Sports Equations: Vave= d/ t or (Vf+Vi)/2 a= (Vf-Vi) t horizontal=Vx= x/ t vertical=Vf=Vi+a t or y=Vi+ t + a t2 or Vf2=Vi2+2a y. TNEOM Equations: Vf=Vi +at x=(Vi+Vf)/2 all times t x=Vit+1/2 at2 2 2 Vf =Vi +2a y Velocity: speed Acceleration: Rollercoaster Equations: weight=mxg *PE=mgh *KE=1/2mv2 * Conversions: with direction * is a change in velocity Efficiency=(work out/work in) x100 *Momentum= MxVeloc * 1m/s=2.24mph vector * vector = 1 mile=1610 meters over time * also a Impulse=Force x t or mass(Vf-Vi) * Work=Fxd * Mech. 1kg=2.22 lbs magnitude (size) vector * a=Vf-Vi / t Advan= Fout/Fin or Din/Dout (for nonfriction). *Power=Work/T 1 foot=.305 meters and direction * 1hp=746 watts * constant change *Accel Circle=V2/r or Acc=(Vf-Vi)/t *Fnet=ma or sum of all v=change in x / t. * 1 Calorie (food) = forces * Friction=coef of friction x normal in speed 1000 calories (heat)
1 calorie = 4.18
J
includes direction*
G’s: loops and hills= Norm/wt Bottom of hill or loop = a/g+1 Side of turn or loop=a/g Top of hill=1-a/g Top inside of loop=a/g-1
NORMAL = WEIGHT
Displacement: the final position-initial position. * is a vector * the area of a velocity graph is VxT, or displacement. *To find displacement on a position graph, find the difference between two positions.* On a velocity graph, it is the product of velocity by time – take the area under the curve. *Displacement is measured in meters. Area under the velocity curve represents displacement.* backing up = neg slope Acceleration vs. Velocity: you accelerate by going faster, slower, or changing direction * When you toss something, velocity is 0 at the highest point. * Acceleration is pos when velocity is increasing (cannot occur in freefall).* Vel is neg and acc is pos when you reach the ground and velocity goes to 0.* Vel is pos and accel is neg when a ball is slowing down while going upward.* Large accel on a velocity slope = big curved slope. * Faster reaction time = quicker start to acceleration, longer time to reach max velocity * speedometer – instant. Velocity * Pos V, Neg a = car going fwd and slowing down Neg V, Pos a = car going backwards and slowing dwn * accel is not pos for free fall, only for horizontal motion like moving cars.* accel and veloc vectors are perpendicular to each other Work: two criteria to see if work is being done – did KE change and did PE change * positive work – giving an object with PE KE by doing work on it. *negative work – slow things down, make an object have more PE and less KE * force needed and distance moved are necessary for work to be done * unit for work – joules * unit for force – Newton * unit for power – watts – power=work/time
Universal Gravitation: FG = (Gm1m2)/r2 * FG = force due to gravitational attraction * G = constant of universal gravitation (6.673 x 10-11 Nm2/kg2 * m1 = mass 1 * m2 = mass 2 * r = distance between center of masses
Velocity Graphs: the slope is the acceleration. *The area is displacement. *Instantaneous velocity is taken directly off the graph. *Displacement is the product of velocity by time – take the area under the curve.* Average velocity found by averaging 2 points over the range you want.* Vave=(X2-X2)/time. A negative value on a velocity graph = moving backwards * show backing up on a displacement graph with neg slope. Most useful graph
Distance: is scalar * the length of the path you took* Newtons Laws: 1. inertia – at motion wish to remain at motion and vice versa 2. a=fnet/mass 3. equal and opposite reactions – action-reaction Mass: only affects the speed of a rollercoaster when there is friction. If there is not friction, mass does not matter * your mass is the same on the moon – does not depend on gravity like weight does. Tension – force in a ride’s cable.
Position Graphs: instantaneous velocity is the slope * displacement is the difference between two positions* average velocity is the average slope from 2 positions on the graph* neg slope – moving backwards * not straight line means acceleration* horizontal line – you stopped. *Area = velocity.*curve = exponential acceleration
Projectiles and Vectors and Scalars: projectiles – moving object whose only influence on its motion is gravity. * vector – has both magnitude and direction * scalar – only has magnitude * vectors – velocity, displacement * scalars – distance, speed * acceleration in x direction for projective is O * add vectors head to tail * horizontal and vertical motion are independent. At the peak: Dt = 1/2 time of flight, Vy = 0 and ay = -9.8 m/s2. y = 0 for all problems where it begins and ends at the same height.
Energy: bungee cord after falling – elastic - all collisions where objects bounce instead of stick* st 1 source of energy – sun * cotton candy = chemical energy * graveyard for all conversions is internal energy, or heat * machines change the force in for distance (not work or energy) Centripetal Forces: revolution – rotation around external axis (sun and earth) * rotation – circular motion around internal 2 2 axis (earth) * centrip.accel = v /r * centrip. force = m x (v /r) * cent. Force depends directly on mass and velocity squared and inversely on the radius. * in order to move in a circle there only needs to be an INWARDS FORCE, and nothing else* accel vector is inwards, the velocity vector is tangent – they are perpendicular to each other. No centrifugal force – no force is ever pushing you to the outside.
Fnet – Fnet = mass/acceleration or Fnet=sum of all forces * constant speed =an Fnet of 0
Linear Speed – meters / sec * v=?r Angular Speed – radians/sec * RPM * v= (?r) / T
Weight v. Mass: weight is dependent on mass and gravity. * mass is independent of gravity – remains the same no matter where you are
Normal Ffrictio Weight = m g
Equilibrium: If an object is at rest (a=0), then the Net Force acting on an object in all directions must be zero (FNET=0).
Normal force = weight Friction: static friction – no motion * sliding kinetic friction – existing motion of object pushing back *static is greater than sliding up on it FApplie * the force of friction is dependent on the 2 surfaces (µ) and the normal force. *Resistance force to motion between two objects in contact. - Results from microscopic electromagnetic forces between two surfaces temporarily attracting each other. *Acts parallel to the surfaces in contact and opposes motion.