# 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.