Investigation 9A: Work and the force versus distance graph

Essential questionsHow are force, distance, and work related graphically?
To lift a mass, you must do work on it against the gravitational force. Similarly, when you stretch a spring, you do work on it to overcome its restoring force. How does the work done on these objects relate to the forces applied to them and the distances they move or stretch? In this investigation you’ll find out by using a Smart Cart to apply those forces so that you can measure both force and distance.
Part 1: Lift a mass

Part 1: Lift a mass
  1. Open the 09A_ForceDistanceGraph experiment file in your software, and then connect your Smart Cart using Bluetooth.
  2. Set up the equipment as in the picture. Be sure the track is level.
  3. In your software, zero the Smart Cart force sensor while nothing is touching the hook.
  4. With the thread reattached to the cart, position the cart so that the mass hanger is suspended just above the floor.
  5. Record force and distance data as you move the cart slowly and steadily to lift the mass a distance of 30 cm, as measured by the markings on the track. Then stop recording data.
  1. Sketch a copy of your force versus distance graph. Be sure to label the axes.
  2. Use the statistics tool in your software to determine the average (mean) force applied to lift the mass.
  3. Determine the actual distance you lifted the mass during data recording.
  4. Use these two values to calculate the work done on the mass to lift it, including units.
  5. Use the statistics tool in your software to find the area under your force versus distance graph, including units. How does this area compare to the work you calculated above? What is the geometric shape of the shaded area?
  6. Did the work done on the mass to lift it change its energy? If so, explain which form of energy changed and whether it increased or decreased.
Part 2: Stretch a spring

Part 2: Stretch a spring
  1. Modify your equipment as shown in the picture. Use the stiffest of the three springs.
  2. Position and hold the cart so that it is just starting to separate the spring’s coils, and then use your software to zero the Smart Cart force sensor.
  3. Record force and distance data as you move the cart slowly and steadily to stretch the end of the spring a distance of 30 cm, as measured by the markings on the track. Then stop recording data.
  1. Sketch a copy of your force versus distance graph. Be sure to label the axes.
  2. Was the force constant? Would it be appropriate to use the formula W = Fd to calculate the work done on the spring? Explain.
  3. Use the statistics tool in your software to find the area under your force versus distance graph, which is the work done on the spring to stretch it.
  4. Did the work done on the spring to stretch it change its energy? If so, explain which form of energy changed and whether it increased or decreased.
Part 3: Match work challenge

The amount of work done to lift the mass in Part 1 was likely different than the amount of work done to stretch the spring in Part 2. You’ll now redesign one of these configurations and record a new run in an attempt to match the amounts of work. Choose one of the following challenges:
  1. Modify the lifting of a mass (as in Part 1) so that the work done on the mass is equal to the work done on the spring in Part 2. OR
  2. Modify the stretching of a spring (as in Part 2) so that the work done on the spring is equal to the work done on the mass in Part 1.
For your selected challenge, first describe and justify your design change. Then collect a run of data to determine how closely the measured work matches the target value.

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