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Topic 2. Work, Energy, Power, Momentum. Constant force and work. The force shown is a constant force. W = F s can be used to calculate the work done by this force when it moves an object from s a to s b .

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topic 2

Topic 2

Work, Energy, Power,


constant force and work
Constant force and work
  • The force shown is a constant force.
  • W = Fs can be used to calculate the work done by this force when it moves an object from sa to sb.
  • The area under the curve from sa to sb can also be used to calculate the work done by the force when it moves an object from sa to sb





variable force and work



Variable force and work
  • The force shown is a variable force.
  • W = Fs CANNOT be used to calculate the work done by this force!
  • The area under the curve from sa to sb can STILL be used to calculate the work done by the force when it moves an object from sa to sb



sample problem
Sample Problem
  • How much work is done by the force shown when it acts on an object and pushes it from x = 2.0 m to x = 4.0 m?
work and energy
Work and Energy
  • Work changes mechanical energy!
  • If an applied force does positive work on a system, it tries to increase mechanical energy.
  • If an applied force does negative work, it tries to decrease mechanical energy.
  • The two forms of mechanical energy are called potential and kinetic energy.
kinetic energy
Kinetic Energy
  • Energy due to motion
  • K = ½ m v2
    • K: Kinetic Energy
    • m: mass in kg
    • v: speed in m/s
  • Unit: Joules
the work energy theorem
The Work-Energy Theorem
  • The net work due to all forces equals the change in the kinetic energy of a system.
  • Wnet = DK
    • Wnet: work due to all forces acting on an object
    • DK: change in kinetic energy (Kf – Ki)
  • Power is the rate of which work is done.
  • P = W/Dt
    • W: work in Joules
    • Dt: elapsed time in seconds
  • When we run upstairs, t is small so P is big.
  • When we walk upstairs, t is large so P is small.
unit of power
Unit of Power
  • SI unit for Power is the Watt.
    • 1 Watt = 1 Joule/s
    • Named after the Scottish engineer James Watt (1776-1819) who perfected the steam engine.
  • British system
    • horsepower
    • 1 hp = 746 W
how we buy energy
How We Buy Energy…
  • The kilowatt-hour is a commonly used unit by the electrical power company.
  • Power companies charge you by the kilowatt-hour (kWh), but this not power, it is really energy consumed.
  • 1 kW = 1000 W
  • 1 h = 3600 s
  • 1 kWh = 1000J/s • 3600s = 3.6 x 106J
potential energy
Potential energy
  • Energy of position or configuration
  • “Stored” energy
  • For gravity: PE = mgh
    • m: mass
    • g: acceleration due to gravity
    • h: height above the “zero” point
  • For springs: PE = ½ k x2
    • k: spring force constant
    • x: displacement from equilibrium position
law of conservation of energy
Law of Conservation of Energy
  • In any isolated system, the total energy remains constant.
  • Energy can neither be created nor destroyed, but can only be transformed from one type of energy to another.
law of conservation of mechanical energy
Law of Conservation of Mechanical Energy
  • E = KE + PE = Constant
    • K: Kinetic Energy (1/2 mv2)
    • U: Potential Energy (gravity or spring)
  • E = KE + PE = 0
    • K: Change in kinetic energy
    • U: Change in gravitational or spring potential energy
  • Momentum is a measure of how hard it is to stop or turn a moving object.
  • Momentum is related to both mass and velocity.
  • Momentum is possessed by all moving objects.
momentum in terms of 2 nd law
Momentum in terms of 2nd Law
  • Therate of change of momentum of a bodyisproportionaltotheresultantforce and occurs in thedirection of theforce.
  • F = Δp / Δt.
calculating momentum
Calculating Momentum
  • For one particle

p = mv

  • For a system of multiple particles

P = pi = mivi

  • Momentum is a vector with the same direction as the velocity vector.
  • The unit of momentum is…

kg m/s or Ns

impulse j
Impulse (J)
  • Impulse is the product of an external force and time, which results in a change in momentum of a particle or system.
  • J = F t
  • J = P
  • Units: N s or kg m/s(same as momentum)
impulse j on a graph
Impulse (J) on a graph




area under curve








t (ms)

sample problem1
Sample Problem


  • This force acts on a 1.2 kg object moving at 120.0 m/s. The direction of the force is aligned with the velocity. What is the new velocity of the object?








law of conservation of momentum
Law of Conservation of Momentum
  • If the resultant external force on a system is zero, then the vector sum of the momentums of the objects will remain constant.
  • SPbefore = SPafter
  • When an object separates suddenly, as in an explosion, all forces are internal.
  • Momentum is therefore conserved in an explosion.
  • There is also an increase in kinetic energy in an explosion. This comes from a potential energy decrease due to chemical combustion.
  • Guns and cannons “recoil” when fired.
  • This means the gun or cannon must move backward as it propels the projectile forward.
  • The recoil is the result of action-reaction force pairs, and is entirely due to internal forces.
  • As the gases from the gunpowder explosion expand, they push the projectile forwards and the gun or cannon backwards.
collision types
Collision Types
  • Elastic collisions
    • No deformation occurs, no kinetic energy lost
  • Inelastic collisions
    • Deformation occurs, kinetic energy is lost
  • Perfectly Inelastic (stick together)
    • Objects stick together and become one object
    • Deformation occurs, kinetic energy is lost