Equations Flashcards
No vf
(Delta)x=vo^2+.5at^2
No (delta)x
A=(vf-vo)/t
No t
Vf^2=vo^2+2a(delta)x
No a
(Delta)x=(vf-vo)t/2
No vo
(Delta)x=vf^2-.5at^2
Newton’s first law
An object will remain in its current state of motion (at rest or moving) unless acted upon by a nonzero external force.
Inertia
An objects resistance to change in motion. Directly proportional to the objects mass.
Newton’s second law
A={f/m
The direction of the acceleration is the direction of the net force acting on the object.
Newton’s third law
Every object that applies a force will have an equal and opposite force applied to it.
Sum if the forces in one dimension
{f=f(net)=ma
Radial acceleration
Ac=v^2/r
Period and frequency
F=1/t
T=1/f
Force of friction
Ffriction=uFn
Universal law of gravitation
Fg=(Gm1m2)/r^2
Potential energy from gravitation
Ug=(Gm1m2)/r
Work
W=Fdcos(theta)
Work is only done if the distance traveled is parallel to the force acting on an object.
Area under the f vs distance graph
Kinetic energy
Ke=.5mv^2
Gravitational potential energy
Gpe=mgh
Elastic force
Fs=k(delta)x
Work-energy principle
Ei+-w=Ef
Power
P=(delta)(energy)/time
P=work/time
Power
P=fvcos(theta)
Momentum
p=mv
Impulse
J=F(delta)(time)
Area under the force vs time graph
Elastic potential energy
Us=.5kx^2
Elastic collision
Momentum and kinetic energy are conserved.
Inelastic collision
Momentum is conserved.
Kinetic energy is not conserved.
Perfectly Inelastic collision
Momentum is conserved.
Collide and stick.
Truths of statics
{fx=0
{fy=0
{tp=0
Torque
t=frsin(theta)
Velocity at any position in simple harmonic motion
V=+-Vo(1-(x^2)/(A^2))^.5
Period of simple harmonic motion
Tshm=2pi(m/k)^.5
Tension force in a simple pendulum
Ftsp=mgcos(theta)
Restoring force of a simple pendulum
Restoring force=mgsin(theta)
Period of a pendulum
Tp=2pi(L/g)^.5
Based on the small angle assumption (theta<15 degrees)
Electric force
Fe=(Kcq1q2)/r^2
Fe=E(q of the charge being affected by the field)
Electric field
E=(Kc(q of charge that creates the field))/r^2
E=Fe/(q of charge being affected be the electric field)
Electric field lines
Electric field lines travel from positive charges to negative charges.
In an enclosed spherical conductor:
- Electric field equals zero within the conductor.
- Electric potential is constant within the sphere, and it equals kq/r, where r is the radius of the sphere, and q is the charge of the conductor.
Nature of electric charge
Charge is quantized: the amount of charge a particle contains equals the product of a positive integer and ec=1.60E-19
Electric potential energy
Ue=qV=(Kcq1q2)/r
Electric Potential
V=u/q=(Kcq)/r
V=Kc((q1/r1)+(q2/r2)+(q3/r3)+…)
Electric potential and electric potential energy when electric field is constant
(Delta)PE=Edq
(Delta)V=Ed
When point charges are infinitely far apart…
Ue and V are zero.
Capacitance (charge)
Q=CV
Capacitance
C=EoA/d
Potential energy of a capacitor
Uc=.5QV=.5CV^2
Current
I=(Delta)(charge)/(Delta)(time)
Ohms law
V=IR
Resistance
R=pl/A
Electrical power
P=IV
P=I^2R
P=V^2/R
RMS and Max Current and Voltage
Imax=(2)^.5(Irms)
Vmax=(2)^.5(Vrms)
Resistance in series circuits
Rs=R1+R2+R3+…
Resistance in parallel circuits
1/Rp=(1/R1)+(1/R2)+(1/R3)+…
Capacitance in series circuits
1/Cs=(1/C1)+(1/C2)+(1/C3)+…
Capacitance in parallel circuits
Cp=C1+C2+C3+…
Properties of series circuits
Current is constant
Voltage and resistance are different
Properties of parallel circuits
Voltage is constant
Current and resistance are different
Properties of capacitors in series
Charge is constant
Voltage and resistance are different
Properties of capacitors in parallel
Voltage is constant
Charge and resistance are different
No current flows through a capacitor
Emf and internal resistance
Emf: voltage battery outputs chemically
Internal resistance: resistance within the battery
Terminal voltage: voltage that the battery outputs after the voltage has been acted upon by its internal resistance
Magnetic field direction
Magnetic field flows from north to south
Right hand rule #1
Thumbs=current
Fingers (curl)=magnetic field
Right hand rule #2
Thumbs=current
Index finger=magnetic field
Palm=magnetic force
Magnetic force
Fb=ILBsin(theta)
Fb=qvBsin(theta)
Theta is the angle between I and B
Behavior of magnetic field
In a constant magnetic field, with velocity of a moving charge perpendicular to the magnetic field, the charge moves in a circle, with magnetic force as the radial force.
