SPH 4U Investigating the Conservation of Energy in an Elastic Spring

Problem: What are the relationships between the gravitational, elastic potential and kinetic energies in a mass-spring system?

Procedure: 1. Determine the ‘k’ – value of the spring being used. Use a graphical method. 2. Set up apparatus as illustrated.

3. Mark the position of the end of the unloaded spring as x0 (no load).

4. Attach a 0.35 kg mass to the spring and lower it gently so that the spring is stretched to ½ the amount the 0.30 kg mass (3.43 N) would normally stretch it (refer to graph produced in Step #1). Designate

this position as x1 and then release the mass so that it falls freely.

Note the maximum extension of the spring (x2).

5. Describe (in words) the types of energy in the spring-mass Earth

system at the points x0, x1 and x2.

6. Determine the loss in gravitational potential energy (Epg) of the

mass as it falls from x1 to x2.

7. Determine the elastic potential energy (Eep) at positions x1 and x2.

Calculate the gain in elastic potential energy (Eep) as the spring

stretches from x1 to x2. Compare this with the loss in gravitational

potential energy, Epg.

8. Repeat steps 4 to 7, this time releasing the 0.35 kg mass from a point that represents ¾ of the normal amount of stretch of the spring (refer to Step #1).

9. Repeat steps 4 to 7 once more, this time releasing a 0.15 kg mass from a point that represents ½ of the normal amount of stretch of the same spring by a 0.15 kg mass (refer to Step #1).

10. Attach a 0.15 kg mass to the spring. Release the mass from the no-load position (x0). Record the

maximum extension of the spring (xmx). Determine the midpoint (x½mx) between x0 and xmx.

11. Describe the types of energy in the spring-mass Earth system at the points x0, x½mx, and xmx.

12. Calculate the loss in gravitational potential energy as the mass falls from x0 to x½mx.

13. Calculate the gain in elastic potential energy as the spring stretches from x0 to x½mx. 14. Compare the loss in gravitational potential energy with the gain in elastic potential energy, from

x0 to the midpoint. Account for any difference. 15. What types of mechanical energy does the system possess when the mass is at the midpoint? 16. Determine the amount of each type. Finally, determine the velocity of the mass at that point. 17. Explain or describe the graph of the relative amounts of each form of energy as the mass falls

from x0 to xmx.

18. Submit an electronic “report” summarizing the findings in this investigation. Show calculations, graphs, and/or annotated diagrams in the “report”.

\sph4U\moment\0b76dd8e4f87a418d4439c28d4adf150.doc CONSERVATION OF ENERGY electronic LAB REPORT Name

Criteria Exceptional Very Good Good Satisfactory Communication

 presentation,  highly effective  good use of  some use of  limited use of organization and use of annotated annotated annotated annotated clarity of report diagrams, graphs, diagrams, graphs, diagrams, graphs, diagrams, graphs, images images images images

 calcuations shown  calculations  calculations  calculations are  calculations are for each spring effectively clearly presented with difficult to follow scenario presented and presented; some usefulness; or relate to corresponds relates easily to relates well to spring scenario clearly to each spring scenario spring scenario spring scenario

 effective use of  highly effective  effective  presentation has  presentation has language; presentation with presentation with few errors several careless grammar and no errors few errors errors spelling 10 9 8.5 8 7.5 7 6.5 6 5.5 5

Knowledge

 calculations  effectively  considerable  some handling of  limited handling shown to properly handles all handling of calculations of calculations represent calculations calculations changes in energy

 data analyzed  conclusively  reasonably shows  shows energy  barely shows correctly to show shows energy energy conserved conserved energy conserved

understanding of conserved between Epg & Eep between Epg & Eep between Epg & Eep

energy changes between Epg & Eep

 understands and  comprehension  comprehension  comprehension  demonstrates can clearly thoroughly clearly somewhat limited explain the demonstrated demonstrated demonstrated comprehension energy graph for the spring system

 properly accounts  thorough account  effective account  some accounting  limited accounting for losses/gains in energy 5.5 5 (#11 – 17) 10 9 8.5 8 7.5 7 6.5 6

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