A force F_{1} is exerted a distance d_{1} from the fulcrum of a lever. What does the force F_{2} at d_{2} from the other end equal?
F_{2} = F_{1}d_{1}/d_{2}
In any system exhibiting mechanical advantage, the force exerted and the distance are inversely proportional, F_{1}d_{1} = F_{2}d_{2}. Rearranging yields the above relationship.
What is the power flowing through a wire, if 1,000 J of energy flow through in 0.1 s.
P = 10,000 W = 10 kW
Power is energy divided by time;
1000 J / 0.1 s = 10,000 W
Note that kW is a commonly-used unit on the AP exam.
the total mechanical energy of a physical system
The total mechanical energy of a physical system is the sum of the kinetic and potential energies of all the objects which make up the system.
E_{total} = KE_{total} + PE_{total}
On the AP exam, you will rarely have to track more than one kinetic and one potential energy in any system.
In the quantum mechanical model, where does the hydrogen electron exist?
In a spherical probability cloud around the nucleus, called the 1s orbital.
Note: the quantum mechanical model is the one used in most chemistry courses and on the AP Chem exam.
emission spectrum
The emission spectrum is the unique spectrum of bright lines or bands of light emitted by a particular substance when it is electronically excited.
This is the second bar in the image.
What will the daughter atom be when uranium-238 undergoes a single alpha decay?
^{234}_{90}Th
In single alpha decay, an alpha particle is emitted. To identify the daughter nucleus: subtract 2 from the parent nucleus' atomic number, and 4 from its mass. Subtracting 2 protons from uranium (92) shifts it to thorium (90).
What will the angle of reflection be for a light ray incident on a surface, making an angle of 35 degrees to the surface?
θ_{r} = 55 degrees
Remember: the angles of incidence and reflection must be measured relative to the surface's normal. 90 - 35 = 55. θ_{i} and θ_{r} are shown below.
How is the path of a light ray affected when the ray crosses a boundary from air (low n) into glass (high n)?
When a light ray crosses from air into glass, it bends towards the normal of the surface once inside the glass.
Any boundary crossing into a medium with a higher index of refraction will cause light to bend towards the normal.
Why is a beam of sunlight separated into a rainbow of different colors as it passes through a prism?
The rainbow occurs due to dispersion.
The white sunlight beam is made up of all the colors of visible light mixed together, as is all white light. The glass of the prism is dispersive, and different colors of light refract differently as they pass through the prism, so they are separated upon exiting the back surface.
Blue light is refracted more than red light in glass.
An optical system consists of an object and a single converging mirror. If the object is a distance between f and 2f from the optic, what are the properties of the final image?
The image is further from the optic than the object is, and the image is real, magnified, and inverted.
Find where the parallel, focal, and center rays cross after reflecting off the mirror to locate the image. Since the rays cross after reflection, the image is real.
How is the buoyancy force of a submerged object calculated?
The buoyancy force of a submerged object is simply the weight of the liquid displaced by the portion of the object that is submerged.
F_{B} = ρ_{liq }* V_{sub}* g
Where:
- F_{B} = the buoyancy force pushing up on the object
- ρ_{liq} = the density of the liquid
- V_{sub} = the volume of the object that is submerged in the liquid
- g = the gravitational acceleration (commonly 10 m/s^{2})
the effective weight of an object submerged in a liquid
The effective weight of an object submerged in a fluid is equal to the object's weight on dry land minus the buoyancy force due to the liquid displaced by the object's submersion.
W_{eff} = m_{obj}g - (ρ_{liq} * V_{obj} * g)
Where:
- m_{obj} = the object's mass
- ρ_{liq} = the liquid's density
- V_{obj} = the object's volume
- g = 10 m/s^{2}
Avogadro's Law
Avogadro's Law states that the volume of a gas is directly proportional to the number of moles at a constant temperature and pressure.
V / n = k
where:
- V = volume in L
- n = number of moles
- k = proportionality constant of the specific gas
What is the enthalpy change when 2 moles of CH_{4} are formed, according to the following reactions?
rxn1: 2H_{2}(g)⇒4H(g)
ΔH_{1}= -870 kJ/mol
rxn2: C(s) + 4H(g)⇒CH_{4}(g)
ΔH_{2}= +794 kJ/mol
-152 kJ
1) Adding the reactions together yields the formation reaction of CH_{4}:
C(s) + 4H(g) + 2H_{2}(g) ⇒
CH_{4}(g) + 4H(g)
Canceling common terms leaves:
C(s) + 2H_{2}(g) ⇒CH_{4}(g)
2) To complete the calculation, combine the reactions' enthalpies in the same way the reactions were combined.
ΔH_{rxn} = ΔH_{1} + ΔH_{2}
-870 + 794 = -76kJ/mol
3) Finally, multiply by the number of moles (2) to get the final answer.
The curve below represents a sample's temperature vs. heat added. What phases (solid, liquid, and/or gas) are present at each labeled point on the plot?
What is the period of the waveform below, if each horizontal division represents 1 s?
The period of the wave is 6.5 s.
Don't make the mistake of thinking the period is measured from one midpoint to the next; that value (3.25 s in this case) is half the period.
What are some classic examples of transverse waves?
Transverse waves include:
- light waves (electromagnetic waves)
- string waves
- pond waves*
- stadium waves
*Technically water waves also fall under the classification of "surface waves", but the AP Physics exam does not require that definition.
Longitudinal wave
In a longitudinal wave, the particles oscillating move with displacement parallel to the direction of propagation.
Calculate the amplitude of the wave below:
The amplitude is 17 meters.
Amplitude is the greatest positive displacement from zero of a wave, measured at its peak.
What does the Doppler effect describe, and what formula can be used to calculate it?
The Doppler effect describes the change in observed frequency of a wave, compared to the original emitted frequency.
f' = f_{o} (v_{c} ± v_{d}) / (v_{c} ± v_{s})
Where:
f_{o }= emitted frequency in Hz
f' = new observed frequency in Hz
v_{c} = constant speed of sound in m/s
v_{d} = speed of detector in m/s
v_{s} = speed of source in m/s