Conservation of Mechanical Energy

• Momentum:

  • Mass in motion
  • Inertia in motion
  • Amount of an object’s momentum is dependent on two variables: 1. Amount in the mass of the object that's moving. 2. Speed or velocity of the moving object.
• Impulse:

  • The force acted upon an object in a specific given time.
  • It is mathematically expressed as I = F * t.
• The Conservation of Momentum: Impulse is the change in momentum.
• Mechanical energy:

  • The energy acquired by an object upon which work is done.
  • It is also the energy possessed by an object due to its motion or due to its position. Can be either kinetic energy or potential energy.
  • Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position.
• The conservation of mechanical energy:

  • Mechanical energy is the total of the potential and kinetic energies in a system. It states that the total mechanical energy in a system remains constant as long as the only forces acting on it are conservative forces.
• Potential energy – stored energy; having the potential to do mechanical work.

  1. Various forms of potential energy:

  • Gravitational Potential Energy (GPE)
  • Elastic Potential Energy (EPE)
• Kinetic Energy – the energy of motion
• Identify whether: "KE", "PE", "Work"

  A) PE

  B) KE

  C) Work

  
• The total amount of mechanical energy is the sum of the PE and KE. The sum is simply referred to as the total mechanical energy or TME. Mathematically described as, TME = KE + PE.
• Formulas (Ans. always in Joules/J):

  • KE = 1/2 mv^2
  • PE = mgh
  • TME = KE + PE

  Where:

  • m = mass
  • v = velocity
  • g = gravity (9.8m/s^2)
  • h = height
• The total mechanical energy of a 20kg falling object is 500J. If its speed

  is 6m/s, what is its potential energy? g = 9.8m/s²

  GIVEN:

  • m = 20 kg
  • v = 6 m/s
  • TME = 500 J

  REQUIRED:

  • PE

  EQUATION:

  • TME - KE = PE

  SOLUTION:

  • 500 − 1/2 mv² = PE
  • 500 - 1/2 (20)(6)² = PE
  • 500 - 360 = PE

  ANSWER:

  • PE = 140 J
• What is the total mechanical energy (TME) of a 1000kg motorcycle

  resting on the top of a 10m hill? g = 9.8m/s²

  GIVEN:

  • m = 1000kg
  • h = 10 m
  • g = 9.8m/s²

  REQUIRED:

  • TME

  EQUATION:

  • TME = KE + PE

  SOLUTION:

  • TME = 1/2 mv² + mgh
  • TME = 1/2 (1000kg)(0 m/s)² + (1000kg)(9.8m/s²)(10 m)
  • TME = 0 + 98000

  ANSWER:

  • TME = 98000 J
• What is the kinetic energy of an airplane with a total mass of 50,000kg

  that is moving at a velocity of 250m/s?

  GIVEN:

  • m = 50000kg
  • v = 250m/s

  REQUIRED:

  • KE

  EQUATION:

  • KE = 1/2 mv²

  SOLUTION:

  • KE = 1/2 (50000kg)(250m/s)²
  • KE = 1/2 (3,125,000,000)

  ANSWER:

  • 1,562,500,000 J
• A 50 kg gorilla is sitting on the limb of a tree 4 meters above the ground.

  What is the potential energy of the gorilla?

  GIVEN:

  • m = 50 kg
  • h = 4 meters

  REQUIRED:

  • PE

  EQUATION:

  • PE = mgh

  SOLUTION:

  • PE = (50kg)(9.8m/s²)(4m)

  ANSWER:

  • PE = 1960 J