Chapter 2: Work and Energy Flashcards
What is energy?
What is kinetic energy? What is the equation for kinetic energy? What are the units of kinetic energy? What’s a good way to remember the units of kinetic energy? Is kinetic energy related to speed or velocity? Why?
Kinetic energy is the energy of motion. Objects that have mass and that are moving with some speed will have an associated amount of kinetic energy.
The SI unit for kinetic energy, as with all forms of energy, is the joule (J). A good way to remember the units of joules is to remember the formula for kinetic energy and do a dimensional analysis.
Kinetic energy is related to speed, not velocity. An object has the same kinetic energy regardless of the direction of its velocity vector.
What should we think about any time an object has a speed?
Example page 57 kinetic energy
What is potential energy?
What is gravitational potential energy? What is the equation for gravitational potential energy?
Gravitational potential energy depends on an object position with respect to some level identified as the datum (ground or zero potential energy position).
Is the zero potential energy position the same for all problems?
Example page 58 potential energy
What is elastic potential energy? What is the equation for elastic potential energy? Units? What is the equilibrium length of a spring? What is the spring constant?
Springs and other elastic systems act to store energy. Every spring has a characteristic link that which it is considered relaxed, or in equilibrium. When a spring is stretched or compressed from its equilibrium length, the spring has elastic potential energy.
The spring, constant, K, is a measure of the stiffness of the spring and is experimentally determined.
What is total mechanical energy? What is the equation for total mechanical energy?
The sum of an object’s potential and kinetic energies as its total mechanical energy.
E=U+K
What is the first law thermodynamics account for?
What are conservative forces? What are non-conservative forces? What are the two most commonly encountered conservative forces on the MCAT?
The most common conservative forces seen on the MCAT are gravity and electrostatic forces.
The transfer of energy from one form to another is a key feature of bioenergetics and metabolism found in biochemistry studies. Think about carbohydrate, metabolism and talk about potential energy converting into electrical potential energy.
There are two equivalent ways to determine whether a force is conservative. What are those two ways? Are non-conservative forces possible to avoid in real life?
Non-conservative forces are impossible to avoid in real life.
One method is to consider the change in energy of a system in which the system is brought back to its original set up. If the net change in energy is zero regardless of the path taken to get back to the initial position, then the force is acting on the object or conservative. Basically, this means that a system that is experiencing only conservative forces will be “given back” an amount of usable energy equal to the amount that had been “taken away” from it in the course of a closed path.
The other method is to consider the change and energy of a system moving from one setup to another. If the energy change is equal, regardless of the path taken, then the forces acting on the object are all conservative.
On non-conservative forces, such as friction, air resistance, or viscous drag (a resistance force created by fluid viscosity) are present, total mechanical energy is not conserved. Express this in an equation.
Are non-conservative forces path dependent?
The work done by non-conservative forces will be exactly equal to the amount of energy “lost” from the system. In reality, the energy is simply transformed into another form of energy, such as thermal energy, that is not accounted for in the mechanical energy equation.
Non-conservative forces, unlike conservative forces, are path dependent. The longer the distance traveled, the larger the amount of energy dissipated.
Example page 61 work done by non-conservative forces
Notice the algebra here. When I’m taking the difference of kinetic energy or something that has the same mass, it is a common factor in the equation. It may have been cumbersome to not factor out mass from this equation.
MCAT concept check page 62 2.1 Energy question 1
MCAT concept check energy page 62 2.1 question 2
Is Work energy?
Work is not energy, but a measure of energy transfer.
The other form of energy transfer is heat. (Member frum kemistrie)
Work=Nm=kgm/s^2 m
What is work?
Work is a process by which energy is transferred from one system to another.
It is one of only two ways in which energy can be transferred. The other way in which energy is transferred is heat.
How many ways can energy be transferred? What are the ways that energy can be transferred?
There are only two ways that energy can be transferred.
The only two ways that energy is transferred is work and heat.
According to the first law of thermodynamics the only two ways energy can be transferred to or from a system are through heat and work; meaning any energy exchange between a system and its surroundings can be categorized as either heat transfer or work done on/by the system.
