Chapter 3: Work, Energy, and Momentum

Question 1

Energy

Answer 1

• defined as the capacity of a physical system to do work
• a property or characteristic of a system to do something or make something happen; different forms of energy have the capacities to do different things

Question 2

Kinetic energy

Answer 2

• energy of motion
• equation:
  KE = (1/2) mv^2
• units = Joule (1J = kgm^2/s^2)

Question 3

Potential energy

Answer 3

• an object with mass has potential energy when it has the potential to do something
• many different types of potential energy (gravitational, electrostatic, mechanical, chemical, etc.)
• gravitational potential energy: depends on a body’s position with respect to some level identified as the “ground”, or the zero potential energy position
• equation
  PE = mgh
• units = Joule

Question 4

Total Mechanical Energy

Answer 4

• the sum of an object’s potential and kinetic energies is the object’s total mechanical energy
  E = PE + KE
• first law of thermodynamics: energy is never created or destroyed, merely transferred from one system to another; this does not imply that E will remain constant because the equation does not account for all types of energy

Question 5

Conservation of mechanical energy

Answer 5

• when there are no non-conservative forces acting on the system:
  ∆E = ∆PE + ∆KE = 0
• when there are non-conservative forces acting on the system:
  W’ = ∆E = ∆PE + ∆KE
  W’ is the work done by the non-conservative forces only

Question 6

Two ways to determine whether a force is conservative

Answer 6

(1) If the net work done to move a particle in any round-trip path is zero, the force is conservative
(2) If the net work needed to move a particle between two points is the same regardless of the path taken, the force is conservative

Question 7

Work (definition)

Answer 7

• a process by which energy is transferred from one system to another
• unit = Joule

Question 8

Calculating work

Answer 8

• Energy is transferred through the process of work when something exerts a force on or against something else
  W = Fdcosø

Question 9

Calculating Power

Answer 9

• Power is the rate at which energy is transferred from one system to another
  P = W/∆t
• Unit = Watt (1W = 1J/s)

Question 10

Work-Energy theorem

Answer 10

• expression of the relationship between work and kinetic energy
  W(net) = ∆KE = KE(f) - KE(i)

Question 11

Momentum

Answer 11

• quality of object’s in motion
• product of an object’s mass and velocity
• vector quantity
  p = mv
• Units = kgm/s

Question 12

Impulse

Answer 12

• Change in an object’s momentum
  J = F∆t = ∆p = mv(f) - mv(i)
• given a particular change in momentum, the longer the period of time through which the impulse is achieved, the smaller the force necessary to achieve the impulse

Question 13

Conservation of momentum

Answer 13

Momentum is conserved in situations where there are no external forces acting on the system, or if there are external forces acting on the system, the vector sum of these external forces is zero

Question 14

Collisions

Answer 14

• Completely elastic collisions: momentum and kinetic energy are conserved
  m(a)v(ai) + m(b)v(bi) = m(a)v(af) + m(b)v(bf)
  0.5m(a)v(ai)^2 + 0.5m(b)v(bi)^2 = 0.5m(a)v(af)^2 + 0.5m(b)v(bf)^2
• Inelastic collisions: momentum is conserved, but kinetic energy is lost
  m(a)v(ai) + m(b)v(bi) = m(a)v(af) + m(b)v(bf)
  0.5m(a)v(ai)^2 + 0.5m(b)v(bi)^2 > 0.5m(a)v(af)^2 + 0.5m(b)v(bf)^2
• Completely inelastic collisions: momentum is conserved, but kinetic energy is lost AND the objects stick together and move as one
  m(a)v(ai) + m(b)v(bi) = m(a+b)v(f)
  0.5m(a)v(ai)^2 + 0.5m(b)v(bi)^2 > 0.5m(a)v(af)^2 + 0.5m(b)v(bf)^2

Question 15

Mechanical advantage

Answer 15

• inclined plane, wedge, axle and wheel, lever, pulley, screw
• the same work is accomplished through a decreased applied force over a greater distance over which force is applied

Question 16

Efficiency

Answer 16

Efficiency = W(out)/W(in) = [(load)(load distance)]/[(effort)(effort distance)]

Question 17

Center of mass

Answer 17

• the point within any two- or three-dimensional object at which the entire object’s mass could be represented as a single point

X = [m(1)x(1) + m(2)x(2) + m(3)x(3) + ...]/[m(1) + m(2) + m(3) + ...]
Y = [m(1)y(1) + m(2)y(2) + m(3)y(3) + ...]/[m(1) + m(2) + m(3) + ...]
Z = [m(1)z(1) + m(2)z(2) + m(3)z(3) + ...]/[m(1) + m(2) + m(3) + ...]