Harmonic Motion
Build the " Funnest" Swing
Our Goal
In order to determine what the parameters would need to be on the world's best swing, we were assigned with the task of creating a swing, taking measurements on the factors going into its performance, and use equations to evaluate the swing on a deeper level. We had to find the tension in the rope of the swing, the velocity of the swing, the height, the angle, and arc length for the simple harmonic motion of a standard swing, and then apply similar principles and calculations to a rotational swing as well.
Evidence of Work
Content
Pendulum: A weight or object suspended from a pivot so that it can swing freely. The equation associated with pendulums is T= 2√(L/g). Our swing is an example of a pendulum, and we used this equation along with the energy ones to find most of our data.
Springs: An elastic object whose form can be changed by a forced and then return back to normal once the force is removed. The equation associated with springs is T= 2√(m/k).
Spring Potential Energy: The energy stored as a result of the deformation of an elastic object. Us=½ kx2
Kinetic Energy: Kinetic energy is the energy an object possess when it's in motion. K = ½ mv2
On the swing, the subject had the most kinetic energy at the lowest point in their swing when all of the initial gravitational potential energy had transferred to the movement of the swing.
Gravity and Orbits: The force by which a planet or body draws objects toward its center. The force of gravity on our planet can be calculated with the equation Fg= m(9.8 m/s2). An orbit is the curved trajectory of one object around another.
Torque: The measure of a force that causes an object to rotate about an axis. In our project we calculated the torque when Katie pushed Nithya so that she started to spin as well as swing. The equation is τ=rFsin(θ).
Rotational Motion: Motion of an object that travels in a circular path. Nithya experienced circular motion when we spun her on the swing.
Momentum: A measurement of mass in motion. Momentum, like energy, cannot be created or destroyed in a closed system. It can be transferred and changed through the action of forces. It is calculated with the equation p=mv.
Collision: An occurence in which one object strikes another. Problems with collisions usually deal with conservation of energy and/or momentum.
Gravitational Potential Energy: Gravitational potential energy is the energy stored in an object as the due to its height. This is a result of the gravitational attraction of the Earth for the object. Ug=mgh
On the swing, the subject began with only gravitational potential energy, which then transferred to kinetic once they had no further to fall vertically.