Work and energy
48 flashcards covering Work and energy for the MCAT Chem / Phys / Psych / Soc section.
Work and energy are fundamental concepts in physics that describe how forces cause motion and transformations in systems. Work occurs when a force moves an object over a distance, essentially transferring energy from one form to another. Energy, on the other hand, is the capacity to perform work and comes in various types, such as kinetic energy (related to an object's motion) and potential energy (stored due to position or configuration). Together, they help explain everyday phenomena like a ball rolling downhill or a car accelerating.
On the MCAT, work and energy typically appear in the Chemical and Physical Foundations section, often through multiple-choice questions involving calculations, conceptual applications, or problem-solving scenarios. Common traps include confusing work with net force or overlooking energy conservation in systems with friction. Focus on key principles like the work-energy theorem, which links net work to changes in kinetic energy, and practice applying formulas for different energy forms. Mastering these will help tackle passages on mechanics and thermodynamics.
Remember to always draw free-body diagrams for work problems.
Terms (48)
- 01
Work
Work is the transfer of energy that occurs when a force causes an object to move in the direction of the force, calculated as the product of the force, the displacement, and the cosine of the angle between them.
- 02
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, given by the formula KE = (1/2)mv², where m is mass and v is velocity.
- 03
Gravitational Potential Energy
Gravitational potential energy is the energy an object has due to its position in a gravitational field, calculated as PE = mgh, where m is mass, g is acceleration due to gravity, and h is height above a reference level.
- 04
Elastic Potential Energy
Elastic potential energy is the energy stored in a stretched or compressed elastic object, such as a spring, given by PE = (1/2)kx², where k is the spring constant and x is the displacement from equilibrium.
- 05
Work-Energy Theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, meaning Wnet = ΔKE.
- 06
Conservation of Mechanical Energy
Conservation of mechanical energy holds that in the absence of non-conservative forces, the total mechanical energy of a system, which is the sum of kinetic and potential energy, remains constant.
- 07
Power
Power is the rate at which work is done or energy is transferred, calculated as P = W/t or P = Fv for constant force and velocity, where W is work, t is time, F is force, and v is velocity.
- 08
Conservative Force
A conservative force is one that does work independently of the path taken, such as gravity or a spring force, and the work done can be recovered as potential energy.
- 09
Non-Conservative Force
A non-conservative force, like friction, depends on the path taken and dissipates energy, often as heat, so the work done is not recoverable.
- 10
Hooke's Law
Hooke's Law describes the force exerted by a spring, stating that the force is proportional to the displacement from equilibrium, given by F = -kx, where k is the spring constant and x is the displacement.
- 11
Net Work
Net work is the sum of all work done by all forces acting on an object, which equals the change in its kinetic energy according to the work-energy theorem.
- 12
Positive Work
Positive work occurs when the force and displacement are in the same direction, resulting in an increase in the object's kinetic energy.
- 13
Negative Work
Negative work happens when the force and displacement are in opposite directions, such as friction opposing motion, leading to a decrease in kinetic energy.
- 14
Zero Work
Zero work is done when the force is perpendicular to the displacement, like the normal force on a horizontal surface, so no energy is transferred.
- 15
Work Done by Gravity
Work done by gravity is the energy transferred due to gravitational force, which is zero for horizontal motion and negative when an object falls, converting potential energy to kinetic energy.
- 16
Work Done by Friction
Work done by friction is always negative because it opposes motion, converting mechanical energy into thermal energy and reducing the object's kinetic energy.
- 17
Efficiency
Efficiency is the ratio of useful work output to total energy input, often expressed as a percentage, and it highlights energy losses due to non-conservative forces.
- 18
Total Mechanical Energy
Total mechanical energy is the sum of an object's kinetic and potential energy, and in isolated systems with conservative forces, it remains constant.
- 19
Energy Transformation
Energy transformation is the process by which one form of energy, such as potential energy, converts to another, like kinetic energy, as in a falling object.
- 20
Joule
A joule is the SI unit of work and energy, equivalent to one newton-meter, representing the energy transferred when a force of one newton acts over a distance of one meter.
