Search Results for “forces”
Crank Slider
For a given input force at the slider C, this app calculates the torque generated at the crank AB. You can observe the ratio of output torque to input force is displayed, along with geometric quantities which can be used to compute this ratio.
The point which minimizes weighted sum of distances to triangle's vertices
In the mechanical simulation, the actuator connecting point D to A exerts a constant force a, the actuator connecting D to B exerts force b, and the actuator connecting D to C exerts force c. At equilibrium, potential energy will be minimized. The PE is proportional to a|AD|+b|BD|+c|CD| Press the hint button to see a geometric construction for this point. Under some circumstances the mass settles at one of the vertices. Can you work out what these circumstances are?
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.
Lifeguard Problem
The actuators exert constant forces reciprocal to the swimming and running speeds. Hence their potential energy is proportional to the time taken for the lifeguard to reach the victim
Maximum Area Triangle
A force proportional to the length of each side are applied to the side's midpoint. This models a constant pressure, and potential energy should be minimized when area is maximized. Press Show to see the tangents to the curve at the points of contact. What do you notice? You can change the definition of the curves, but be careful, or the masses might escape!
Maximum Perimeter Triangle
Constant force actuators push outwards. As the potential energy in each actuator is equal to its length, this machine should settle where the triangle's perimeter is maximum. Press Show to see the reflections in the tangents of a beam of light transmitted along one edge of the triangle.
