SPH4U Grade 12 Physics Energy and Momentum Test

Work done by a constant force

  • Work is the energy transferred to an object when a force acting on the object moves it through a distance.

W = (F cos θ) Δd

    • If the force is causing an object to undergo a displacment is at an angle to the displacement, only the component of the force in the direction of the displacement does work on the object.
  • Joule: (J) a unit used to measure energy. 1 Joule is equal to 1 N / m displaced.
  • Under certain conditions, zero work is done on an object even if the object experiences an applied force or is in motion.


Kinetic Energy and the work-energy theorem

  • Kinetic Energy: Ek is the energy of kinetic motion. A scalar quantity measured in (J)

Ek = 0.5mv2


  • Work-Energy Theorem: The total work done on an object equals the change in the object’s kinetic energy, provided there is no change in any other form of energy.

Wtotal = 1/2mvf2 – 1/2mvi2

= Ekf – Eki

Wtotal = ΔEk

Gravitational Potential Energy at Earth’s Surface

  • Gravitational Potential Energy: the energy due to the elevation above earth’s surface

Eg = mgh or Eg = mg Δy

    • Positive values of y show displacement upwards.
  • Gravitational potential energy is always stated relative to a reference level

The Law of Conservational Energy

  • For an isolated system, energy can be converted into different forms, but cannot be created or destroyed.
  • Isolated System: a system of particles that is completely isolated from outside influences
  • Thermal Energy: internal energy associated with the motion of atoms and molecules

Eth = Fk * d

  • The work done on a moving object by kinetic friction into thermal energy
  • Mechanical Energy: total energy in an isolated system


Elastic Potential Energy and Simple Harmonic Motion

  • Hooke’s Law: the magnitude of the force exerted by a spring is directly proportional to the distance the spring has moved from equilibrium

Fx = -k * x

    • k is the force constant the spring creates
    • If x is negative, then the equation represents force exerted by the spring
    • If x is positive, then the equation represents force exerted to a spring
  • Ideal Spring: a spring that obeys Hooke’s Law because it experiences no internal or external friction
  • Elastic Potential Energy: the energy stored in an object that is stretched, compressed, bent, or twisted.

Ee = 1/2 kx2

  • Simple Harmonic Motion: (SHM) periodic vibratory motion in which the force and acceleration is proportional to the displacement
    • Friction is negligible in SHM. The vibration goes on indefinitely.

T = 2 pi root (m/k)    Period

f = 1/2pi root (k/m)      Frequency

  • Energy in simple harmonic motion shows that when energy is released from a spring, it transforms into kinetic energy.

Et = 1/2 kx2 + 1/2 mv2

    • k is the force constant
    • x is the displacement of mass from equilibrium position
    • v is the instantaneous velocity of the mass
  • Damped Harmonic Motion: periodic motion which amplitude of vibration and the energy decreases over time due to friction.

Momentum and Impulse

  • Linear Momentum: the product of the mass of a moving object and its velocity; a vector quantity. Unit is kg*m/s

p = m*v

  • Impulse: the change in momentum. Vector quantity in N*s.

I = Sum of all Forces * time

  • In a force vs time graph, Impulse is the area under the graph


Conservation of momentum in one dimension

  • If the net force acting on a system of interacting objects is zero, then the linear momentum of the system before the interaction equals the linear momentum of the system after the interaction.

Δp1 = Δp1

m1Δv1 = m2Δv2


Conservation of momentum in one dimension

  • Elastic Collision: a collision in which the total kinetic energy after the collision equals the total kinetic energy before the collision
    • Ek = Ek’
    • p = p’
  • Inelastic Collision: a collision in which the total kinetic energy after the collision is different from the total kinetic energy before the collision
    • p = p’
  • Completely Inelastic Collision: a collision where there is a maximum decrease in kinetic energy after the collision since the objects stick together and move at the same velocity

mAΔvA + mBΔvB = (mA + mB) vB

  • In some 2 D collisions, it would be more efficient if the vectors were broken into vector components before solving.