Download Physics Equations

Physics Equations
Terms : Speed
Distance traveled
Time
Displacement
Initial Velocity
Acceleration
Final Velocity
Physics Equations
Formulas :
Average Speed
(straight line motion)
Displacement
Average Velocity
Average Acceleration
All formulas deal with finding average values over a period of time. The motion over this period of time does not have to be constant to use these formulas.
1
Physics Equations
for uniform acceleration
When a body is undergoing uniform acceleration for a time interval, the average velocity will not change. Because of that, there are formulas that can be used to calculate the displacement, the initial velocity, the final velocity and the acceleration given the correct information.
Formulas :
For bodies in freefall, they are in uniform acceleration. The precise value for the acceleration due to gravity is g = ­9.8 m/s2.
Formulas :
Formulas are similar to those for uniform acceleration but have g as the constant acceleration.
Remember, Δy is the vertical displacement
2
Projectile motion : Projectile motion includes vertical motion and horizontal motion.
The motion in the vertical or y direction must include acceleration.
The motion in the horizontal direction has an acceleration of zero.
Horizontal motion :
Vertical Motion :
Newton's Second Law
The formula for the 2nd law is:
Fnet = manet
Fnet : is the net force for the system
m : mass of the body or connected bodies
anet : net acceleration for the body or system the net force is acting on
The Net force is the sum of all the forces acting on a body.
3
Possible forces that act on a body that should be included in a Free Body Diagram if present.
Applied Force
Force of Gravity ­ Weight
Fgrav = mg
Normal Force
Frictional Force
Tension Force
Spring Force
Air Resistance Force
Uniform Circular Motion
T : Period : Time to complete one revolution
: Frequency : number of revolutions that occur per second.
v : linear speed : how fast the body is moving along the circular path.
ac : centripetal acceleration
C : Circumference : distance around the edge of a circular path
4
Uniform Circular Motion
Formulas :
Period
T = Frequency
Circumference
C = 2πr
Linear Speed
Centripetal Acceleration
Centripetal Force
Universal Law of Gravitation
m1m2
Fg =G d2
Fg ≡ Force of Gravitational Attraction
G = 6.67 x10­11 N
Universal Constant of Gravitation
m1 ≡ mass of body 1
m2 ≡ mass of body 2
d ≡ distance between bodies as measured from center to center
5
Kepler's Third Law of Planetary Motion
T2
3
=k
R
Where :
T = period of orbit
R = semi­major axis or orbital radius
k = kepler's constant
Momentum
p = mv
Where: p = momentum
m = mass
v = velocity
6
Change in momentum
Δp = mΔv = m(vf ­ vi)
Where :
Δp = change inmomentum
m = mass
vi = initial velocity
vf = final velocity
Impulse
J = F*Δt
Where :
J = Impulse
F = Force
Δt = time interval
7
Impulse ­ Momentum theorem
Impulse experienced is equal to the change in momentum for a body.
J = F*Δt
mΔv = Δp J = F*Δt
mΔv = Δp F*Δt
mΔv
Conservation of Momentum
The sum of the momenta before a collision will be equal to the
sum of the momenta after the collision as long as the net
external force is zero.
Σpi = Σpf
p1i + p2i = p1f + p2f
m1v1i + m2v2i = m1v1f + m2v2f
8
Work
• Work is the measure of the change in energy for a body because of a force.
W=F d
W = Work done by the force
F = Force
d = displacement
Power
Power is the rate at which work is done.
W
P=
t
P = power produced by a force
W = Work done by the force
t = time work was done in.
9
Law of Work
Win = Wout
Expanding the equation ~
Fede = Frdr
Fe = effort force – force you apply
de = effort distance – distance applied
force acts over
Fr = resistance force – force machine
gives
dr = resistance distance – distance
machines force acts over
The reduction is determined by
Mechanical Advantage – ratio of effort to resistance
force
MA =
Fr
Fe
Fe = effort force - force you apply
Fr = resistance force
10
Ideal Mechanical Advantage :
ratio of effort distance to resistance distance.
de
IMA =
dr
dr = resistance distance
de = effort distance
Efficiency = (work out divided by work in)
Wout
Eff =
Win
Percent efficient is just efficiency as a percentage.
% Eff = Eff * 100%
11
Potential NRG : PE
Gravitational Potential NRG can be calculated.
PE = mgh
PE = Potential Energy
m = mass in kilograms
g = 10 m/s/s
h = height of the object above the ground.
Kinetic Energy Equation
KE = ½ mv2
Where
KE = kinetic energy in J
m = mass of the object in kg
v = speed of the object in m/s
The units of Kinetic Energy are Joules
12
Work - NRG Theorem
Work done equals the change in
kinetic NRG for a body.
Wnet = ∆KE
Wnet = KEf - KEi
Work done by gravity
Wg = -∆PE = -(PEf - PEi)
Wg = PEi - PEf
Law of Conservation of NRG
The total mechanical NRG of a closed
system stays constant
TME = KE + PE
and
PEi + KEi = PEf + KEf
for a
closed
system
When friction is involved :
PEi + KEi = PEf + KEf + Wother
13
Coulomb's Law
F=k
F = electric force in Newtons
k = constant (just a #) = 9.0x109 Nm2/C2
q1 = charge of object #1 in Coulombs (C)
q2 = charge of object #2 in Coulombs (C)
d = distance between two charges in meters
Ohm's Law
R=
V
Where:
V : voltage : Volts : V
I
V = IR
I : current : Ampere: A
R : Resistance : Ohms: Ω
P : Power : Watt : W
P = VI
2
V
P = I 2R =
R
14
Equivalent resistance :
Series
Req = R1 + R2 + R3 +.....
Parallel
1
1 + 1 + 1
=
Req
R1 R2 R 3
Wave Equation
v = λf
where :
v ≡ Wave speed in m/s
λ ≡ wavelength in meters
f ≡ frequency in Hz
15