WORK & POWER

Energy Review: What is energy?

The capacity to cause change

Stored within system(Eg, Eel, Ek, Eint)

Added to or removed from the system through “working”(W)

Basic Energy Model: Expanded

Etotal = Ek + Eel + Eg + Eint

Amount of Energy Transferred = Change in Energy Stored

W = ∆Etotal = ∆Ek + ∆Eel + ∆Eg + ∆Eint

WITHIN

the system

External to

the system

Tote bag demo

Draw a force diagram for the tote bag at rest

Draw a force diagram for the tote bag with a constant velocity

Tote bag demo – continued

When bag is lifted at a constant velocity, the lifting force (FLIFT) is equal to the weight (mg) for the entire time.

Lifting an object, ADDS energy that is stored as Eg (gravitational potential).

Work = energy added to system

FLIFT

Fg = mg

Tote bag demo – continued

When bag is lifted at a constant velocity, the lifting force (FLIFT) is equal to the weight (mg) for the entire time.

Work = energy added to system

Work = (FLIFT) (height lifted) = (mg) (h)

FLIFT

Fg = mg

Work = (Force Applied)*(Distance Applied)Work = F ∆x

Working: Other Examples

Block pushed across floor = (Fpush)*(∆x)

Block pushed with force of 200 N for 30 m

Work = (200 N)*(30 m) = 6000 J

Working: Other Examples

Work done on elevator lifted 100 m W = (Flift)*(∆y)

Elevator with mass 1000 kg and weight 9800 N lifted 100 m

Work = (9800 N)*(100 m) = 980,000 J

Power

Rate at which work is done

OR

Units of Measurement for power = = Watts (W)

Power: Example

 When doing a chin-up, a physics student with a weight of 480 N lifts her body a distance of 0.25 meters in 2 seconds. How much work are the student’s muscles

doing? Work = Force (∆y) = (480 N)*(0.25 m) =

120 J

How much power are the student’s muscles supplying?

Power = Work / Time = 120 J / 2 sec = 60 Watts

Energy – and signs

Vectors… examples? Velocity Acceleration

Is energy a vector? Hint: Is money a vector?

But, we DO use signs when talking about energy transfer… What do they mean? + means energy transferred into the

system - means energy transferred out of the

system

Working: Calculations

Work done on tote bag = Energy transferred to bag

W = ∆Ek + ∆Eel + ∆Eg + ∆Eint

Work = ∆Eg = (FLIFT * h) = F*∆y

Gravitational Energy (Eg)

0

EK Ee

0

Initial

box

W

FT

Eg

Final

EK Eg Ee Eint

Energy Flow Diagram

=

Working: Definition

Transfer of energy by an external agent applying a force parallel to the direction of motion External – transfer of energy into or out of the

system Parallel – aligned with motion

Ex: x-direction of motion

Basic Energy Model: 2 types of problems

W = ∆Etotal = ∆Ek + ∆Eel + ∆Eg + ∆Eint

W = 0 W = ∆Etotal

Tote bag demo – continued

Area under a force (F) vs. displacement (∆ y) curve = energy

Spring Lab (Eel):

Lifting an Object (Eg):

∆ y

Working: Calculations

Energy transferred to, and then stored in, spring: Area under F vs. ∆x graph ∆ Energy = W = F * ∆x

Work is energy transferred during an interaction that results in a displacement of the point of application of the force

Energy Storage

How or where can energy be stored?

In a stretched spring or elastic material: = k(Δx)2

In a moving object: = mv2

By raising an object off the ground: = mg∆y

In the motion of atoms or molecules:

Solving Other Problems

Changing gravitational energy to kinetic energy is useful for solving many different types of problems. Straight

Ramps

1

Curved Ramps

11

2

FreefallPendulums

2 2

1

2h

The speeds will be the same, but the directions different!

Mechanical Energy

 In all instances, an object that possesses some form of energy supplies the force to do the work.

 In all instances in which work is done, there is an object that supplies the force in order to do the work.In the instances described here, the objects doing the work (a student, a tractor, a pitcher, a motor/chain) possess chemical potential energy stored in food or fuel that is transformed into work. In the process of doing work, the object that is doing the work exchanges energy with the object upon which the work is done. When the work is done upon the object, that object gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy.Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position 

An object that possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Any object that possesses mechanical energy - whether it is in the form of potential energy orkinetic energy - is able to do work. That is, its mechanical energy enables that object to apply a force to another object in order to cause it to be displaced.

A dart gun is still another example of how mechanical energy of an object can do work on another object. When a dart gun is loaded and the springs are compressed, it possesses mechanical energy. The mechanical energy of the compressed springs gives the springs the ability to apply a force to the dart in order to cause it to be displaced. Because of the springs have mechanical energy (in the form of elastic potential energy), it is able to do work on the dart. Mechanical energy is the ability to do work.

Mechanical Energy: Conserved

Whiteboard Problem

How high should the cart be placed so that it will have a velocity of 1m/s when it goes through the photogate?

(Photogate)

h = ?h = 0m

m = 0.291kg