Linear Motion:
Variables to know - x or y = Distance (m) vi = Initial Velocity (m/s) vf = Final Velocity (m/s) a = Acceleration (m/s^2) t = Time (sec)
Formulas - x=(vi+vf2)t Vector - Measurement with direction
Examples: displacement, velocity, weight
Designated by an arrow above a variable
Scalar - Measurement without direction
Examples: distance, speed, mass
Projectile Motion:
Types of questions: Kicking/throwing an object through the air. Objects falling/rolling off of a level vy is 0 at the peak vx = vicos(ϴ) vy = visin(ϴ)
Dynamics:
Variables -
F = Force (N) - This is a vector quantity (answers must have direction)
G = Gravitational constant 6.67E-11 (Nm2kg2) m = Mass (g) m1 = mass one m2 = mass two (not the mass times two) d = Distance (m) g = acceleration due to gravity
Newton’s Laws -
1) Inertia - An object tends to stay in motion in a straight line at a constant speed and an object at rest tends to stay at rest unless an unbalanced force acts on it
Equilibrium: F=0
2) F=ma
Force causes acceleration
Weight: Fg=mg Weight is the force of gravity on an object
Gravitational Force: F=Gm1m2d2
Equilibrium:
Static - Forces are balanced with no motion
Dynamic - Forces are balanced without acceleration (constant motion or straight line motion)
Tensions - The force transmitted through a string
Friction:
Variables: uk = Coefficient of Kinetic Friction (no unit)
Ff = Force of Friction (N)
Fn = Normal Force (N)
F|| = Parallel Force (N)
Fp = Perpendicular Force (N)
Fnet = Net Force (N)
Formulas:
uk = Ff/Fn uk = tan(ϴ)
Fnet = F|| - Ff
Depends on weight and the contact of two surfaces
Coefficient of Kinetic Friction - describes the surfaces after they are sliding across one another
Large coefficients are good for grip (tires)
If a coefficient is greater than 1, more force than the object weighs is required to move the object
Friction on an inclined plane:
For calculations, break up weight into their X and Y components
If Fr = F||, the object is either at rest or at a constant velocity
Circular Motion:
Variables - ac = Centripetal Acceleration (m/s^2) r = Radius (m) vc = Velocity around a circle (m/s) pi = 3.14
Formulas:
ac = (v^2)/r Acceleration around a circle vc = (2pir)/t Velocity around a circle
F = (mv^2)/r Centripetal Force a = (gm1)/d^2 Gravity on the surface of a planet
The direction of motion is tangent to the circle, but force and acceleration are towards the center (centripetal forces)
Momentum
Variables: p = Progress (kgm/s) This is a vector quantity
Formulas:
Ft=mv Impulse momentum Theorem m1v1+m2v2 = m1vf+m2vf Conservation of Momentum m1v1+m2v2 = vf(m1+m2) Inelastic Momentum p = mv Momentum (quantity of motion)
.5*m1vi12+.5*m2v2i2=.5*m1v1f2+.5*m2v2f2 Elastic Collisions
Impulse is the change of momentum (force provided over time)
Collisions
Both objects experience equal and opposite forces
Both are experiencing the force for the same amount of time
Both experience the same change in momentum
In a closed system, the total momentum before the collision is the same afterwards
Elasticity during Collisions
Collisions are categorized by the amount of change in shape they chase
This ranges from elastic to inelastic (momentum is always conservered)
Elastic collisions exhibit no loss of kinetic energy (like billiards)
The shape of the object deforms slightly, but then bounces back
Clean collisions (no sticking)
In perfectly inelastic collisions two objects collide and move together as one object (stick together)
Energy and Work:
Variables:
KE = Kinetic Energy (J)
PE = Potential Energy (J)
PEe = Potential elastic energy (J)
PEg = Potential energy due to gravity
K = Spring constant h = height (m) x = stretch distance
W = Work (J)
Wfr = Work done by friction (J)
P = Power (W)
Formulas:
PEg = mgh
KE = .5mv^2
PEe = .5Kx^2
W=KE Work and Kinetic energy Theorem v=2gh Velocity of a pendulum (only when swinging through)