## Studio Session 5

### Work and Energy

Energy conservation for an isolated system is a fundamental principle of physics.  Energy for an isolated system is always conserved.  It may change forms, but the total amount of energy in an isolated system is constant.  Energy can, however, be converted from one form to another form.  Work is the conversion of one form of energy into another.  Energy comes in different forms, kinetic energy, potential energy, chemical energy, thermal energy, etc.  If an object has energy, it has the potential to do work.

There are several forms of potential energy.  Kinetic and potential energy are called mechanical energy or ordered energy.  Thermal energy is disordered energy.  Friction converts mechanical energy into disordered energy.
When no disordered energy is produced, then mechanical energy is conserved.

Today we will track the mechanical energy in various systems and explore the relationship between work and energy.

Equipment needed:

• Track with bumper and plunger cart
• Force sensor
• Motion sensor
• Ruler and metal block
• 50 g mass

How does the motion sensor work?

An electrostatic transducer in the face of the Motion Sensor transmits a burst of 16 ultrasonic pulses with a frequency of about 49 kHz.  The ultrasonic pulses reflect off a target and return to the face of the sensor.  The target indicator flashes when the transducer detects an echo.

The sensor measures the time between the trigger rising edge and the echo rising edge. It uses this time and the speed of sound to calculate the distance to the object. To determine velocity, it used consecutive position measurements to calculate the rate of change of position. Similarly, determines acceleration by using consecutive velocity measurements.

Note:  The motion sensor must face the target.

Open a Microsoft Word document to keep a log of your experimental procedures and your results.  This log will form the basis of your studio session report.  Address the points highlighted in blue.  Answer all questions.  Include the information that your answers are based on.

Experiment 1

In this experiment you will do work compressing a spring.  You will then let the spring do work converting elastic potential energy into gravitational potential energy.

• Set up a track with a motion sensor attached to one end and a bumper to the other end.  Set the range switch on top of the motion sensor to short range ().
Note:  You will use the motion sensor for experiment 2 only.
• Place the feet of the track at ~10 cm and ~120 cm and make sure the leveling screws are turned all the way in.
• Plug the Pasco motion sensor into digital channels 1 and 2 of the Pasco 850 interface and the USB/Bluetooth force sensor into a USB port of the computer.  Open the Capstone program.
• In the Hardware Setup window add a motion sensor and check that the force sensor appears in the window.  Select only the force measurement and deselect all other measurements.  If you want to connect via Bluetooth, unplug the sensor from the USB port.  If more than one sensor appears in the hardware setup window, select the one that matches the device ID XXX-XXXX number found on the front of the sensor.  Click the properties gear for the force sensor check "Zero sensor measurement at start."  Close the Hardware setup window.
• Choose a sample rate of 40 Hz for both instruments.
• Place a plunger cart on the track and level the track.  The cart should remain stationary and the track should rest on all four feet.
• The cart has a three-position spring plunger, activated by a trigger located on the front end cap.  Use the force sensor to measure the force as you compress the plunger spring all the way to the third position.  Make sure that, while you compress the spring, you hold the force sensor horizontally.  Monitor the force on a graph.  Repeat a few times to get a value for the maximum force Fmax required to compress the spring.  Record Fmax.
• Use a ruler to measure the distance d the plunger moved.  Record it.
• The work you do in compressing the spring is W = Faverage *d.  What is Faverage?  Why?  Calculate the work you do to compress the plunger spring to the third position and record it.
• Take the cart off the track, put the plunger into position 3 and put the cart vertically on the table.  Place a 50 g mass on top of the plunger.
• Release the trigger and measure with a ruler the maximum height above its starting position to which the mass jumps.  Calculate and record the maximum change in potential energy of the mass.  Repeat a few times to get a reliable measurement of the maximum height.
• Compare the work done to compress the plunger spring to the maximum change in potential energy of the mass.
• Was some energy "lost" in the process?  If so, where did it go?  Elaborate!

Experiment 2

In this experiment you will lift one end of the track.  You will then measure the conversion of gravitational potential energy into kinetic energy.

• Lift the end of the track with the motion sensor and place the feet on the metal block.

• Place the cart near the motion sensor and let it accelerate towards the bumper.  You will measure the cart's speed when it is between 0.2 m and 0.7 m from the motion sensor.
• In Capstone, drag two graphs, one for position versus time and one for velocity versus time onto the main display.
• Click "Recording Conditions" below the main display.  Choose Start Condition, Measurement Based, Position, is above 0.2 m.
• Choose Stop Condition, Measurement Based, Position, is above 0.7 m.
• Start taking data.  Let the cart accelerate.  Determine its speed when it is at 0.2 m and when it is at 0.7 m from the motion sensor.
• Measure the difference in the height of the track at positions 0.5 m apart.  (Attach your calculations)
• Compare the change in the gravitational potential energy of the cart to the change in its kinetic energy when its distance from the motion sensor changes from 0.2 m to 0.7 m.  Attach your calculations.  Discuss your number.

Discussion

• Can you jump keeping your legs completely straight?  Does the amount of bending of your legs have any relation to how far up you can jump?  Try this out and describe your results.
Is energy stored in your legs when bent?  How do you know?

Exploration

Use an on-line simulation from the University of Colorado PhET group to track mechanical energy in a skate park.

• You can build tracks, ramps and jumps and view graphs of kinetic energy, potential energy and friction as the skater moves.
• You can also take the skater to different planets or into free space.

(a)  Explore the interface!
Note:

• You can resize the windows.
• You can Pause the simulation and then put the Skater anywhere.  Return  Skater returns the Skater to this spot and you can rerun the scenario.
• You can use the Save feature in the File menu to save a track and Skater position.
• The Energy Position Graph has a few subtle features.  It erases as the simulation plays, but you can Pause the simulation and the graph will not change.
• The Copy button will let you freeze the graph to compare different scenarios, but it cannot be saved as a file.  If you Zoom, the graph clears; you can make a new graph by rerunning your scenario.
• If you use the Show Path feature, you can click on the purple dots and show quantitative information.  Height refers to height from the Potential Energy Reference line.  Click again to hide.
• Step is a good way to incrementally analyze the motion.  Use the step button in the large window and in the Energy Time window.
• When the Skater lands on the track, some of the kinetic energy will be dissipated and the skater will subsequently move along the track.

(b)  As a group, design your own frictionless track.  You session instructor will give you some design guidelines that you should follow.

• Design a track that is fun, challenging and relatively safe.
• Use the Energy Graphs to track the Skater's mechanical energy.  Decide which graphs or charts best help you understand what makes your track successful.
• Explain why your track is successful in terms of conservation of mechanical energy.  Refer to Charts or Graphs to help explain your reasoning.
• Using conservation of mechanical energy, explain what things need to be considered when designing any successful track.