Mechanical Energy. Unit 4 - PDF Free Download

Mechanical Energy Unit 4

Expectations Cell phones put away, or upside down on your desk No talking during notes Raise your hand to ask a question Everyone will follow along and copy into their own notes (only) Sharpen pencil when teacher is NOT talking, otherwise stay seated No one leaves during notes Be prepared to participate

Definition and Mathematics of Work

I Can... Define work and explain why it is more scientific than everyday language. Compare work done in different situations.

Questions What is work? How is it different from the work you do in daily life? How much work is done moving 3 boxes up 6 floors versus 6 boxes up 3 floors? How much work is done on a barbell that I am holding above my head?

Definition and Mathematics of Work We have analyzed motion from several perspectives: Newton s laws: force x mass = acceleration Acceleration = velocity or displacement change Velocity = speed in a given direction Speed = rate an object is moving

We will now be investigating how motion is affected by: Work Energy Height Velocity Power

Work When a force acts on an object to cause movement, work is done on that object. 3 things are required for work to be done: 1. Force 2. Displacement 3. Cause - must be the applied force

Are these work? A teacher applies a force to a wall and becomes exhausted. A book falls off a table and free falls to the ground. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. (This one is a tricky one. We ll talk more about it in 2 slides) A rocket accelerates through space.

The talented waiter In order for the waiter to be doing work on the tray, the force he is applying to the tray MUST cause the displacement of that tray. He is applying an upward force, but an vertical force can never cause a horizontal displacement.

Negative work Negative work occurs when a force acts upon an object to hinder, or prevent, displacement. The force acts opposite to the object's movement in order to stop or slow the object.

Unit of work Work and energy are measured in the same units, Joules. Joules are abbreviated J. One Joule is equal to one Newton of force causing a displacement of one meter. 1J = 1N x 1m In the US you might see foot x pound. Weird, right?!

Questions What is work? How is it different from the work you do in daily life? How much work is done on a barbell that I am holding above my head?

I Can... Calculate the amount of work done when something is moved.

Questions How do you calculate the amount of work that is done given the force and the distance? Given a force of 10N, how much work is done if it is moved 5 meters? Given a force of 25N, how much work is done if it is moved 2 meters?

Work Work is done by force(s) upon an object(s) to cause displacement.

Work Equation Mathematically, work is calculated: force x distance x cos Θ (theta) The theta is the angle between the force and displacement vectors. We will be simplifying this and not be dealing with angles. If the there is no angle, the cos of 0 is one and does not change the answer in any way.

Practice What is our force? What is our distance? How much work is done?

A 10-N force is applied to push a block across a friction free surface for a displacement of 5.0 m to the right. What is the net force? What is the distance? What is the amount of work done?

Energy Types and Transformations

I Can... Identify the kind of energy in a given situation. Describe the transformation between potential and kinetic energy. Explain why all mechanical systems require an external energy source to maintain their motion. Rank the amount of kinetic energy in examples of moving objects. Calculate both kinetic and potential energy in given situations.

Questions Explain how PE can be increased. What two variables can increase/decrease PE? How much potential energy is in a ball before it is thrown from a height of 3 meters if it has a mass of 15kg? How much potential energy is in the same ball if it flies through the air at 10m/s? If the height of an object doubles, what happens to the PE?

Potential Energy An object can store energy because of its position. This is potential energy.

Types of Potential Energy There are several types of potential energy. Gravitational Elastic Chemical Spring Nuclear Electric

Gravitational Potential Energy Gravitational potential energy is stored energy that depends on the height of the object and its mass. The higher a mass is raised, the more gravitational potential energy the object stores. Another way to increase the gravitational potential energy is to increase the mass of the object (not always easy).

The relationship between gravitational PE, height and mass is as follows: PE grav = mass x height So, based on the position of zero height we can measure the height of an object and determine the PE.

Practice How much PE would be at each location, A-F?

Practice If an object has a mass of 3kg and it is 3 m above the tabletop, what is its PE? If an object has 28J of PE, and it has a mass of 7-kg, how high is it from zero height? If the PE from the problem above needed to be increased, what height would it need to be moved to?

