Physics 1025F Mechanics. ENERGY. Dr. Steve Peterson Steve.firstname.lastname@example.org. Chapter 6: Work and Energy. We have been using forces to study the translational motion of objects; Energy (and work) can provide an alternate analysis of this motion. ENERGY. Energy ….
Dr. Steve Peterson
We have been using forces to study the translational motion of objects; Energy (and work) can provide an alternate analysis of this motion
Although energy is hard to define and comes in many different forms, every system in nature has associated with it a quantity we call its total energy.
The total energy (E) is the sum of all the different forms of energy present in the system, i.e.
Energy transformations can occur within a system.
A system is what we define it to be.
Energy can be transformedwithin the system without loss.
Energy is a property of a system.
An exchange of energy between system and environment is called an energy transfer.
Two primary energy-transfer processes: Work & Heat
Work is a mechanical transfer of energy to or from a system by pushing or pulling it.
Heat is a non-mechanical transfer of energy from the environment to the system (or vice versa) because of a temperature difference between the two.
Work done on a system represents energy that is transferred into or out of the system.
The energy of the system (ΔE) changes by the exact amount of work (W) that was done.
Work-Energy Principle: The total energy of the system changes by the amount of work done on it.
Suppose we have an isolated system, separating it from its surroundings in such a way that no energy is transferred into or out of the system.
Law of Conservation of Energy: The total energy of an isolated system remains constant.
There is a fact, or if you wish, a law, governing all natural phenomenathat are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.
- Richard Feynman
The work done by a constant force Fon an object is equal to the product of the force multiplied by the distance through which the force acts.
Therefore if the motion is in the same direction as the applied force the magnitude of the work done W is:
Dot Product: Vector Multiplication
If, on the other hand, the applied force Fmakes an angle θ with the subsequent displacement,dthen the work done is
Note: Work is a scalar quantity
In the SI system, the units of work are joules:
Work is positive when lifting the box
Work would be negative if lowering the box
A sled loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at 20.0° above the horizontal. The sled moves a distance of 20.0 m on a horizontal surface. The coefficient of friction between the sled and surface is 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sled? (c) What is the mechanical energy lost due to friction?
Kinetic energy is the energy of motion.
All moving objects have kinetic energy.
It is sometimes possible within a system to store energy so that it can be easily recoverable.
This sort of stored energy is called potential energy.
We will look at gravitational potential energy (due to the force of gravity) and elastic potential energy (due to the force from a spring).
Interaction forces that can store useful energy are called conservativeforces.
Gravitational potential energy (UG) depends only on the height of the object and not the path the objects took to get to that position.
Assuming UG = 0 when y = 0
The force exerted by a spring (FS) is called Hooke’s Law.
Energy can be stored in a spring as elastic potential energy (US).
Thermal energy is related to the microscopic motion of the molecules of an object.
The molecule’s motion produces kinetic energy and the spring-like molecular bonds produce potential energy.
The sum of these microscopic kinetic and potential energies is what we call thermal energy.
If work is done in the presence of friction, then thermal energy (heat) is generated - heat is another form of energy and therefore some of the work has gone into producing the heat.
i.e. the work done on the body is converted into changes in KEand/or changes in PEand/or changes in heat.
Any change in the energy of a system is the result of work done on the system
So, if there is no work done on the system?
This gives rise to the Law of Conservation of Energy which can be stated as:
"Energy can be neither created nor destroyed, but can be converted from one form to another or transferred from one system to another”.
If there is nofriction present and noexternal forces (other than gravity) acting on the system we have
This is a very powerful equation, and we often refer to the sum of KEand PEas "mechanical energy”.
To say a physical quantity is conservedis to say that the numerical value of the quantity remains constantthroughout any physical process although the quantities may change form.
In Conservation of Energy, the total mechanical energy remains constant
In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant.Conservation of Mechanical Energy
Work and energy associated with the force can be recovered
The forces are generally dissipative and work done against it cannot easily be recovered
Potential energy can only be defined for conservative forces.Conservative & NonconservativeForces
A stone is dropped from a 60-m high cliff onto the ground below. (a) What is the speed of the stone when it hits the ground?
(b) Now, the stone is thrown upwards at 20 m/s from the top of the cliff. What is the speed of the stone when it hits the ground?
(c) How would the final speed change if the stone were thrown upward at an angle?
The rate at which energy is transformed is called the power (P) and defined as:
Power is also defined as the rate at which work is done.
In the SI system, the units of power are measured in joules per second or watts (W):
A 2-kg block is pulled up a frictionless incline (30° above horizontal) by a 15 N force. What is the speed of the block after traveling 6-m?
1-kgand 2-kg masses hang from opposite ends of a string hanging over a frictionless pulley. The 1-kg mass sits on the ground and the 2-kg mass is 5-m in the air. With what speed will the 2-kg mass hit the ground?