Presentation on theme: "Review Chap. 7 Potential Energy and Energy Conservation"— Presentation transcript:
1Review Chap. 7 Potential Energy and Energy Conservation PHYS 218 secReviewChap. 7Potential Energy and Energy Conservation
2Gravitational potential energy Energy associated with the position of bodies in a systemA measure of the potential or possibility for work to be doneThe work done on the object to change its position is stored in the object in the form of an energyGravitational potential energyy2y1When the body moves up, the work done by the gravitational force is negative and the potential energy increases.
3Potential energyThe potential energy is a relative quantity. You have to specify the reference point when you define the potential energy. For example, the gravitational potential energy is mgy and the point where y = 0 should be specified, which is the reference point when you define the potential energy.What is physically meaningful is the change of the potential energy. The absolute value does not have physical meaning. Note that the work done by a force is equal to the negative of the potential energy change.
4Conservation of mechanical energy So, K + U is conservedThis defines the total mechanical energy of the system.Conservation of mechanical energy
5Height of a baseball from energy conservation Ex 7.1Height of a baseball from energy conservationEnergy conservation is very useful to obtain speed or position, in particular, when it its very difficult to use Newton’s laws of motion.
6When forces other than gravity do work Therefore, for example, if there is friction force, the total mechanical energy is not conserved. Instead, we have
7Work and energy in throwing a baseball Ex 7.2Work and energy in throwing a baseballFrom y = 0 to y1State 3State 2From y = y1 to y2State 1Two solutions; moving up and moving downHere we use different choice for the y-axis from the textbook. But the final answers are the same as it should be.
8Gravitational potential energy for motion along a curved path Only Dy contributesThe total work becomesThe total work done by the gravitational force depends only on the difference in height
9Calculating speed along a vertical circle Ex 7.4Calculating speed along a vertical circlePoint 1Speed at the bottom of the rampWhat we need is speed not velocity, so v2 is positivePoint 2Normal force at the bottom of the curve
10Vertical circle with friction: same as Ex 7 Vertical circle with friction: same as Ex 7.4 but there is friction force. What is the work done by the friction force?Ex 7.5
11Inclined plane with friction Ex 7.6Inclined plane with frictionMotion of a crate: Point 1 (speed v1) g Point 2 (speed v2 = 0) g Point 3 (speed v3)Point 2equal to Point 1Magnitude of a constant friction forcePoint 1, 3Consider the motion from Point 1 to Point 2
12Consider the motion from Point 1 to Point 3 Speed at Point 3Consider the motion from Point 1 to Point 3Be careful:Speed is always positive while velocity can be negativeWhat we want is speed not velocity, so v3 is positive
13Elastic potential energy Energy stored in an ideal spring.This is a potential energy that is not gravitational in origin. Although this is not one of the fundamental forces in nature, its potential energy can be defined.
14Gravitational potential energy plus Elastic potential energy
15Motion with elastic potential energy Ex 7.7Motion with elastic potential energymPoint 1mPoint 2What is v2?
16Motion with elastic potential energy and work done by other forces: similar to Ex 7.7 The object is moving to the right. So the negative value, -0.6 m/s, is not the solution although it is a mathematical solution.
17Motion with gravitational, elastic, and friction forces Ex 7.9Motion with gravitational, elastic, and friction forcesm=2000 kgPoint 1Choose Point 1 as y = 0Point 2
18Conservative and nonconservative forces Allows two-way conversion between kinetic and potential energiesConservative forceProperties of the work done by a conservative forceThe potential energy function can be defined.It is reversible.It is independent of the path of the body; depends only on the starting & ending pointsWhen the starting & ending points are the same the total work is zero.fIIIi
19Nonconservative force Does not allow two-way conversion between kinetic and potential energiesThe work done by a nonconservative force cannot be represented by a potential energy.Under the influence of some nonconservative force, the body looses its energy. So this is also called a dissipative force.Under the influence of some nonconservative force, the body gets its energy.Potential energy cannot be defined for nonconservative forces!
20Conservative or nonconservative? Ex 7.11Conservative or nonconservative?Leg 3Leg 4Leg 2Leg 1
21Force and potential energy integrateForcePotential energydifferentiateFor 3-dim caseFor 1-dim casepartial derivative
22Energy diagram: a graph of energy vs position Energy diagramsEnergy diagram: a graph of energy vs positionIt contains the shape of the potential energy and the total energy is a straight horizontal line as it is a constant once a body is given an energy.This allows to know the motion of the body even if the functional form for the potential energy is not known.Slope of the tangent line is positive, so the force is negative.The body is moving always toward the minimal potential energy point.Slope of the tangent line is negative, so the force is positive.
23maximum of the potential: unstable equilibrium point Turning pointMinimum of the potential: stable equilibrium point