Spring energy and spring constant of a dynamics cart
Objectives
To determine the potential energy stored in the spring of a dynamics cart.
Theory
Potential spring energy, Espring, is produced as work is done to compress the plunger of the cart.
This spring energy varies directly with the square of the distance of compression, x, according to
Espring = ½ k x2
where k is the spring constant.
Potential spring energy is converted to kinetic energy, Ek, when the spring mechanism is released.
ΔEtotal = 0
and
ΔEtotal = ΔEspring + ΔEk
therefore
ΔEspring = – ΔEk
When compressed, there is only potential spring energy and no kinetic energy. As the spring decompresses, it
loses potential energy and the increase in kinetic energy is observed as the cart accelerates and its speed
increases. When the spring has maximum decompression, the only energy is kinetic energy.
Etotal = Espring before = Ek after
½ k x2 = ½ m vf2
The total energy of the system can be determined from the mass of the cart and the maximum speed of the cart
(at maximum decompression before friction converts nmechanical to thermal and vibrational energy).
Materials
PASCar dynamics cart (mass labelled on bottom)
Xplorer GLX datalogger with motion sensor (50 – 100 Hz)
Procedure
Determine and record the mass of the dynamics cart.
Measure the length of the extended plunger (record in metres)
Hold down the release button and compress the spring until the plunger is even with the end of the cart
Place the compressed plunger against a stationary object (lab desk) and press play on the GLX
Release the cart as efficiently as possible to get the greatest possible speed.
Use the GLX to gather sufficient data to determine the maximum speed.
Repeat until you have three similar maximum speeds.
Results
Mass of cart (m): _____________________ kg
dynamics track
ruler
Length of compression (x): _____________ m
Trial
Maximum speed
vmax (m/s)
Maximum Kinetic Energy
Ek (J)
Mean
Conclusion:
Identify the two major assumptions that were made in the calculations.
Spring constant
k (N/m)