Ch 7_8 Work & Kinetic Energy And Potential Energy

CH 7 & 8 Work & Kinetic Energy and Potential Energy CH 7 Work and Kinetic Energy Subject Work Done by A Constant Force

Relevant Equations

W=Fd S.I= J (N•m) 1 J = 1kg•m2/s2 Scalar quantity W=FdcosΘ S.I.=J

Relationships •Work is equal to 0 if distance d is equal to 0. Work done by a force is (i) The component or force in the direction of displacement times the magnitude of displacement. (ii) The component of displacement in the direction of the force times the magnitude of the force.

Force at an Angle to Displacement

(i) (ii) (iii)

Negative Work and Total Work

K=½mv2 S.I.=kg• m2/s2 or Joules, J Wtotal = ΔKE = ½mvf2-½mvi2

Work is positive if the force has a component in direction of motion (Θ<90°). Work is negative if Θ >90°. Work is zero if Θ=90°

•Whenever the total work done on an object is positive, its speed increases. •When negative, speed decreases. •Kinetic energy is NEVER negative.

Kinetic and Work Energy Theorem •Work done by a force in moving an object from x1 and x2 is equal to the corresponding area between the force one and the x axis.

Work Done by a Variable Force

W=½kx2 Spring

S.I J, Joule

P=W/t S.I= J/s or Watt, W P=Fv 1 hp=746 W Power

•Work done by a spring can be positive or negative.

CH 7 & 8 Work & Kinetic Energy and Potential Energy CH 8 Potential Energy and Conservative Forces Subject

Conservative and Nonconservative Forces

Potential Energy

Relevant Equations Relationships Conservative •Work done by a conservative force is stored in the form of energy and released at a later time. •Each conservative force has its own potential energy. Examples are gravity and spring force. Definition 1: Conservative force does 0 total work on a closed path. Definition 2: Work done by a conservative force in going from point A to point B is independent of the path from A to B.

Wc=-ΔU S.I.= J Gravity: Wc = mgy vi=mgy+vf = Δv = mgy Ui >Uf U=mgh. Gravity: Wc=mgy Ui = mgy + vf -ΔU = mgy Ui > Uf U=mgh Springs Wc=½kx2 U=½ kx2 Wtotal=4µkmgd

Work Done by NC and C Forces Peg=mgh

Gravitational Potential Energy

Non Conservative •Work done by nonconservative Force cannot be recovered later as kinetic energy. Examples of nonconservative forces are friction and tension.

•Only conservative forces have a potential energy storage system.

Nonconservati Conservative ve Gravity: Wc=mgy Ui = mgy + vf -ΔU = mgy Ui > Uf U=mgh Friction Springs Wtotal=4µkmgd Wc=½kx2 Tension U=½ kx2 •Nonconservati U depends on x2, which is ve forces always positive. •Spring's change the potential energy is always amount of greater than or equal to 0 mechanical so it increase whenever energy in a displaced from equilibrium. system. •Gravitational potential energy only depends on the height "y." But just because y increases, PE doesn't necessarily increase. •PE increases as an object is lifted higher.

CH 7 & 8 Work & Kinetic Energy and Potential Energy Conservation of Mechanical Energy

E=U + K v=√(2gh)

•E is always conserved. In systems with a conservative force, only E is conserved. •E=U+ K = constant.