Alabama Science in Motion Energy: What is the Relationship between
Work and Energy?
What is the Relationship between Work and Energy?
EquipmentQUIPMENT:
Laptop with Xplorer GLXDataStudio / Supermart Pulley w/ photogateDynamics TrackDynMotion Sensoramics Track / Mass Super Pulley with clampHanger Set & String
Collision CartForce Sensor / PowerLinkCollision Cart or 2 USB Links
HighMass Set Resolution Force Sensor / Digital AdapterString
Purpose:
The purpose of this activity is to compare the work done on a cart to the change in kinetic energy of the cart. Determine the relationship of work done to the change in energy.
BackgroundTheory:
Newton’s 2nd Law (F=ma) states that an object accelerates when it experiences a net force. In other words, the force causes the object to undergo a change in velocity and move through some displacement.
The work W done on an object is equal to the net force Fn multiplied by displacement d:
W = Fn · d
* It is important to note that because force is a vector, we only multiply the amount of force (the component) that acts along the direction of displacement d. For example, if you push a block across a table, gravity does zero work on the block, because gravity acts straight down and the block moves straight across. In that case, the only the force of friction and the force of your push do is the only force that does work.
Since the object’s velocity changes, we can also calculate its change in kinetic energy. For an object with mass m that experiences a net force Fnet over a distance d that is parallel to the net force, the equation shows the work done, W.
∆KE = ½ m vf2 – ½ m vi2
Where m is the object mass, vf is the final speed of the object, and vi is initial speed. If the object starts from rest, as in this experiment:
∆KE = ½ m vf2
The Work-Energy Theorem states that the work done on an object is equal to its change in kinetic energy:
W = ∆KE
If the work changes the object's vertical position, the object's gravitational potential energy changes. However, if the work changes only the object's speed, the object's kinetic energy, KE, changes as shown in the second equation where W is the work, vf is the final speed of the object and vi is the initial speed of the object.
Predictions:
1. As work is done to accelerate the cart, what will happen to its kinetic energy? (Record on Student Response Sheet)
2. How would the work done on the cart compare to its final kinetic energy? (Record on Student Response Sheet)
Equipment Setup:
In this experiment, you will use a Half-Atwood machine to investigate the relationship between work and kinetic energy. A Half-Atwood machine is shown below: a string connects two objects (one object is on a surface while the other object hangs from the string) over a pulley. (Note: Do not connect any sensors until you open file “Work and Energy”)
1. Place the track on a horizontal surface. If the cart rolls freely toward either end, then adjust the track so it is level (the cart should not roll).
One end of the track should hang about two inches off the edge of the table. Attach the pulley Smart Pulley to this end. The pulley clamps to the track, and the photogate mounts to the slot below the pulley wheel.
Mount the force sensor to the top of the cart. Using a balance, find the total mass of the cart and sensor. Record this mass in the Student Data section.
Attach a string to the hook on the force sensor and put the string over the pulley. Tie the other end of the string to the mass hanger. The string should not be longer than the distance from the pulley to the floor (the height of the table).
Adjust the pulley so that the stretched string is parallel to the track. Adjust the photogate so that its beam travels through the spokes of the pulley. Your setup should look like this:
2. Connect the force sensor to the PowerLink. Using the digital adapter, connect the photogate to the PowerLink.
3. Open DataStudio and connect the PowerLink USB to the computer.
4. Click on ‘Open Activity’ and choose the Work_Energy.ds file from the ASIM Labs folder. DataStudio should display three open graphs: Force vs. Position, Acceleration vs. Position, and Velocity vs. Position.Turn on the GLX. Choose Data Files and open the file labeled “Work Energy” from the flash memory.
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6. Go to the Home Screen and select Graph. The graph screen opens with a graph of Position and Time.
7. Connect the Motion Sensor to Port 1 and connect the Force Sensor to Port 2 on the top of the GLX.
8. Set the range selection switch on top of the Motion Sensor to the ‘near’ (cart) setting.
9. Place the track on a horizontal surface and level the track. If a cart rolls one way or the other on the track, raise or lower one end of the track so the carts does not roll.
10. Attach the Super Pulley with Clamp to one end of the track. Mount the Motion Sensor at the other end of the track and adjust the sensor so it is aimed at the pulley
11. Mount the Force Sensor on the top of the cart. Add a 200 g (0.2 kg) mass to the cart. Place the cart on the track. Press the ZERO button on the sensor to zero the sensor.
12. Attach a string to the cart and put the string over the pulley. Adjust the length of the string so that when the cart is almost to the pulley, the end of the string almost reaches the floor. The back of the cart should come no closer than 15 cm in front of the motion sensor.
13. Put a 20 g (0.02 kg) mass on the end of the string. Adjust the pulley up or down so the string is parallel to the track.
14. Record the mass total of the cart, force sensor, string, and 200g mass on the Student Response Sheet before you begin.
Recording Data:
NOTE: The procedure is easier if one person handles the cart and a second person handles the Xplorer GLX data collection in DataStudio.
1. Before taking data, hold the mass up with your hand so that no tension is pulling on the force sensor. Zero the force sensor. Repeat this step before each new data run.
2. PPull the cart away from the pulley back until the hanging mass is just below the pulley.
NOTE: Hold the force sensor cable out to the side of the cart, so that the cable does not drag and the cart can roll freely. You will need to keep holding the cable after you let the cart go.
