**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 = 0.5mv^{2}

**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.

W_{total} = 1/2mv_{f}^{2} – 1/2mv_{i}^{2}

= Ek_{f} – Ek_{i}

W_{total} = 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

E_{th} = F_{k} * 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

F_{x} = -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.

E_{e} = 1/2 kx^{2}

**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.

E_{t} = 1/2 kx^{2 }+ 1/2 mv^{2}

- 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.

Δp_{1 }= Δp_{1}

m_{1}Δv_{1 }= m_{2}Δv_{2}

**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

m_{A}Δv_{A }+ m_{B}Δv_{B }= (m_{A }+ m_{B}) v_{B}’

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