Conservation of Energy Lab

Purpose: To demonstrate conservation of energy, using a spring mass system. By determining the spring constant, mass and length of the spring, and the mass of the hanging mass on the spring the kinetic energy and potential energy for the spring and mass can be found, using the position and velocity of the hanging mass. This can then be used to find the total energy of the system and if this is constant, the energy is conserved.

Procedure: A rod was clamped to a lab table with a perpendicular rod extending over the floor. A force sensor was attached to the perpendicular rod. A spring was attached to this and a mass hanger to the spring. A motion sensor was placed directly under the

• Spring Constant: The spring was extended while the force and position were recorded. By plotting the force vs distance and finding the slope of this line, the spring constant was found. The spring constant was determined to be BLANK.
• Conservation of Energy: The mass was pulled down and the spring mass system oscillated while the position and velocity of the the mass was recorded using the motion detector.

Data Analysis: The gravitational potential energy of the spring was calculated by using the fact that the the center of mass of the spring only moved 1/2 the distance of the end of the spring, therefore, GPE=(1/2)*Mspring*g*y. The gravitation energy of the spring was calculated as GPE=M*g*y. The Kinetic energy of the mass was calculated as (1/2)*M*V^2. The elastic potential energy was also calculated as EPE= 1/2K*stretch^2.

Conclusion: The total energy of the system was conserved within 4%. Given the precision of the equipment used, this shows that the kinetic energy was conserved. To reduce the error, better equipment would be needed and a better model would need to be used. This model would take into account the fact that the spring does not have equal stretch over the spring, due to the mass of the spring. Also, the kinetic energy of the spring could be taken into account.