3. Support the Force Sensor’s cable so the cart can move freely.
4. Press Start () to start recording data. Release the cart so it moves toward the pulley. DataStudio will take data before stopping automatically.
5. CatchPress to stop data recording just before the cart just before it reaches the pulley. Do not let the cart hit the pulley.
NOTE: Repeat data runs until you obtain Force and Acceleration graphs that are flat. If you stop the cart too soon (before data recording stops) your data will be thrown off at the end, and there will be spikes in your data curves. Your Force graph will show a negative value because the force sensor reads negative when something pulls on it. For your calculations in the analysis section, take the absolute value of your Force reading.
· NOTE: Don’t let the cart hit the pulley.
· Prior to each data run, press the tare button on the side of the Force Sensor to zero the sensor.
6. Examine the Position versus Time graph. Look for a smooth curve to analyze.
Analysis
1. MMeasure the mass of the cart/force sensor together; record this value in the Data table. If the cart’s mass is given, add 95 grams (0.095 kg) due to the mass of the force sensor.
2. If a printer is available, print the graphs from your best data run. If a printer is not available, sketch your graphs in the Student Data section.
3. DataStudio should display maximum/minimum/mean values for each graph. If not, Sselect the Force graph. Under the Σ menu, select ‘Mean’ and ‘Area’. DataStudio will highlight and display the average force value and the total area under the curve. Record these values in the Data table.
NOTE: The area under the force curve equals the total work done on the cart. Taking the area is equivalent to multiplying the force value from the y-axis times the total displacement from the x-axis -- W = F·d. In calculus, taking this area under the curve is called ‘taking an integral’.
4. Mean and Maximum values should also be displayed in the Velocity and Acceleration graphs. If not, select the Velocity graph. Under the Σ menu, select ‘Maximum’. DataStudio will display the maximum velocity value from your graph. Next select the Acceleration graph; under the Σ menu, click on ‘Mean’. DataStudio will display the average acceleration value from your data. Record these values in the Data table.
5. Find the cart’s displacement due to the tension force. You can find this value using your graphs in DataStudio. The x-axis of your graphs shows how far the cart traveled. To find this distance exactly, select the ‘Smart Tool’ cursor () and click on the last data point in your Velocity graph; the x-coordinate is the distance.
6. To change the Graph screen to show a specific run of data, press to activate the vertical axis menu. Press the arrow keys () to move to ‘Run #_’ in the upper left hand corner. Press to open the menu, select the data run in the menu, and press to activate your choice.
7. Change the Graph screen to show Velocity versus Time. Press to activate the vertical axis. Press to open the vertical axis menu. Use the arrow keys to select ‘Velocity’ and press again to activate your choice.
8. Move the cursor to the maximum value of velocity and record the value in the Data Table.
9. To analyze a Force vs Position graph press twice and choose ‘Force, pull positive’ to change the vertical axis and press then press until you highlight the horizontal axis, press and choose ‘Position’ to change the x axis. Sketch this curve on your Student Response Sheet.
10. To find the area under the curve move the cursor to the beginning of the data. Press F3 () to open the ‘Tools’ menu. Select ‘Area Tool’ and press to activate your choice.
11. The area under the horizontal part of the curve to be analyzed. If you need to take off a part of the curve, in the ‘Tools’ menu choose ‘Swap Cursor’ to move to opposite end of curve and hit to take off section NOT linear. Record the value of the area under curve as the work done on your Student Response Sheet.
12. Use the maximum velocity and the total mass of the cart (cart, sensor, string, and 200g mass) to calculate the final kinetic energy of the cart. Record in your Student Response Sheet.
Data Sheet
Name(s): Period ______
Period:
Date: artner’s Name: Date:
Predictions
1. As work is done to accelerate a cart, what will happen to its kinetic energy?
2. If the cart starts from rest, Hhow would the work done on the cart compare to its final kinetic energy? How about if the cart is already moving when we do work on it?
Sketch your graphs below. Each graph displayed in DataStudio shares a position axis. Include units and labels for your axes.
a graph of velocity versus time and a graph of force versus position for one run of data. Include units and labels for your axes.
Run # ______
Data TableData Table
Total mass of cart (kg)Item / ValueMaxiTotal mass of cartmum velocity
Velocity, maximumAverage acceleration
AverageWork done force
Area under Force curveKinetic energy, final
Displacement
Percent difference
Calculations
Use the total mass of the cart and the final (maximum) velocity to calculate the final kinetic energy of the cart. Compare this value to the work done (the area under the position curve). We can also use our acceleration graph to calculate work done. From the average acceleration value, calculate the tension force on the cart (F=ma). Check this value by comparing it with the average force value you entered above. Then, to calculate work done, multiply the tension force times the displacement.
Kinetic energy is where m is the mass and v is the velocity.
Calculate the percent difference between the work done (area under force-position curve) and the final kinetic energy final kinetic energy and the work done on the cart, for both work values you calculated.
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Questions
3. What happens to the kinetic energy as work is done on the cart?
4. How does the final kinetic energy compare to the work done?
5. The kinetic energy is measured in joules and the work done is measured in newton•meters (N m). What is the relationship between a joule and a newton•meter?
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7. Do your results support your predictions?
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Revised 03/20109/2008