Transcript A Conservation of Energy Gravitational Potential

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
Gravitational Potential Energy
Vg = Wy
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
Ex 1
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 = 60o,
and the cable is released when the plane is at rest.
Determine the speed of the plane just before crashing into the ground,
q = 15o. 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.
20 cos60o
60o
Conservation of Energy
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 va = 2 m/s
(a) it is released from rest at A
Gravitational Potential Energy
- mgy
Elastic Potential Energy
½ kscb2
Conservation of Energy
(b) it is released at A with an upward velocity va = 2 m/s
Conservation of Energy