Search Results for “mechanics”
Ball Throw Modeled with Mechanical Expressions
A simulation of a projectile created using Mechanical Expressions. The Mechanical Expressions model for a projectile involves constraining the coordinates of the point, giving the coordinates velocity (vx,vy) and setting the constraint to be free to accelerate. A mass has to be given to the point. Simulating the motion is done in the app.
Mechanical Location of the Fermat Toricelli Point
The Fermat Toricelli Point minimizes the sum of the distances to the vertices of a triangle. This app simulates a physical method for finding the point. Press Hint to see a geometric method.
A Chaotic Flywheel
The left hand flywheel is driven at a constant velocity. The right hand wheel is connected by a spring, whose natural length is equal to the distance between the centers of the flywheels, and whose stiffness is k. Output is the angle (in radians) of the flywheel. Note that when k is approximately 5, the motion is regular. Try different values of k, and observe the onset of chaos.
Drive in Movie Problem
This machine computes the best location to view a drive in movie (maximizes the angle). The machine is composed of a pair of mechanical jaws attached at the ends to the top and bottom of the screen and at the middle to the viewing plane. The jaws are pushed apart by a compressed spring, which will find equilibrium when the jaws are as far open as possible..
Fermat Toricelli
The Fermat Toricelli Point of a triangle is the point which minimizes the sum of the distances to the vertices of the triangle. This app represents a mechanical device for computing the point. Balls dangling from strings which pass through the vertices of the triangle naturally settle at the point of lowest potential energy. Can you see why this solves the Fermat Toricelli Problem?
Gear pair
A crossed over belt makes wheels rotate in opposite directions. This mimics the action of a gear pair. Drag the red point to see how the involute curves mimic the motion generated by the belt.
gear related to belt
We imagine two wheels connected by a belt which is wrapped in a figure 8, so that the wheels rotate in opposite directions. We show half the belt. Drag the red point to see it move. Now imagine we cut the belt at the blue point. You can drag the two blue points to see the involute curves. Press Show to turn the curves on permanently. Now drag the red point again, to observe how involute gears mimic a belt drive.
Falling faster than gravity
A uniform bar AB is hinged at A and tips over under the influence of gravity. Press the play button to watch and compare with mass D which falls freely. Under some starting conditions, B actually falls faster than D. You can experiment by pressing refresh, dragging B and D to new locations, then pressing Play again.
Fermat Toricelli Geometric Proof
We use rotations to construct a path equal in length to the sum of the distances AE+BE+CE, whose end points are fixed. Minimum for AE+BE+CE occurs when this path is a straight line. So long as no angles of the original triangle are greater than 120 degrees, this works. What goes wrong when an angle does exceed 120 degrees?
