Download Conservation of Energy

LAB 7
Conservation of Energy
OBJECTIVES
1. Observe and verify that mechanical energy is transformed between potential and
kinetic energies.
2. Graphically interpret conservation of energy.
3. Design and execute your own experiment.
EQUIPMENT
Motion sensor, spring, masses, meter sticks, supports, various stockroom supplies.
THEORY
The mechanical energy E of a system is the sum of its kinetic (K) and potential (U):
E = K + U. If only conservative forces do work within an isolated system, then the
mechanical energy E of the system cannot change. This is the principle of conservation of
energy and can be written as:
Etotal = constant = K1 + U1 = K 2 + U2
PROCEDURE
Part 1: Mass-Spring System
Attach a hanging mass to a spring and stretch it from its equilibrium position. When the
mass is released, energy will be transferred between the spring potential energy US = ½ kx2,
the gravitational potential energy Ug = mgy and the kinetic energy K = ½ mv2. Use a motion
sensor to measure the motion of the spring-mass system and display the 3 types of energies.
Part 1A: Measuring the Spring Constant k and Unstrectched Position x0
1) Hang a spring from a support rod and clamp and suspend a 50 g weight hanger from it.
2) Connect a motion sensor to Capstone and set it up to measure position. Place it on the
lab bench directly below the spring and weight hanger.
3) Create a digits display of the position and record in your notes:
•
x0 – the unstretched length of the spring (as measured by the motion sensor)
4) Design and execute an experiment to determine the spring constant of the spring.
Part 1B: Setup and Data Taking
1) Suspend a total mass m = 100 g from the spring and allow the system to come to rest.
2) Open the "SpringEnergy.cap" activity in Newton/Experiments/Physics 4A and
identify the following variables in the data list:
•
•
•
•
•
•
•
•
•
position x (motion sensor)
velocity v (motion sensor)
spring stretch s = xo - x (calculation)
height h = x (calculation)
spring potential energy Us = ½ ks2 (calculation)
gravitational potential energy Ug = mgh (calculation)
total potential energy U = Us + Ug (calculation)
kinetic energy K = ½ mv2 (calculation)
total mechanical energy E = K + U (calculation)
3) Double-click on each of the calculation variables and check that the equations and
units are correct. Set the constants k, xo, m and g to the correct values.
4) Pull the mass down to stretch the spring about 10 cm below the equilibrium position,
release from rest and start recording data. Be sure the mass hanger moves up-anddown without much side-to-side motion. Stop recording after several oscillations.
Part 1C: Data Analysis
1) Identify the spring potential energy US, the gravitational potential energy Ug, the
kinetic energy K, and the total energy E on the plot.
2) Focus on one complete cycle of the mass-spring system and indicate on your plot the
two turning points (lower and higher) and the equilibrium point.
3) For each of the three positions, answer the following questions:
• Is Ug is a minimum, a maximum, or neither? Explain why.
• Is US is a minimum, a maximum, or neither? Explain why.
• Is K is a minimum, a maximum, or neither? Explain why.
4) Answer the following questions:
•
Why does the kinetic energy curve peak twice per cycle?
•
Are your results consistent with the hypothesis that mechanical energy is constant
(i.e., that ∆E = 0 or Ef = Ei)? If not, can you identify (and possibly eliminate)
systematic errors in your data?
Part 2: Conservation of Energy
Using any of the equipment located on the lab carts, design a simple experiment to show
whether or not mechanical energy is conserved. Your experiment should include at least
10 trials and the appropriate error analysis as explained by the instructor.