MCAT Physics and Math Review
Chapter 2: Work and Energy
The conceptualization of energy as the capacity to do something or make something happen is a very broad definition. However, such an all-encompassing definition allows us to understand everything from pushing a rock up a hill to melting an ice cube, from stopping a car at an intersection to harnessing the energy of biomolecules in metabolism, to all be forms of energy transfer. Indeed, energy on its own has little significance without considering the transference of energy, either through work or heat. The work–energy theorem is a powerful expression that will guide our approach to many problems in the Chemical and Physical Foundations of Biological Systems section. We also covered the application of energy and work with simple machines, such as levers, inclined planes, and pulleys. These devices assist us in accomplishing work by reducing the forces necessary for displacing objects.
Preparing for the MCAT is hard (mental) work, but you are well on your way to achieving success on Test Day. This MCAT Physics and Math Review book (and all the materials provided in your Kaplan program) is part of a set of tools—your simple machines, if you will—that will provide you with the mechanical advantage to ease your efforts toward a higher score.
· Energy is the property of a system that enables it to do something or make something happen, including the capacity to do work. The SI units for all forms of energy are joules (J).
· Kinetic energy is energy associated with the movement of objects. It depends on mass and speed squared (not velocity).
· Potential energy is energy stored within a system. It exists in gravitational, elastic, electric, and chemical forms.
o Gravitational potential energy is related to the mass of an object and its height above a zero-point, called a datum.
o Elastic potential energy is related to the spring constant (a measure of the stiffness of a spring) and the degree of stretch or compression of a spring squared.
o Electrical potential energy exists between charged particles.
o Chemical potential energy is the energy stored in the bonds of compounds.
· The total mechanical energy of a system is the sum of its kinetic and potential energies.
· Conservative forces are path independent and do not dissipate the mechanical energy of a system.
o If only conservative forces are acting on an object, the total mechanical energy is conserved.
o Examples of conservative forces include gravity and electrostatic forces. Elastic forces, such as those created by springs, are nearly conservative.
· Nonconservative forces are path dependent and cause dissipation of mechanical energy from a system.
o While total energy is conserved, some mechanical energy is lost as thermal or chemical energy.
o Examples of nonconservative forces include friction, air resistance and viscous drag.
· Work is a process by which energy is transferred from one system to another.
o Work may be expressed as the dot product of force and displacement, or the product of force and distance traveled with the cosine of the angle between the two.
o Work may also be expressed as the area under a pressure–volume (P–V) curve.
· Power is the rate at which work is done or energy is transferred. The SI unit for power is the watt (W).
· The work–energy theorem states that when net work is done on or by a system, the system’s kinetic energy will change by the same amount. In more general applications, the work done on or by a system can be transferred to other forms of energy as well.
· Mechanical advantage is the factor by which a simple machine multiplies the input force to accomplish work.
· The six simple machines are the inclined plane, wedge, wheel and axle, lever, pulley, and screw. Simple machines provide the benefit of mechanical advantage.
· Mechanical advantage makes it easier to accomplish a given amount of work because the input force necessary to accomplish the work is reduced; the distance through which the reduced input force must be applied, however, is increased by the same factor (assuming 100% efficiency).
· The load is the output force of a simple machine, which acts over a given load distance to determine the work output of the simple machine. The effort is the input force of a simple machine, which acts over a given effort distance to determine the work input of the simple machine.
· Efficiency is the ratio of the machine’s work output to work input when nonconservative forces are taken into account.
Answers to Concept Checks
1. Kinetic energy is the energy of motion. It is related to the mass of an object as well as its speed squared.
Potential energy is energy associated with a given position or intrinsic property of a system; it is stored in gravitational, electrical, elastic, or chemical forms. Gravitational potential energy is directly related to the mass of the object and its height above a reference point.
What happens to total mechanical energy of the system?
Decreases (energy is dissipated)
Does the path taken matter?
Yes; more energy is dissipated with a longer path
What are some examples?
Elastic forces (approximately conservative)
1. The unit of work is the joule, which is also the unit for energy. Work and energy are related concepts. By performing work, the energy of a system is changed. Work, along with heat, is a form of energy transfer.
2. Three methods for calculating work discussed in this chapter are:
1. W = Fd cos θ (the dot product of the force and displacement vectors)
2. W = PΔV (the area under a pressure–volume curve)
3. Wnet = ΔK (the work–energy theorem)
1. As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving the object the same displacement) decreases.
2. As the effort (required force) decreases in a pulley system, the effort distance increases to generate the same amount of work.
3. The decrease in work output is due to nonconservative or external forces that generate or dissipate energy.
4. When a device provides mechanical advantage, it decreases the input force required to generate a particular output force. Generally, this is accomplished at the expense of increased distance over which the force must act.
5. The six simple machines are: inclined plane, wedge, wheel and axle, lever, pulley, and screw.
Equations to Remember
(2.1) Kinetic energy:
(2.2) Gravitational potential energy: U = mgh
(2.3) Elastic potential energy:
(2.4) Total mechanical energy: E = U + K
(2.5) Conservation of mechanical energy: ΔE = ΔU + ΔK = 0
(2.6) Work done by nonconservative forces: Wnonconservative = ΔE = ΔU + ΔK
(2.7) Definition of work (mechanical): W = F · d = Fd cos θ
(2.8) Definition of work (isobaric gas–piston system): W = PΔV
(2.9) Definition of power:
(2.10) Work–Energy theorem: Wnet = ΔK = Kf – Ki
(2.11) Mechanical advantage:
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o DNA and Biotechnology
· Biochemistry Chapter 9
o Carbohydrate Metabolism I
· Biochemistry Chapter 12
o Bioenergetics and Regulation of Metabolism
· General Chemistry Chapter 7
· Physics and Math Chapter 1
o Kinematics and Dynamics
· Physics and Math Chapter 3