Elastic Potential Energy Elastic Potential Energy is energy stored as the result of stretching or compressing elastic materials Examples: rubber bands, bungee cords, trampolines, springs, etc. How much Elastic PE depends on the amount of stretch - more stretch, more stored energy

Springs Springs are a special type of elastic PE because they can be stretched or compressed. Force is required to compress the spring, and the more compression, the more energy is stored. F spring = k x k- spring constant, x- stretch or compression Follows Hooke s Law - no compression or stretch = no energy

Work and Energy The amount of work that is done to an object to move it against gravity is equal to the amount of change in the PE of an object. So, it seems you really do have to put work into something in order to get something out of it!

Questions What kind of energy is present in a rock rolling down a hill? If a high diver has a mass of 40-kg and has 12000 J of KE before they hit the water, what is their velocity? Which vehicle below has more kinetic energy if they have the same velocity? Explain how you know.

Kinetic Energy Energy of motion Types Vibrational Rotational Translational

KE We will be focusing on translational KE, or movement from one location to another The amount of KE depends on two variables: Mass and velocity The relationship can be shown as: KE = ½ mass x v 2

Kinetic energy is a scalar quantity and does not have a direction. Measured in Joules If the velocity doubles, the KE will increase 4 times. If the velocity triples, the KE will increase 9 times. If the velocity is halved, the KE is decreased to ¼ This should be a familiar pattern from gravitation!

Practice What is the KE of a roller coaster with a 600-kg mass that is moving at 20 m/s? What is the mass of the roller coaster is doubled? Instead, what is the KE if the velocity is changed to 40 m/s? Or, reduced to 10 m/s?

I Can... Identify the kind of energy in a given situation. Describe the transformation between potential and kinetic energy.

Questions What is mechanical energy? Describe the transfer of energy as a rock rolls down a hill. How do we find total ME?

Mechanical Energy When work is done the object that does the work exchanges energy with the object that has work applied to it. If I lift a book off of the floor, the book gains energy from me. A pitcher supplies the force to do work on a baseball that accelerates towards home plate. The energy acquired by the object is called mechanical energy.

Mechanical energy is the energy that is possessed by an object due to its motion or position. Potential energy Kinetic energy Objects have ME if they are in motion and/or at some position relative to the zero PE position.

An object that has ME has the ability to do work. ME allows an object to apply a force to another object and cause displacement.

Real Life When does the wrecking ball have the most PE? KE? Do work? Where did the energy come from?

Examples of ME Bowling ball does work on bowling pins Hammer does work on a nail Springs in a Nerf gun to work on the darts Wind does work on windmills

Total Mechanical Energy Mechanical energy is the result of the motion and/or position of an object. The total amount of ME is found by finding the sum of the PE and KE. TME = KE + PE

What do you notice about the TME in the example below?

The sum of the skier is the PE and KE added together. The sum of the energy is 50,000J, and is constant throughout the ski jump.

Questions What is mechanical energy? Describe the transfer of energy as a rock rolls down a hill. How do we find total ME?

Questions What kind of energy is present in a rock rolling down a hill? Describe the transfer of energy as that rock rolls. Why is external energy required for all mechanical systems? How can be calculate the amount of velocity of an object from the PE, assuming it is experiencing internal forces?

Internal vs. External Forces Forces can be categorized We ve talked about contact and noncontact forces Now we will sort them based on whether they can change an object s TME. These are called internal and external forces.

What Does Work Do? If the work done on an object keeps the TME the same, only internal forces are at work. External forces can cause a net gain or loss of energy, thus changing the TME. Internal Forces Gravity Spring Magnetic Electrical External Forces Applied Normal Tension Friction Air Resistance

Internal forces cause kinetic and potential energy to change forms back and forth, but do not cause a loss or gain of the total energy. *Energy is conserved*

External forces can cause the TME to increase or decrease In the example below, the TME is conserved. What external forces are present in real life to change the TME?

Energy is conserved in all situations, due to its inability to be created or destroyed. Mechanical Systems and External Energy In reality, most situations involve external forces of some kind. So, work done to the object(s) will change the TME, however, if external forces are not present, the TME will remain the same. In order to keep mechanical systems going, external forces (energy) must be applied.

Problems As the red ball moves from A to D, the TME. The minimum PE can be found at. The maximum PE can be found at. The KE at point C is less than the KE at.

Problems Determine the skier s speed at B,C,D, and E. (mass = 500)