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Objectives Recognize the difference between the scientific and ordinary definitions of work. Define work by relating it to force and displacement. Identify where work is being performed in a variety of situations. Calculate the net work done when many forces are applied to an object.

Definition of Work Work is done on an object when a force causes a displacement of the object. Work is done only when components of a force are parallel to a displacement.

Work The result of force moving an object. Work is therefore done on the object. Note: If the object does not move, than no work has been done. You can try and push the wall for 2 hours, use all that energy, and still not have done any work! Work is a transfer of energy.

Definition of Work F d W = Fd

W = Fd Force x Distance = Newton x meters = Newton-meters = Joule
Definition of Work W = Fd Force x Distance = Newton x meters = Newton-meters = Joule

Definition of Work

Sign Conventions for Work

Example of Work W = Fd

Example of Work W = Fd

Homework Read and Outline Chapter 3 part 1 pages 61-73
Vocabulary Define Key Terms within outline Underline clearly for future study Part 1 due Friday Part 2 due Monday

Review W = Fd Force in same Direction as motion
Force opposes Direction of motion Force perpendicular to Direction of motion No Motion

Objectives Identify several forms of energy.
Calculate kinetic energy for an object. Apply the work–kinetic energy theorem to solve problems. Distinguish between kinetic and potential energy. Classify different types of potential energy. Calculate the potential energy associated with an object’s position.

Law of the Conservation of Energy
Energy is the Ability to do work. We cannot do anything without energy. When something happens, energy is transferred Law of the Conservation of Energy Energy can neither be created nor destroyed, it can only be transformed from one form to another. Within a closed isolated system energy can change form, but the total amount must stay constant.

Kinetic Energy Kinetic Energy
The energy of an object that is due to the object’s motion is called kinetic energy. Kinetic energy depends on speed and mass.

Kinetic Energy Moving objects have Kinetic Energy. Movement can be in any direction, horizontal, vertical, etc. Forms of Kinetic Energy Vibrational – Due to vibrating Rotational – Due to rotation Translational – Motion from one place to another Note: When using KE, we are referring to Trans. KE

Kinetic Energy The kinetic energy of an object is directly proportional to the square of its velocity. That means it takes four times an objects kinetic energy to double its velocity. Nine times for three times the velocity. Scalar Quantity You can also use speed to solve for KE.

Kinetic Energy = ½ mass x velocity2
KE = ½ m v2 1 Joule = 1 kg x (m/s)2 KE is Measured in Joules

Kinetic Energy

Kinetic Energy, continued
Work-Kinetic Energy Theorem The net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy. The net work done on a body equals its change in kinetic energy. Wnet = ∆KE net work = change in kinetic energy

Work-Kinetic Energy Theorem

Sample Problem Work-Kinetic Energy Theorem
On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the kinetic friction is 25 N

Sample Problem Work-Kinetic Energy Theorem
On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the kinetic friction is 25 N Wnet = Change in KE KE = ½ mv2

Review W = Fd KE = ½ mv2 Wnet = Change in KE

Potential Energy Three Forms Gravitational Energy
Elastic Potential Energy Chemical Potential Energy Both have energy due to their position.

gravitational PE = mass  free-fall acceleration  height
Potential Energy Potential Energy is the energy associated with an object because of the position, shape, or condition of the object. Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies. Gravitational potential energy depends on height from a zero level. PEg = mgh gravitational PE = mass  free-fall acceleration  height

Potential Energy The greater an object’s Mass, the greater its Gravitational Potential Energy. The greater an object’s Height, the greater the Gravitational Potential Energy. Doubling an object’s Height will result in a doubling of the PE. Tripling the Height will increase PE by a factor of 3.

Potential Energy

Sample Problem Potential Energy
A 70.0 kg stuntman is about to jump off a bridge spanning a river from a height of 50.0 m. What is his gravitational potential energy?

What is the Potential Energy of each Ball?
Practice Exercise #1 What is the Potential Energy of each Ball?

B = 30 J A = 30 J C = 20 J D = 10 J E = 0 J

Practice Exercise #2 What is the PE of a 50 Kilogram object that is 10 meters above the ground? Calculate the PE of 75 Kilogram rock sitting on the edge of a 235 meter high cliff. What is the mass of an object that has a PE of 400 Joules at a height of 70 meters? How high is a 50 gram mass that has a PE of 14,000 J?

