Search Results for “mass”
Mass on a cycloid curve
Regardless of where you start the mass from (it can be dragged), it will oscillate with the same period.
Pendulum Spring Mass
A simple chaotic mechanism comprising a pendulum attached by a spring to a mass which is free to slide horizontally.
Minimum Perimeter Inscribed Triangle
Three masses are constrained to lie on the edges of a triangle. Equal constant force actuators (with force F) are attached to each pair of masses. When this system finds equilibrium, the potential energy will be at a minimum. However, the PE in each actuator is simply F times L, where L is the length of the actuator. Hence minimum PE is achieved when the masses sit at the vertices of the minimum perimeter inscribed triangle. Press Show to see the normals to the sides of the triangle at the location of the masses.
A Three Body Problem
Three masses are joined by springs and let loose on a horizontal, frictionless plane. You can reposition the masses by dragging, if you can catch them.
Regiomontanus Problem
We seek the place on the earth's surface where a vertically suspended bar (or the rings of Saturn) look the biggest. A machine to solve this problem consists of a mass fixed to the earth's surface and a couple of bars attached to the mass and constrained to pass through the ends of the bar. A spring between the bars pushes them apart. The machine reaches equilibrium when the bars are as far apart as possible, hence finding the solution to Regiomontanus' Problem. You can drag the ends of the bar to change the problem. Press Show to see the circumcircle of the ends of the bar and the mass. You should notice something about the position of this circumcircle at equilibrium. Can you explain what you have noticed?
Tautochrone pendulum
By allowing the pendulum to wrap around a cycloid curve, we can constrain its mass to follow another cycloid (this, technically is because the evolute of a cycloid is a cycloid). As the cycloid is a tautochrone, the pendulums will have the same period no matter what their amplitude. Try dragging one mass close to horizontal, while leaving the other close to vertical. Do you observe that they have the same period?
Pendulums
Change the ratio of the mass at B to the mass at C. Try and match the speed of the pendulum FG.
Equilibrium
We show the solution to a mechanical equilibrium problem: one mass is free to swing, the other slides in an inclined slot, they are joined by rigid bars. Gravity acts downwards. One mass wants to slide down the slot, but in so doing lifts the other. Somewhere along the line, an equilibrium is reached. Where?
