# Lesson 1: Basic Terminology and Concepts Work Definition and Mathematics of Work

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### Transcript of Lesson 1: Basic Terminology and Concepts Work Definition and Mathematics of Work

Lesson 1: Basic Terminology and ConceptsWork Definition and Mathematics of Work Calculating the Amount of Work Done by Forces Potential Energy Kinetic Energy Mechanical Energy Power

In physics, work is defined as a _________ acting upon an object to ____________ a __________________. forcecausedisplacementDefinition and Mathematics of WorkWork is being doneWork is not being doneWork is not being done

Lets practice work or no workA student applies a force to a wall and becomes exhausted. A calculator falls off a table and free falls to the ground.A waiter carries a tray full of beverages above his head by one arm across the roomA rocket accelerates through space.

Calculating the Amount of Work Done by Forces W = Fdcos

F - is the force in Newton, which causes the displacement of the object.d - is the displacement in meters = angle between force and displacementW - is work in Nm or Joule (J). 1 J = 1 Nm = 1 kgm2/s2Work is a _____________ quantity Work is independent of time the force acts on the object.scalarOnly the horizontal component of the force (Fcos) causes a horizontal displacement.

W = FdcosPositive worknegative work - force acts in the direction opposite the objects motion in order to slow it down. no workpositive, negative or zero work

To Do Work, Forces Must Cause DisplacementsW = Fdcos = 0

The angle in work equationThe angle in the equation is the angle between the force and the displacement vectors.

F & d are in the same direction, is 0o.W = Fdcos

exampleA 20.0 N force is used to push a 2.00 kg cart a distance of 5.00 meters. Determine the amount of work done on the cart by the force.

20.0 N

exampleHow much work is done in lifting a 5.0 kg box from the floor to a height of 1.2 m above the floor?

exampleA 2.3 kg block rests on a horizontal surface. A constant force of 5.0 N is applied to the block at an angle of 30.o to the horizontal; determine the work done on the block a distance of 2.0 meters along the surface.

30o5.0 N2.3 kg

practiceMatt pulls block along a horizontal surface at constant velocity. The diagram show the components of the force exerted on the block by Matt. Determine how much work is done against friction.

8.0 N6.0 N3.0 mF

exampleA neighbor pushes a lawnmower four times as far as you do but exert only half the force, which one of you does more work and by how much?

Force vs. displacement graphThe area under a force versus displacement graph is the work done by the force.

Displacement (m)Force (N)workExample: a block is pulled along a table with 10. N over a distance of 1.0 m. W = Fd = (10. N)(1.0 m) = 10. Jheightbasearea

Potential energyAn object can store energy as the result of its position. ________________________ is the stored energy of position possessed by an object. Two form:GravitationalElasticPotential energy

Gravitational potential energyGravitational potential energy is the energy stored in an object as the result of its _________________________The energy is stored as the result of the _____________ attraction of the Earth for the object.The work done in raising an object must result in an increase in the object's _______________________The gravitational potential energy of an object is dependent on three variables:The mass of the objectThe height of the objectThe gravitational field strengthEquation: ______________________m: mass, in kilogramsh: height, in metersg: acceleration of gravity = 9.81 m/s2vertical position (height).gravitationalPEgrav = mghgravitational potential energy

GPEGPE = mghThe equation shows that . . .

. . . the more gravitational potential energy its got.

the more mass a body has or the stronger the gravitational field its in or the higher up it is

GPE and work done by gravityWhen an object falls, gravity does positive work. Object loses GPE.Wgrav = mg(hi hf) Wgrav = - mg(hf hi) = - mghhihfAs long as the falling height is the same, gravity did The same amount of work regardless of which path is taken.

GPE and work against gravityWhen an object is raised against gravity at constant speed (no change in kinetic energy), gravity does negative work. Object gains GPE.Work done against gravity = mghhfhiAs long as the object is raised to the same height, work done against gravity is the same regardless of which path is taken.

