Download SPH 4U Conservation of Energy in a Mass

SPH 4U
Problem:
Conservation of Energy in a Mass-Spring System
Lab Investigation
What are the relationships between the gravitational, elastic
potential and kinetic energies in a mass-spring Earth system?
Procedure:
1.
Use a Hooke’s Law spring with a known k–value along with a 300 g mass and
a 150 g mass.
2. Set up the apparatus as illustrated.
3. Mark the position of the end of the unloaded spring as xo (no load).
4. Attach a 300 g mass to the spring and lower it gently so that the spring is
stretched to ½ the amount the mass would normally stretch the spring
(refer to k-value graph from previous investigation). 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 xo, x1,
and x2.
6. Determine the loss in gravitational potential energy -∆Epg of the mass as it falls from x1 to x2.
7. Calculate the gain in elastic potential energy ∆Eep as the spring stretches from x1 to x2.
Compare this with -∆Epg.
8. Repeat steps 4 – 7, this time using a 150 g mass.
9. **Attach the 150 g mass to the spring and release it from the no-load position x0. Mark the
maximum extension of the spring xmx. **
10. **Use Video Physics to capture the video of the mass falling to its maximum extension. Set the
origin at ½ the maximum extension ( ½-way between x0 and xmx). Explain why the y-velocity
graph has the shape it does.
11. **Use Data Studio to capture the motion of the mass falling to its maximum extension.
12. Calculate the -∆Epg as the mass falls from x0 to the ½–way point (x½ mx) of xmx. Calculate the
∆Eep from x0 to x½ mx. How does the loss of Epg compare to the gain in Eep? Account for any
difference. Where did the lost energy go? How much of the total Epg is there at x½ mx?
13. Predict the graphs of the elastic potential energy, the kinetic energy, the gravitational
potential energy and the total energy of the system on one set of axes.
14. Use the Calculation button in Data Studio to produce formulae for Ek, Epg, Eep and ET that can be
graphed.
15. Confirm the findings in #12 with the graphs of Ek, Epg, Eep and ET. What types of energy exist
when the mass is at x½ mx? How much is each type relative to the total energy of the system, E T?
\sph4U\moment\840986830
Evaluation
20
30
Section
Procedure
Abstract
Criteria
 Complete with purpose,
brief description of
method, and conclusion,
including possible sources
of experimental error(s)
I
#5-7
 ½ amount of stretch to
max. ext.
 conserv’n of energy using ∆Epg & ∆Eep
II
#8
 Same as above using
different mass
III
#10
 Vertical velocity video; why
does the graph have its
shape?
IV
#11-15





Compare -∆Epg with ∆Eep
Account for differences
Predicted E graphs
Graph of Epg, Eep, Ek, ET
Ratios of
,
Overall
,
@ x½max
Uses calculations, annotated graphs and
captions to clearly confirm conservation of
energy in a spring-mass system
Comments:
\sph4U\moment\840986830
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