Question

. A bead of mass m under the influence of gravity slides along a frictionless and massless wire whose height is given by a function y(x). Assume that at position (x, y) = (0, 0) the tangent of the wire is horizontal and the bead passes this point with a given speed v0. What should y(x) be so that the horizontal speed remains v0 at all times (that is what is the shape of the wire)? One simple solution is y = 0, find the other solution. (Hint: It should

Answer 1

y = constant

Step-by-step explanation:

Bodies moving on the surface of Earth are subject to gravity, and they have a potential and kinetic energy. If there is no friction, the sum of the kinetic and potential energy remains constant.

Since potential energy depends on height, changes in altitude affect potential energy. Going higher increases this energy, this is accompanied by a reduction of kinetic energy and speed (since kinetic energy is related to speed). If the body goes down potential energy is reduced, but kinetic energy and speed increase.

For speed to remain constant the kinetic energy must remain constant. For the kinetic energy to remanin constant, the potential energy must remain constant, and for the potential energy to remain constant the height must remain constant.