Each path up to the seat top requires the same amount of work. The amount of work done by a force on any object is given by the equation W = Fdcoswhere F is the force, d is the displacement and is the angle between the force and the displacement vector. In all three cases, equals to 0oThe increase in an object's potential energy equals the work done in raising an object

exampleThe diagram shows points A, B, and C at or near Earths surface. As a mass is moved from A to B, 100. joules of work are done against gravity. What is the amount of work done against gravity as an identical mass is moved from A to C?

Unit of energyThe unit of energy is the same as work: _______1 joule = 1 (kg)(m/s2)(m) = 1 Newton meter1 joule = 1 (kg)(m2/s2)JoulesWork and energy has the same unit

Gravitational potential energy is relativeTo determine the gravitational potential energy of an object, a _______ height position must first be assigned. Typically, the ___________ is considered to be a position of zero height. But, it doesnt have to be:It could be relative to the height above the lab table. It could be relative to the bottom of a mountainIt could be the lowest position on a roller coasterzeroground

exampleHow much potential energy is gained by an object with a mass of 2.00 kg that is lifted from the floor to the top of 0.92 m high table?

The graph of gravitational potential energy vs. vertical height for an object near Earth's surface gives the weight of the object. The weight of the object is the slope of the line.Weight = __________

Elastic potential energyElastic potential energy is the energy stored in ______________ materials as the result of their stretching or compressing.Elastic potential energy can be stored inRubber bandsBungee coresSpringstrampolineselastic

Hookes LawF = kx Spring force = spring constant x displacement

F in the force needed to displace (by stretching or compressing) a spring x meters from the equilibrium (relaxed) position. The SI unit of F is Newton.k is spring constant. It is a measure of stiffness of the spring. The greater value of k means a stiffer spring because more force is needed to stretch or compress it that spring. The Si units of k are N/m. depends on the material made up of the spring. k is in N/mx the distance difference between the length of stretched/compressed spring and its relaxed (equilibrium) spring.

exampleA spring has a spring constant of 25 N/m. What is the minimum force required to stretch the spring 0.25 meter from its equilibrium position?

exampleThe graph below shows elongation as a function of the applied force for two springs, A and B. Compared to the spring constant for spring A, the spring constant for spring B issmaller larger the same

Elastic potential energy in a springElastic potential energy is the Work done on the spring.

PEs = Favgd = Favgx = ( kx)x = kx2Note: F is the average force

k: spring constantx: amount of compression or extension relative to equilibrium positionPEs = kx2

Elastic potential energy is directly proportional to x2elongationElastic potential energy

exampleA spring has a spring constant of 120 N/m. How much potential energy is stored in the spring as it is stretched 0.20 meter?

exampleThe unstretched spring in the diagram has a length of 0.40 meter and a spring constant k. A weight is hung from the spring, causing it to stretch to a length of 0.60 meter. In terms of k, how many joules of elastic potential energy are stored in this stretched spring?

exampleDetermine the potential energy stored in the spring with a spring constant of 25.0 N/m when a force of 2.50 N is applied to it.

exampleAs shown in the diagram, a 0.50-meter-long spring is stretched from its equilibrium position to a length of 1.00 meter by a weight. If 15 joules of energy are stored in the stretched spring, what is the value of the spring constant?

exampleA 10.-newton force is required to hold a stretched spring 0.20 meter from its rest position. What is the potential energy stored in the stretched spring?

A force of 0.2 N is needed to compress a spring a distance of 0.02 meter. What is the potential energy stored in this compressed spring?

Kinetic energyKinetic energy is the energy of _______. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy. The equation for kinetic energy is:

__________________

Where KE is kinetic energy, in joulesv is the speed of the object, in m/sm is the mass of the object, in kgmotion

Kinetic EnergyKE = m v 2The equation shows that . . .

. . . the more kinetic energy it has. the more mass a body has or the faster its moving

KE is proportional to v 2, so doubling the speed quadruples kinetic energy, and tripling the speed makes it nine times greater.

speedKinetic energymassKinetic energyKE is directly proportional to m, so doubling the mass doubles kinetic energy, and tripling the mass makes it three times greater.

ExampleA 55 kg toy sailboat is cruising at 3 m/s. What is its kinetic energy?

Note: Kinetic energy (along wit

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