Applied Force button on the far left of the screen or by entering numbers on the Applied Force button.

B. In this lab, you will measure Applied Work. Collapse the graph that shows forces by clicking the minimize button in the top right corner of the graph. Click the button that says Work Graph. The Applied Work will be shown in yellow-orange on the graph during trials.

C. To the right of the graph are different items that you can select for the man to push across the floor. Notice that the masses of these items are given. Begin by choosing the file cabinet. Record this as well as its mass in Table 1.

D. Below the part of the screen where you can choose the object to slide along the ramp, there is a button you can click to make the ramp frictionless. Make sure that this button is checked.

E. Below the Frictionless button, there are two sliders. The top one allows you to change the position of the “man” along the ramp. You can also type in a position in the button under the slider. The other slider allows you to change the angle of incline of the ramp. Begin with an incline of 10 degrees.

F. To the far left of the graph are buttons that you can use to start a trial so that the various forces are recorded on the graph. Before the recording starts, you need to click Go. To clear the graph before a new trial, click Clear. You must click Go again to start a trial.

G. In the very top left of the screen, there are numbers that record the time since you clicked Go, and that tell you the velocity of the object. Make sure you can locate these buttons, as you will use them in your experiment.

5. Calculate the Applied Force that will make the object move up the ramp with

constant velocity. Because the ramp is frictionless, the only force pushing the object down the ramp is the component of gravity that is parallel to the ramp. This is equal to mg sin theta (?) where m is the mass of the object, g is the acceleration due to gravity, and ? is the angle of incline. Calculate this value in Table 1. (Note that some spreadsheet programs like Microsoft Excel use radians in trigonometric functions. You can convert degrees to radians by multiplying degrees by p (Pi) and then dividing by 180. In Excel, use the function Pi() for p; multiply the angle of incline by the ratio Pi()/180 in order to convert to radians.)

6. Type the value you calculated for Applied Force into the Applied Force box on the left of the screen. Move the object to the bottom of the ramp by typing, 0.0, into the position button. Click Go. Watch the object move up the ramp, and make sure it moves with a constant velocity, or very close to a constant velocity. Remember that you can check the velocity of the object by looking at the number in the left top corner of the screen. Click Pause before the object hits the wall. Record the value of Applied Work in Table 1. Notice the position of the object under the position slider. Record this value in Table 1 as well.

7. Choose two more angles of incline and repeat Steps 5 and 6.

8. Choose a different object. Repeat steps 5 through 7, using the same angles of incline that you used for the file cabinet. You should end up with six trials in total.

Pulley

9. The pulley lab allows you to load masses on a pulley setup and lift the load. You can change the number of pulleys using the button on the right top of the lab. You can change the weight of the load and the weight of the pulleys using buttons on right of the screen in the green background. The virtual lab calculates the force necessary to lift each load after you make your selections. This is the same as input force.

10. Pick a weight for the load and for the pulleys. You should keep these values constant for all of your trials. Notice that if you create a load that is too heavy, the program will default to a value it can handle (less than 10 newtons). Record these values in Table 2.

11. Start with a 2-pulley system. Lift the load by pulling down on the string. Do this a couple times so that you can see how the load and the string move.

12. Using a ruler, measure the vertical change in height of the end of the string as you lift the load from the table. Record this value in Table 2. Now measure the vertical change of height of the load and record it in Table 2.

13. Repeat step 12 using a 4-pulley system and a 6-pulley system.

Analysis

Inclined Plane

1. Organizing Data: For each trial, make the following calculations. You should add columns to your spreadsheet for the calculations.

a. the change in height of the object, which is the distance along the ramp multiplied by the sine of the ramp angle

b. the output force, which is the same as the weight of the object being raised?

c. the output work, which is the product of the output force and the change in height of the object?

d. the mechanical advantage, which is equal to the ratio of the output force to the input force (or the applied force)?

e. the efficiency, which is equal to the ratio of the work output to the work input. (Remember that W = F • d)

2. Analyzing Results: In which trial did the machine perform the most work? In which trial did it perform the least work?

3. Analyzing Results: Under what conditions was the mechanical advantage the greatest? When was it the least?

4. Analyzing Results: How did changing the mass of the object change the mechanical advantage of the machine?

Pulley

5. Organizing Data: Make the following calculations for each trial. You should add columns to your spreadsheet for the calculations:

a. the work input, which is equal to the product of the necessary force and the change in height of the string

b. the work output, which is equal to the sum of the weights of the pulleys and the load multiplied by the change in height of the load

c. the mechanical advantage, which is equal to the ratio of the output force (the sum of the weights of the pulleys and the load) to the input force (or the necessary force)

d. the efficiency, which is equal to the ratio of work output to work input (output/input)

6. Analyzing Results: In which trial, did the machine perform the most work? In which trial, did it perform the least work?

7. Analyzing Results: Under what conditions was the mechanical advantage the greatest? When was it the least?

Conclusions

1. Drawing Conclusions: Based on your calculations, which machine has the most mechanical advantage: a pulley system or an inclined plane?

2. Drawing Conclusions: Based on your calculations, is an inclined plane or a pulley system more efficient? Explain your answer.

3. Evaluating Methods: How would performing this experiment in a hands-on laboratory affect your calculation of efficiency? What differences you might expect doing these experiments with real-life machines that you are neglecting in a virtual setting?

4. Evaluating Hypotheses: How did your hypothesis compare to the results of your experiments?