Physics 111A - Lab Report
Lab 125: Conservation of Mechanical Energy in a Spring-Mass System
Introduction
This lab explored the behavior of a spring mass system. In part 1, the spring constant was
determined, focusing on the static equilibrium of the system. In part 2, we explored the dynamic
nature of a spring system. A mass was attached to the spring, pulled down, and released. This
created oscillations. By noting the position and velocity, we aimed to investigate the
conservation of energy in the system. This lab verifies that without non-conservational forces
such as friction or air resistance, the total mechanical energy, also known as potential energy +
kinetic energy, will remain constant.
Theoretical Background
Hooke’s Law describes the relationship between force and elastic objects, like springs.
According to Hooke’s Law, the further one pulls a spring, the more force is required to hold it in
that position. This works the same way if one was to compress the spring. Hooke’s Law is also
applied the same for vertical and horizontal springs. The relationship between displacement and
force is one of this: the greater one pulls the spring (increasing x), the larger the force (F) will be
to bring the mass attached to the spring to its original position. Thus, Fsp=kx where Fsp is the
magnitude of the spring force, k is the spring constant, and x is the displacement from the
equilibrium position at rest. X is positive when stretched and negative when compressed. When
discussing the conservation of energy in the system we must keep track of the potential energy
and kinetic energy throughout the system during the experiment.
Spring potential energy is the potential energy stored in the spring when it is compressed or
stretched. It is given by the equation:
Gravitational potential energy of the hanging mass is found through the equation:
, Kinetic energy of the cart is given by
KEcart= ½ mcvc^2
Kinetic energy of the hanging mass is given by
KEhanging=½ mhvh^2
Where the vc=-vh
The total mechanical energy of the system is found by adding these energies up and simplifies to
Emech=½ (mc+mh)vc^2+½ k 🔺x^2+(mh)gy which remains constant throughout the experiment
Procedure
-Equipment:
● -Data collection system
● -Dynamics Track
● -Smart Cart
● Cart Mass
● Spring
● Pulley
● Mass and Hanger set
● String
● Digital Protractor
-Set up
Part 1:
Set up all relevant equipment for the experiment. Connect sensor to computer. After clicking
Record in the program, gently pull the cart down until it reaches around 20 cm from equilibrium.
Then, by using the Force vs. Position graph, determine the spring constant of the spring. (Take
five points and determine the slope). Record all data.
Lab 125: Conservation of Mechanical Energy in a Spring-Mass System
Introduction
This lab explored the behavior of a spring mass system. In part 1, the spring constant was
determined, focusing on the static equilibrium of the system. In part 2, we explored the dynamic
nature of a spring system. A mass was attached to the spring, pulled down, and released. This
created oscillations. By noting the position and velocity, we aimed to investigate the
conservation of energy in the system. This lab verifies that without non-conservational forces
such as friction or air resistance, the total mechanical energy, also known as potential energy +
kinetic energy, will remain constant.
Theoretical Background
Hooke’s Law describes the relationship between force and elastic objects, like springs.
According to Hooke’s Law, the further one pulls a spring, the more force is required to hold it in
that position. This works the same way if one was to compress the spring. Hooke’s Law is also
applied the same for vertical and horizontal springs. The relationship between displacement and
force is one of this: the greater one pulls the spring (increasing x), the larger the force (F) will be
to bring the mass attached to the spring to its original position. Thus, Fsp=kx where Fsp is the
magnitude of the spring force, k is the spring constant, and x is the displacement from the
equilibrium position at rest. X is positive when stretched and negative when compressed. When
discussing the conservation of energy in the system we must keep track of the potential energy
and kinetic energy throughout the system during the experiment.
Spring potential energy is the potential energy stored in the spring when it is compressed or
stretched. It is given by the equation:
Gravitational potential energy of the hanging mass is found through the equation:
, Kinetic energy of the cart is given by
KEcart= ½ mcvc^2
Kinetic energy of the hanging mass is given by
KEhanging=½ mhvh^2
Where the vc=-vh
The total mechanical energy of the system is found by adding these energies up and simplifies to
Emech=½ (mc+mh)vc^2+½ k 🔺x^2+(mh)gy which remains constant throughout the experiment
Procedure
-Equipment:
● -Data collection system
● -Dynamics Track
● -Smart Cart
● Cart Mass
● Spring
● Pulley
● Mass and Hanger set
● String
● Digital Protractor
-Set up
Part 1:
Set up all relevant equipment for the experiment. Connect sensor to computer. After clicking
Record in the program, gently pull the cart down until it reaches around 20 cm from equilibrium.
Then, by using the Force vs. Position graph, determine the spring constant of the spring. (Take
five points and determine the slope). Record all data.
