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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