Conservative Forces and Potential Energy The force is called a conservative force when; The work done by a force in moving a particle from a one point to another is independent of the path followed by the particle. Weight – depends only on the particle’s vertical displacement. Spring force – depends only on the compression and extension of the spring Friction – the longer the path, the greater the work.  noncorsercvative force

V g = W y Gravitational Potential Energy

Elastic Potential Energy V is always positive since, in the deformed position, the force of the spring has the capacity or potential for always doing positive work on the particle when the spring is returned to its unstretched position.

Conservation of Energy

The gantry structure is used to test the response of a plane during a crash. The plane [ mass = 8 Mg ] is hoisted back until q = 60 o, and the cable is released when the plane is at rest. Determine the speed of the plane just before crashing into the ground, q = 15 o. Also what is the maximum tensioned developed in the supporting cable during the motion? Neglect the effect of the lift caused by the wings during the motion and size of the airplane. Ex 1

Conservation of Energy 20 cos60 o 60 o

Tension in the cable is perpendicular to motion  no work So, use Newton’s Equation of Motion

Ex 2 A smooth 2-kg collar C, fit loosely on the vertical shaft. If the spring is unstretched when the collar is in the position A, determine the speed at which the collar is moving when y = 1 m, if (a) it is released from rest at A (b) it is released at A with an upward velocity v a = 2 m/s

(a) it is released from rest at A Conservation of Energy Gravitational Potential Energy - mgy Elastic Potential Energy ½ ks cb 2

(b) it is released at A with an upward velocity va = 2 m/s Conservation of Energy