MOMENTUM

• momentum is dependent on mass and velocity (direction and magnitude)

• also a vector quantity

• law of conservation of momentum= when 2 or more bodies’ momentum are acting up on each other unless an outside force is applied

• impulse= the amount of force on an object over a period of time which causes an object to change momentum

  • another idea to keep in mind is when a graph is presented - impulse is the area under the curve/graph

• there are 3 types of collision when it comes to momentum:

  • elastic= no change of total kinetic energy in the system (there is no energy that is dissipated by friction or transferred to internal energy)

    • ex’s: atomic or nuclear particles with similar charges, magnets with similar poles facing each other

    • DOES NOT LOSE ENERGY

  • partly inelastic= some of the initial energy is transferred into thermal/sound/internal energy

    • ex’s: a well inflated basketball or any ball that bounces some amount

  • completely inelastic energy= after the collision the objects are stuck together and the maximum amount of energy is transferred into thermal, sound, or internal energy

    • ex’s: a block of soft clay dropped onto a hard floor, a bad car accident where the cars stick together, two train cars colliding and sticking together

    • LOSES ENERGY

Formulas

p=mv

𝛥P=P_f-P_i (final - initial to get the CHANGE in momentum) —> 𝛥P=m𝛥v (v_f-v_i for the change in velocity)

• units of measurement are kg x m /s

p=fv

• only if the question implies that there is a force and velocity

F=ma —> 𝛥tF = m𝛥v (this is the equation for impulse that can be derived from the F=ma equation)

• also known as J=F𝛥t

• units of measurement are N x S = kg x m /s

• J=𝛥p (impulse is also equal to the change in momentum…..in case you forget the impulse equation)

Conservation of momentum: total Pi= total Pf

MaVai + MbVbi = MaVaf + MaVbf

• you can factor out the velocity if the problem states that the collision caused the two objects to stick together

  • if this ^^ doesn’t happen than DON’T factor out the velocities

Example:

A car with a mass of 1200 kg is traveling at a velocity of 25 m/s. It collides with a stationary car with a mass of 800 kg. After the collision, the two cars stick together and move forward at a velocity of 15 m/s. Determine the change in momentum of the system.

ENERGY + POWER

• use LOL diagrams to solve problems (initial and final graphs along with the types of objects in the system being affected by energy [in the circle])

• law of conservation of energy= in the absence of any work, heating, or radiating, the total amount of energy in a system REMAINS CONSTANT

• kinetic energy= (E_k or KE) whenever an object is moving, the faster it is the more kinetic energy it has

  • determined by speed and mass

  • if you double the mass you double the energy

  • if you double the velocity you multiply by 4 to get the energy

• gravitational potential energy= (E_g or GPE) changes in gravitational potential energy occur when an object has a change in height

  • set E_g = 0 at the lowest point (relative 0)

    • you can choose wherever that is in the problem

  • also area under the curve (A= l x w)

• elastic potential energy= (E_s) whenever an elastic object has a change in shape by stretching or compressing; the more stretch or compression the more elastic energy is stored

  • Hooke’s Law (spring constant is the area under the slope of the curve) —> k= F/𝛥x

    • units are N/m

    • if there is a low spring constant (loose spring)

    • if there is a high spring constant (stiff spring)

  • area under the F vs. x-graph (A = ½ bh)

• thermal energy= (E_int) this is also known as internal energy, but whenever friction acts on an object creating a rise in temperature

• work= a means of transferring energy from one system to another via force

  • units of measurement for work and energy are joules (J)

  • when work is positive, velocity increases

  • when work is negative, velocity decreases

  • friction does negative work cause it OPPOSES the motion

• TME= total mechanical energy

• power is how fast we give energy (how busy or how fast energy is given)

  • unit of measurement: watts (W)

Formulas

E_k= ½ mv² (kinetic energy equation)

E_g=mgh (gravitational potential energy equation)

E_el=½ k 𝛥x² (elastic potential energy)

E_int=F_f 𝛥x (thermal energy)

W= F(d)

• cos(x) is only there if it is given in the problem…otherwise just multiple force with distance

P= W/𝛥t