Magnetic field in a straight wire
B=(UoI)/(2pir)
Force between two wires
Fw/l=(I1I2Uo)/(2piL)
Direction of force between two parallel wires
If current in both wires flow in same direction, forces will point inward and wires move toward each other.
If current in both wires flow in different directions, forces will point outward and wires move away from one another.
Magnetic flux
Flux=BAcos(theta)
Theta is angle between the magnetic field and the line normal to the face of the coil.
Faradays law of induction
Emf=-N((Delta)flux)/(Delta)time)
N=number of loops of wire
Lenzs law
An induced emf always gives rise to a current whose magnetic field opposes the original change in flux in the enclosed region
Work pulling a wire out of a magnetic field
W=IBhL
Power pulling a wire out of a magnetic field
P=IBhL/t
Emf of a moving conductor
Emf=Blv
Reflection off of a plane mirror
(Theta)i=(theta)r
Focal point
F=r/2
Concave mirror with object outside the radius of curvature
Image is smaller, inverted, and real.
Concave mirror with object within the radius but outside the focal point
Image is larger, inverted, and real.
Concave mirror with object within the focal point
Image is larger, upright, and virtual
Convex mirrors
Image is always smaller, upright, and virtual
Mirror equation
(1/si)+(1/so)=(1/f)
Magnification equation
M=hi/ho=-si/so
Negative M yields an inverted and real image
Positive M yields an upright and virtual image
Index of refraction
n=c/v
C=speed of light=3.00E8
Snells law
n1sin(theta1)=n2sin(theta2)
If n1thetar)
If n1>n2, then the light refracts away from the normal (thetai<thetar)
Critical angle
Sin(critical angle)=n2/n1
Sin(critical angle)=1/n
When thetai>critical angle, then law of reflection applies
Relationship between index of refraction and wavelength
Shorter wavelengths can bend more
Longer wavelengths bend less
Converging lenses
Cause all parallel rays to pass through the lens and refract toward the focal point
Converging lens with object outside the radius of curvature
Image is smaller, inverted, and real
Converging lens with object within the radius but outside the focal point
Image is larger, inverted, and real
Converging lens with object within the focal point
Image is larger, upright, and virtual
Diverging lens
Cause all parallel rays to pass through the lens and refract away from the focal point
Image is always larger, upright, and virtual
Ray tracing
- Ray drawn from top of object parallel to the principle axis. Reflect ray off the mirror back through the focal point.
- Ray drawn from top of object through focal point. Reflect ray off the mirror back parallel to the principle axis.
- Straight line drawn from the top of the object through the center point
Velocity of a traveling wave
V=lambdaf
Frequency
Number of wavelengths occur in 1 sec
Period
Number of seconds it takes to complete one cycle
Transverse waves
Particles move in a direction perpendicular to the wave propagation
Longitudinal waves
Particles move in a direction parallel to the wave propagation
Law of superposition
The combination of two or more physical states, such as waves, to form a new state.
Constructive interference
When the total displacement of two or more waves in superposition is greater than the displacement of any individual wave.
Height equals the sum if the positive heights of the waves at a certain point
Destructive interference
When the total displacement of two or more waves in superposition is less than the displacement of any individual wave.
Height equals the sum if the negative heights of the waves at a certain point
Frequency of a standing wave
Fn=nV/2L
Frequency of a standing wave in an open tube
Fn=nV/2L
Frequency of a standing wave in an closed tube
Fn=nV/4L for n=1,3,5,7,…(odd positive integers)
Beat frequency
Fbeat=f2-f1 (where f2>f1)
Wave intensity
I=power/area (of a sphere)
I=(Energy/time)/4pir^2
Relationship between wave energy and wave amplitude
E=.5kA^2
E directly proportional to A^2
Relationships between wave intensity and wave amplitude with wave radius
I directly proportional to 1/r^2
A directly proportional to 1/r
Doppler effect
When a wave source moves closer to an observer, the wave frequency increases
When a wave source moves away from an observer, the wave frequency decreases
Constructive interference from two stationary wave sources
Distance y is a multiple of lambda
Remember the triangle!!
Destructive interference from two stationary wave sources
Distance y is a multiple of (lambda plus .5lambda)
Remember the triangle!!
Wave nature of light
When a wave hits the edge of an obstacle or passes through a slit, it will diffract in all directions
Properties of the refraction of light
Frequency is unchanged
Velocity changes: v=c/n
Wavelength changes: lambda n=lambda/n
Double slit interference
Xm=m(lambda)L/d
For constructive interference, m is an integer value (1,2,3,4,…)
For destructive interference, use m+.5, where m is an integer value
Single slit interference
Sin(theta)=m(lambda)/D
Integer values of n produce destructive interference