The unit of work and energy are both joule. This suggest that they are the same thing. Are they the same thing?
No. Work is the process by which a quantity of energy is moved from one system to another.
What is the mathematical expression for work? Is it a dot or cross product? What are the implications of this mathematical function?
Work is a dot product. As such, it is a function of the cosine of the angle between the vectors. This means that only forces (or components of forces) parallel, or anti-parallel to the displacement vector will do work (that is, transfer energy).
How do we approach work in a system of gases?
In systems of gases, we approach work as a combination of pressure and volume changes.
We can analyze the relationship between pressure, volume, and work. When the gas expands, it pushes up against the piston, exerting a force that causes the piston to move up and the volume of the system to increase. When the gas is compressed, the piston pushes down on the gas, exerting a force that decreases the volume of the system.
We say that work has been done when the volume of the system has changed due to and applied pressure. Gas expansion and compression processes can be represented in graphical form with volume on the X axis and pressure on the Y axis, such as in the image:
What is the difference between work done by a system and worked on on system?
When work is done by a system (gas expands) the work is said to be positive. When work is done on a system (the gas compresses) the work is said to be negative.
The area under a graph of pressure (x) and volume (y) is the work done on or by a system.
More elaborately: the work done on or by a system undergoing a thermodynamic process can be determined by finding the area enclosed by the corresponding pressure volume curves.
When gas expands, what can we say about the work done? When the gas compresses?
When a gas expands, we say that work was done by the gas and the work is positive.
When the gas is compressed, we say that work was done on the gas and the work is negative.
In which thermodynamic process is no work done?
No workers done in an isovolumetric (isochoric) process. This is a process in which the volume stays constant as pressure changes (deltaV=0). Understanding that work done is the area under the pressure volume curve, we can extrapolate this visually using the following graph:
Look at the equation W=PdeltaV. Importance of ΔV: The change in volume is the critical factor determining if work is done, even if pressure changes.
The image shows a process in which neither pressure nor volume is held constant. How would you calculate the work?
Work is the area underneath the pressure volume curve. This is simply taking the area of a triangle in the area of a rectangle in calculating the sum of the two separate areas. We can see that area one indicates a change in pressure and volume. Area one change in volume. We need to take the sum of area one and two such that:
What is Power? What does Power refer to (hint: rate)? What is the SI unit for power? What are the unit units for power? What is the equation for power?
Power is defined as the amount of work done per unit time.
POWER REFERS TO THE RATE AT WHICH ENERGY IS TRANSFERRED FROM ONE SYSTEM TO ANOTHER.
The SI unit for power is watt (W). W=J/s
Talk about and understand this:
Work (measured in joules) is not a form of energy, but is a process by which energy is transferred from one system to another. Work can be thought of as a change in energy.
Power is a change in energy per unit time, and is measured in joules per second. Power is the rate at which energy is transferred from one system to another. The unit for what is joule per second, or Watts.
What are a few situations in which power is calculated?
Unit review time. What are the units for:
Power
Work
Energy
Force
Acceleration
Velocity
Mass
Length
Temperature
Time
Write out the kinematic equations.
What is the work – energy theorem? Relate the first law thermodynamics to the work-energy theorem. What is the equation for the work-energy theorem?
The work energy theorem is an expression of the relationship between work and energy. It offers a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy of that object. The net work done by forces acting on an object will result in an equal change in the objects kinetic energy.
What is the work – energy theorem? What is the equation for the work-energy theorem?
The work energy theorem is an expression of the relationship between work and energy. It offers a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy of that object. The net work done by forces acting on an object will result in an equal change in the objects kinetic energy.
Relate the first law thermodynamics to the work-energy theorem.
The work energy theorem can be applied to changes in other forms of energy. The first law thermodynamics is essentially a reiteration of the work energy theorem in which the change and internal energy (deltaU) is equal to the heat transferred into the system (Q) minus the mechanical work done by the system (W).
Example page 66 work calculation.
Oh recognize what this question is asking us. It’s asking us to find work done by providing a mass and a velocity. Net work done is equal to the change in kinetic energy.
