Work, Energy, and Power

Question 1

Energy

Answer 1

Ability to do work

• Different forms of energy as there are different types of forces
  
  • Kinetic energy (E.g. train)
  • Gravitational energy (E.g. meteor)
  • Elastic energy (E.g. rubber band)
  • Thermal energy (E.g. oven)
  • Radiant energy (E.g. sunlight)
  • Electrical energy (E.g. lamp)
  • Nuclear energy (nuclear power plants)
  • Mass energy (E= mc²)
• Energy can come into a system or leave it via various interactions that produce changes

Question 2

Force, Work, Energy

Answer 2

• Force acts as agent of change
• Energy acts as measure of change
• Work acts the way of transferring energy from one system to another

Question 3

Law of Conservation of Energy

Answer 3

Total amount of energy in a given process will stay constant- it will be conserved

• Equivalent to the first law of thermodynamics
• Energy cannot be created or destroyed; it can only be transferred (from one system to another) or transformed (from one form to another)
  
  • E.G. electrical energy can be converted into light and heat (lightbulb)

Question 4

Work

Answer 4

The application of force over a distance and the resulting change in energy of the system give rise to the concept of work

• If a constant foce F acts over a distance d, and F is parallel to d, then the work done by F is the product of force and distance
  
  • If a constant force F acts over a distance d, and θ is the angle between F and d, then the work done by F is the product of the component of force in the direction of the motion and the distance
    
    • W= Fdcosθ
      
      • W= Fdcosθ only works when the force does not change as the object moves
• Although work depends on two vectors (F and d, where d points in the direction of the motion), work itself is not a vector
  
  • Work is a scalar quantitiy

Question 5

Antiparallel

Answer 5

Angle of 180^o

Question 6

Values of Work

Answer 6

• Work may be positive, negative, or zero
• If θ is less than 90^o, then the work is positive
  
  • cosθ is positive in this case
• If θ= 90^o then work is zero
  
  • cos90^o= 0
• If θ is greater than 90^o, then the work is negative
  
  • cosθ is negative in this case
• If a force helps the motion, then the work done by the force is positive
  
  • If the force opposes the motion then the work done by the force is negative

Question 7

Breaking force into components F_⟂ and F_||

Answer 7

F_⟂ is the component perpendicular to the direction of the motion

F_|| is the component in the direction of the motion (or opposite if it is negative)

W= F_||d

• Used for situations where θ is something other than 0^o, 90^o, or 190^o

Question 8

Work Done by Variable Force

Answer 8

• If force remains constant over the distance through which it acts, then the work done by the force is the just the product of force and distance
  
  • If force doesn’t remain constant, then the work done by the force can be calculated through integrated area

Question 9

Kinetic Energy

Answer 9

The energy an object posseses by virtue of its motion is therefore defined as 1/2mv² and is called kinetic energy: K= 1/2mv²

• Force acting on an object from rest causing it to acclerate, work done by force: W= 1/2mv²
  
  • The work done on the object has transferred energy to it, in the amount 1/2mv²
• Stopping an object means changing its kinetic energy to 0
• Kinetic ernegy, like work, is a scalar quantitiy

Question 10

The Work-Energy Theorem

Answer 10

The total work done on an object- the work done by the net force- is equal to the object’s change in kinetic energy

W_total= ΔK

Question 11

Kinematics Vs. Work-Kinetic Energy

Answer 11

For objects moving in a straight line with a constant force, you can use the work-kinetic energy theorem or kinematic equations for problems where time is not involved

Question 12

Potential Energy

Answer 12

Independent of motion and arises from the object’s position; energy an object or system has by virtue of its position

• Sybmolized by U or PE
• Work was done to put an object at its given position (E.g. ball placed at a top of a table)
  
  • Work is a means of transferring energy, energy was stored and can be retrieved as kinetic energy
• When an object falls, gravity does positive work, giving the object kinetic energy
• Kinetic energy comes from a “storehouse” of energy, this energy is called potential energy
• As there are different types of forces there are different types of potential energy

Question 13

Gravitational Potential Energy

Answer 13

Energy stored by virtue of an object’s position in a gravitational field

• Symbolized by U_grav
• Energy can be converted to kinetic energy as gravity pulls object to ground/floor
• W_{by gravity}= -mgh
• ΔU_grav= -W_{by gravity}
• E.G. a ball resting on a tabletop, gravity “did work” of -mgh to place ball on tabletop storing potential energy, as ball falls to the floor the change of potential energy as energy is converted to kinetic energy
• Increase in an object’s gravitational potential energy as a raised height can be found by
  
  • ΔU_grav= mgh

Question 14

Conservative Force

Answer 14

Gravity is said to be a conservative force

• Work done by gravity as the object is raised does not depend on the path taken by the object, the ball could be lifted straight upward or a curved path, it will make no difference

Question 15

Gravitational Potential Energy General Equation

Answer 15

W_{by grav}= GMm(1/r₂ - 1/r₁)

since ΔU_grav= -W_{by grav}

U₂ - U₁= -GMm(1/r₂ - 1/r₁)

U= 0 at reference level as r₂ approaches infinity

• U= -GMm/r
  
  • According to this equation, the gravitational potential energy is always negative, meaning energy has to be added to bring an object (mass m) bound to the gravitational field of M to a point very far from M, at which U= 0

Question 16

Mechanical Energy

Answer 16

The mechanical energy, E, is the sum of the kinetic energy, K, and the potential energy, U

E= K + U

Question 17

Conservation of Mechanical Energy

Answer 17

Assuming no nonconservative forces (E.G. friction) act on an object or a system as it undergoes some change, mechanical energy is conserved

• The intial mechanical energy, E_i, is equal to the final mechanical energy E_f
  
  • K_i + U_i= K_f + U_f
• Shorthand conservation of mechanical energy formula:
  
  • v= Radical(2gh)

Question 18

Escape Speed

Answer 18

Speed needed in order to escape Earth’s gravitational field

Question 19

Shorthand Formula For When a Nonconservative Force Does Work

Answer 19

W_total= ΔK

• Work done by gravity replaces the change in potential energy

Question 20

Power

Answer 20

Rate at which work is done (or energy is transferred, which is the same thing)

• Power= Work/time
  
  • P= W/t
• Unit of power is joule per second (J/s)
  
  • Renamed the watt and symbolized W (not to be confused with the symbol for work, W)
  • One Watt is 1 joule per second: 1 W= 1 J/s
• E.G. two machines doing the same amount of total work, but one doing the work in less time is considered more powerful