Work done and KE

Work done Workdone by a force is defined as Force Displacement = Fd Cosθ

A box rests on a horizontal, frictionless surface A box rests on a horizontal, frictionless surface. A girl pushes on the box with a force of 18 N to the right and a boy pushes on the box with a force of 12 N to the left. The box moves 4.0 m to the right. Find the work done by (a) the girl, (b) the boy, and (c) the net force.

A box rests on an 30 deg inclined surface, with Static Coeff = 0 A box rests on an 30 deg inclined surface, with Static Coeff = 0.2 and Kinetic Coeff = 0.1 . A girl pushes on the 10Kg box with a force of 100 N upwards. The box moves 1.0 m on the incline. Find the work done by (a) the girl, (b) the gravity, and (c) the friction (d) net Force.

What do you think? If a Force increases velocity of an object , would you call the Wok done by this force as POSITIVE or NEGATIVE ? Why?

Work-Energy Theorem Prove using Vf2-Vo2 = 2ad Work done by a Force = Change in Kinetic Energy Prove using Vf2-Vo2 = 2ad

If KE is lost where does it go? If KE is gained where does it come from?

change in vertical height Work done by gravity end dist dist∥ start change in vertical height W=mg Work = F x dist∥ = -mg x Change in height = - Change in mg h

Gravitational Potential Energy Workgrav = -Change in mgh This is called: “Gravitational Potential Energy” (or PEgrav) Change in PEgrav = -Workgrav Workgrav = -change in PEgrav

If gravity is the only force doing work…. Work-Energy theorem: - change in mgh = change in ½ mv2 0 = change in mgh + change in ½ mv2 change in (mgh + ½ mv2) = 0 mgh + ½ mv2 = constant

Conservation of energy mgh + ½ mv2 = constant Gravitational Potential energy Kinetic energy If gravity is the only force that does work: PE + KE = constant Energy is conserved

Free fall height t = 0s 80m V0 = 0 75m t = 1s V1 = 10m/s 60m t = 2s

m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0 750J 50J V1 = 10m/s; h1=75m 800J t = 2s V2 = 20m/s; h2=60m 600J 200J 800J t = 3s V3 = 30m/s; h3=35m 350J 450J 800J t = 4s V4 = 40m/s; h4=0 0 800J 800J

A 10-N force is applied to push a block across a frictional surface at constant speed for a displacement of 5.0 m What is the net Work done on the block? DO NOW

T is always ┴ to the motion pendulum T W=mg Two forces: T and W T is always ┴ to the motion (& does no work)

Roller coaster

r Vector and dr vector Work Done by a variable Force

Work Done by a variable Force dr Work Done by a variable Force dr

Spring - Hooke’s Law

Graphically |Work done by the spring| = Area under the curve = ½ Kx2

Work done by spring = - change in ½ kx2 Work done by a spring Relaxed Position F=0 x When you compress the spring (+ work done; spring does -work) Work done by spring = - change in ½ kx2

Spring Potential Energy Workspring = -change in ½ kx2 This is the: “Spring’s Potential Energy” (or PEspring) Workspring = -change in PEspring change in PEspring = -Workspring

If spring is the only force doing work…. Work-energy theorem: -change in ½ kx2 = change in ½ mv2 0 = change in ½ kx2 + change in ½ mv2 change in ( ½ kx2 + ½ mv2) = 0 ½ kx2 + ½ mv2 = constant

Conservation of energy springs & gravity mgh + ½ kx2 + ½ mv2 = constant Gravitational potential energy spring potential energy Kinetic energy If elastic force & gravity are the only force doing work: PEgrav + PEspring + KE = constant Energy is conserved

Summary Net Work Done on an object = KE final – KE initial That it is + when the system gains KE energy And it is - when it loses KE energy

An elevator cab of mass m = 500 kg is descending with speed vi = 4 An elevator cab of mass m = 500 kg is descending with speed vi = 4.0 m/s when its supporting cable begins to slip, allowing it to fall with constant acceleration a=g/5 (1) During the fall through a distance d = 12 m, what is the work Wg done on the cab by the gravitational force ? During the 12 m fall, what is the work WT done on the cab by the upward pull of the elevator cable?

(3) What is the net work W done on the cab during the fall? (4) What is the cab's kinetic energy at the end of the 12 m fall?

Conservative and non- conservative forces

Path in-dependence of conservative forces

1) If a coconut falls from a tree from a height of 20 m 1) If a coconut falls from a tree from a height of 20 m. It falls on a leaf that provides a constant resistance of 2N for a distance of 0.5 m before the coconut starts to fall freely. What is the total mechanical energy of the coconut before it starts to fall? What is the work done by the resistive force of the leaf? 2) In a second scenerio, a person climbs the tree and throws the coconut down from the same height of 20m. He pushes the coconut down with a force of 1N by moving his hand vertically through a distance of 0.25m. What is the total mechanical energy of the coconut when it starts to fall? What is the work done by the person’s applied force ?

3) In a third scenerio, the person throws the coconut down from the same height of 20 m. But he pushes the coconut down with a force of 5N by moving his hand vertically through a distance of 0.25m. What is the total mechanical energy of the coconut when it starts to fall? This time, the coconut falls on a sandy surface and the coconut makes a dent of 0.2 m on the surface before coming to stop. What is the work done by the sand on the coconut ? Draw the scenerio before solving.

What are the graphical models and the mathematical models that are used to represent the energy of a system? Frictionless surface ( hypothetical) Frictional Surface H