Potential Energy, continued
Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration. The symbol k is called the spring constant, a parameter that measures the spring’s resistance to being compressed or stretched.

Potential Energy, continued
Elastic potential energy is the energy available for use when a deformed elastic object returns to its original configuration. It is based on two things: The spring constant (i.e. how strong the spring is) The displacement of the spring (i.e. how far you push it or stretch it from a relaxed position)

Elastic Potential Energy

Spring Constant

Objectives Identify situations in which conservation of mechanical energy is valid. Recognize the forms that conserved energy can take. Solve problems using conservation of mechanical energy.

Conserved Quantities When we say that something is conserved, we mean that it remains constant.

Mechanical Energy Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects. ME = KE + ∑PE Mechanical energy is often conserved. MEi = MEf initial mechanical energy = final mechanical energy (in the absence of friction)

Conservation of Mechanical Energy

Sample Problem Conservation of Mechanical Energy
Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

Sample Problem, continued
Conservation of Mechanical Energy 1. Define Given: h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m Unknown: vf = ?

Sample Problem, continued
Conservation of Mechanical Energy 2. Plan Choose an equation or situation: The slide is frictionless, so mechanical energy is conserved. Kinetic energy and gravitational potential energy are the only forms of energy present.

Sample Problem, continued
Conservation of Mechanical Energy 2. Plan, continued The zero level chosen for gravitational potential energy is the bottom of the slide. Because the child ends at the zero level, the final gravitational potential energy is zero. PEg,f = 0

Sample Problem, continued
Conservation of Mechanical Energy 2. Plan, continued The initial gravitational potential energy at the top of the slide is PEg,i = mghi = mgh Because the child starts at rest, the initial kinetic energy at the top is zero. KEi = 0 Therefore, the final kinetic energy is as follows:

Sample Problem, continued
Conservation of Mechanical Energy 3. Calculate Substitute values into the equations: PEg,i = (25.0 kg)(9.81 m/s2)(3.00 m) = 736 J KEf = (1/2)(25.0 kg)vf2 Now use the calculated quantities to evaluate the final velocity. MEi = MEf PEi + KEi = PEf + KEf 736 J + 0 J = 0 J + (0.500)(25.0 kg)vf2 vf = 7.67 m/s

Sample Problem, continued
Conservation of Mechanical Energy 4. Evaluate The expression for the square of the final speed can be written as follows: Notice that the masses cancel, so the final speed does not depend on the mass of the child. This result makes sense because the acceleration of an object due to gravity does not depend on the mass of the object.

Mechanical Energy, continued
Mechanical Energy is not conserved in the presence of friction. As a sanding block slides on a piece of wood, energy (in the form of heat) is dissipated into the block and surface.

Objectives Review ideas connecting work and energy
Relate the concepts of energy, time, and power. Calculate power in two different ways. Explain the connection between power, work and energy

HW Problem

Power Power is the rate of doing work.
A more powerful system is one which is producing/transferring a larger amount of energy. or one that transfers the same amount, just in a shorter period of time. Units for Power are Watts.

Rate of Energy Transfer
Power is a quantity that measures the rate at which work is done or energy is transformed. P = W ∆t power = work ÷ time interval

Power

Power Work (= F x D) Power = Time (in seconds) Joules Watts = s

Practice How much power is required to do 100 J of work on an object in a time of 0.5 s? How much power is required if the same work is done in 1s?

Rate of Energy Transfer
How much work is required to pull a sled if you use 60J of work in 5 seconds? How much work does an elephant do while moving a circus wagon 20meters with a pulling force of 200N? If it takes 5 seconds for you to do 1000J of work, what is your power output?

Rate of Energy Transfer
An alternate equation for power in terms of force and speed is P = Fv power = force  speed

Practice How much power is required to lift a 500 N block of ice with a velocity of 4 m/s?

Practice If the power is 2000 Watts, over 5 seconds, how much Work is done?

Practice By the way, if the velocity is 4 m/s and it takes 5 seconds, what is the height? What is the Potential Energy of the 500 N block?

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