- 21
Watt
A watt is the SI unit of power, equal to one joule per second, measuring the rate at which energy is transferred or work is done.
- 22
Work Formula
The formula for work is W = Fd cosθ, where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
- 23
Kinetic Energy Formula
The formula for kinetic energy is KE = (1/2)mv², used to calculate the energy of an object based on its mass and speed.
- 24
Gravitational Potential Energy Formula
The formula for gravitational potential energy is PE = mgh, applied to objects near Earth's surface to determine energy based on height.
- 25
Spring Constant
The spring constant is a measure of a spring's stiffness, denoted by k in Hooke's Law, and determines how much force is needed to stretch or compress the spring.
- 26
Common Trap: Forgetting the Angle
A common error in work calculations is neglecting the angle between force and displacement, which must be included as cosθ in the formula to get accurate results.
- 27
Strategy for Energy Conservation Problems
To solve energy conservation problems, set the total initial mechanical energy equal to the total final mechanical energy and solve for unknowns, accounting for any non-conservative forces.
- 28
Work on an Incline
Work on an incline involves calculating the component of the force parallel to the displacement, such as gravity's component along the slope, to find energy changes.
- 29
Example: Work Lifting an Object
In lifting an object at constant speed, the work done by the lifting force equals the increase in gravitational potential energy, calculated as mgh.
- 30
Power in Electrical Contexts
Power in electrical systems is the rate of energy transfer, given by P = VI, where V is voltage and I is current, relating to mechanical work through energy conversion.
- 31
Internal Energy
Internal energy is the total energy within a system due to the kinetic and potential energies of its molecules, which can change through work and heat transfer.
- 32
First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy of a system equals the heat added minus the work done by the system, linking work and energy in thermal processes.
- 33
Heat as Energy Transfer
Heat is the transfer of thermal energy between systems due to temperature differences, often resulting from work done by non-conservative forces like friction.
- 34
Adiabatic Process
An adiabatic process is one where no heat is exchanged with the surroundings, so any change in internal energy is due solely to work done on or by the system.
- 35
Isothermal Process
An isothermal process occurs at constant temperature, meaning the internal energy of an ideal gas remains constant, with heat added equaling work done.
- 36
Work in PV Diagrams
In PV diagrams, work is the area under the curve representing the process, calculated as the integral of PdV for a gas expanding or compressing.
- 37
Thermal Energy
Thermal energy is the kinetic energy of random molecular motion within a substance, which can be increased by work done on the system or heat transfer.
- 38
Common Trap: Confusing Work and Power
A frequent mistake is equating work and power, but power is the time rate of work, so always check units and context when solving problems.
- 39
Strategy for Calculating Power
To calculate power, determine the work done and divide by time, or use force and velocity if applicable, ensuring consistent units like watts.
- 40
Example: Power of a Motor
For a motor lifting a 50 kg object at 2 m/s, power is calculated as the force times velocity, equating to the rate of increase in potential energy.
- 41
Conservation of Energy in Collisions
In elastic collisions, total kinetic energy is conserved, while in inelastic collisions, it is not, though total energy is always conserved when accounting for other forms.
- 42
Potential Energy in Electric Fields
Potential energy in electric fields is the energy of a charged particle due to its position, similar to gravitational potential energy but based on electric potential.
- 43
Work by Variable Force
Work by a variable force is calculated using integration, such as the area under a force-displacement graph, to find the total energy transferred.
- 44
Energy Density
Energy density is the amount of energy stored per unit volume, relevant for systems like capacitors or springs, helping compare energy storage efficiency.
- 45
Dissipative Forces
Dissipative forces, like air resistance, convert mechanical energy into thermal energy, reducing the total mechanical energy of the system.
- 46
Roller Coaster Energy
In a roller coaster, energy conservation shows how potential energy at the top converts to kinetic energy at the bottom, minus losses from friction.
- 47
Work-Energy Bar Charts
Work-energy bar charts visually represent the energy forms before and after an event, helping track conservation and identify where work is done.
- 48
Instantaneous Power
Instantaneous power is the power at a specific moment, calculated as P = Fv at that instant, useful for varying speed scenarios.