Recognize that the maximum height, the velocity will equal zero (final velocity).
When the equation became a matter of algebra, I did it two ways which boiled down to when I made my approximations.
One way the the book approximated getting to -900/16=-900/15=-60.
The other way I made my approximation for -900/8 being about 110, then halved to get 55J.
We need to be comfortable with making approximation during these calculations while recognizing the impact of my app approximation on the final result.
Concept check 2.2 page 66 Work question 1
The units of work is the joule. Work can be thought of as deltaE in calculations of power. Work is a transfer of energy into a system.
Work and energy have the same unit (J) but are not the same, however they are related topics. By performing work, the energy of a system has changed. Work, along with heat, is a form of energy transfer.
Concept check 2.2 page 66 Work question 2
Concept check 2.2 page 66 Work question 3
What is mechanical advantage?
Mechanical advantages is the ratio of magnitude of the force exerted on an object by a simple machine to the force actually app applied on the simple machine.
What is a large mechanical advantage mean (general answer and also in terms of a ratio)?
A large mechanical advantage means a larger output of force (by machine) than input of force (applied to machine).
In the ratio of mechanical advantage, output of force is the numerator and input of force is the denominator.
Example page 68 inclined plane, force, work.
What’s the mechanical advantage?
The mechanical advantage of the system is two.
Couple things to know about this question:
Noticed that it gave us the weight (mg) of the block. Mass and weight are not the same thing.
If you rotate your coordinate system to be parallel to the force applied, noticed that the force of gravity in the direction equals the force applied (Fgx=max=mgcostheta).
Work equals the product of force and distance (fdcostheta). Cosine of 0° is one. This is a good way to remember.
Section C asks us to find the force and work required to lift the block 10 m. Knowing that the work will be the same as calculated previously, and the distance will be 10 m, we can solve for force required to lift the block.
How do you calculate the mechanical advantage of an incline plane?
The mechanical advantage of an incline plane will simply be the length of the incline plane divided by the height of the incline plane. Stare at this for a minute and really understand it:
The mechanical advantage portions are in black .
The purpose of this card is to solidify our understanding of pulleys.
What is the equation for efficiency? Define all the terms.
What is the equation for efficiency? How is efficiency often expressed? What does efficiency measure?
How does effort and effort distance change in a system of pulleys?
How much will effort and effort distance change if you had a system of six pulleys?
Effort will reduce an effort distance will change proportionally to the amount of pulleys put in the system.
A system with six police will require 1/6 the effort, but six times the distance.
Ask KC about the angle of the load over a pulley and the force (effort) applied.
Example page 73 pulley system efficiency
The following pulley system has an efficiency of 80%. A person is lifting a mass of 200 kg with the pulley.
A. What is the distance through which the effort must move to raise the load a distance of 4 m?
B. What is the effort required to lift the load?
C. What is a work done by the person lifting the load through a height of 4 m?
MCAT concept check page 74 2.3 question 1
As the length of an incline plane increases, the force required to move an object the same displacement is less (the amount of force necessary to perform the same amount of work). The efficiency of an inclined plane is the length of the incline surface divided by the height of the incline surface. Less force is required to move an object as the length of the inclined plane increases.
MCAT concept check page 74 2.3 question 2
As effort decreases in a pulley system, the effort distance to maintain the same output increases to maintain the same amount of work.
MCAT concept check page 74 2.3 question 3
The difference between work inputting out putting in a system that operates at less than 100% efficiency is due to distribution of energy to non-conservative or external forces that generate or dissipate energy, like friction.
MCAT concept check page 74 2.3 question 4
When device has mechanical advantage, it means that the force out is greater than the force in for the same amount of work. Mechanical advantages unit less as it is a ratio.
From the book: when a device provides mechanical advantage, it decreases the input of force required to generate a particular output force. Generally, this is accomplished at the expense of increased distance over which the force must act.
MCAT mastery work and energy page 52 question 1
Couple things about this equation.
It asked us to calculate Work. We know three equations for work (in black in middle right on image)
We could have used potential energy to solve this problem given that the force supplied was 0°, in the changing in kinetic energy is zero.
The book used work equals fd cosine theta.
Again with approximation. We approximated acceleration due to gravity as 10, making our approximation slightly larger than actual calculated.
Zero work is required to hold the weight at the height because there is no displacement. This doesn’t mean that it doesn’t require energy to keep it there.
MCAT mastery work and energy page 52 question 2
We got confused slightly on this question. We got worked up about the mass and the gravity of the object. However, the question gave us the force tension that the tractor was applying, and the question asked how much work was the tractor doing? If the tractor was applying some force of tension that was making this mass move on a horizontal surface, then the answer will be worktractor=fdcostheta.
Again with the approximations. We approximated 0.866 to 0.9. We need to understand that this will create a large larger number than actual.
MCAT mastery work and energy page 52 question 4
This is an interesting question that we need to learn from. The total mechanical energy of that system will be equal to the potential energy before the object is released (potential energy plus kinetic energy, and kinetic energy is zero). Therefore, once released, potential energy will be transformed into kinetic energy BUT STILL HAVE A TOTAL MECHANICAL
ENERGY EQUAL TO THE INITAL CONDITION of mgh (40x10x5=2,000 J).
The total mechanical energy of this system will remain unchanged. The potential energy of the system before releasing is 2000 J, the sum of the potential and kinetic energy after release and it has fallen 2 m is still 2000 J.
From the book: assuming negative illegible, air resistance, conservation of energy, states that the total mechanical energy of the block is constant as it falls. At the starting high to 5 m, the block only has potential energy equal to 2000 J. Because the kinetic energy at this point is 0 J, the total mechanical energy is 2000 J at any point during the blocks descent.
MCAT mastery work and energy page 52 question 6
This question is bookmarked because it seeming counterintuitive. Perhaps this is one we could ask KC.
I’m getting confused about two things:
First. The signs of the acceleration it’s accelerating up 2 m/s squared, and down 10 m/s squared. Where do I count for these in the equation?
Second. If it’s accelerating upward at 2 m/s squared, why would that cause an increase in effort? If it weren’t accelerating, the effort would calculate to 50 N.
It makes sense how the books solved the problem. The net force is on the object are 2T - mg. Fnet=ma and acceleration is 2 m/s squared.
MCAT mastery work and energy page 52 question 7
Air resistance is a non-conservative force as it dissipates mechanical energy.
Friction is a nonconservative force as it dissipates mechanical energy.
Gravity is a conservative force because it is pathway independent and does not dissipate mechanical energy.
Convection is a non-conservative force (it is a measure of heat transfer)
MCAT mastery work and energy page 52 question 8
MCAT mastery work and energy page 53 question 9
MCAT mastery work and energy page 52 question 3
The work done by the engine is equal to the change in kinetic energy of the car.
We needed to use Long division to find out 900÷6, make sure we know how to do that well.
Be careful to follow the units.
MCAT mastery work and energy page 52 question 5
MCAT mastery work and energy page 53 question 10
MCAT mastery work and energy page 53 question 11
A couple things about this question.
You would think since Josh is heavier, and has more potential energy, he would gain more of velocity than Sarah who is lighter. However this is not the case, as you can see by the calculations I made of potential energy of Josh and kinetic energy of Josh versus potential energy of Sarah and kinetic energy of Sarah. They will both have a velocity of 20 m/s when they hit the net, and will therefore bounce to the same height. It would be handy to remember this for questions like this as the math gets easier when we cancel out the mass to try to calculate for velocity, knowing the height of an object.
Josh will experience a greater force upon impact because the net exerts a force proportional to the weight: the higher the weight, the larger the force exerted by the net.
The correct answer is A.
MCAT mastery work and energy page 53 question 12
MCAT mastery work and energy page 53 question 13
MCAT mastery work and energy page 53 question 14
MCAT mastery work and energy page 53 question 15
This is a tricky question. I suppose with unlimited fuel and unlimited time and ignoring non-conservative forces, the vehicles would have unlimited velocities.
Equations and units we need to be familiar with four for chapter 2: work in energy
