Test Yourself: AP Physics 2 Fundamentals

How would you determine the density of an object?

ρ = m /V . So, all we need to do is find mass and volume. Mass can be found using a balance. If the object has a geometric shape, measure it with a ruler and calculate its volume. If it is irregular, fill a container to the rim with water. Submerge the object, and collect and measure the overflow volume of water.

What is the physical mechanism in a fluid that causes a force on a surface?

The simple answer is pressure, but what causes the pressure? Fluids are made of a bajillion tiny molecules in constant random motion. These individual molecules are colliding with and recoiling from any surface touching the fluid. This imparts an individual molecular impulse to the surface that is perpendicular to that surface. Add up all these individual impulses and you get pressure.

Mathematically how do you calculate force knowing the pressure? OK, now we are looking for an equation.

F = PA . Remember that the force caused by fluid pressure is always perpendicular to the surface.

For the equation P = P 0 + ρ gh ,

(a) for what kind of situation is the equation valid?

(b) what does P 0 stand for (careful!)?

(a) This is valid for a static (not moving) column of fluid.

(b) P 0 stands for pressure at the top of the fluid; not necessarily, but sometimes, atmospheric pressure.

Write Bernoulli's equation.

P(1)+pgy(1)+1/2pv^2(1)=P(2)+pgy(2)=1/2pv^2(2)

State Archimedes' principle in words by finishing the following sentence: "The buoyant force on an object in a fluid is equal to . . ."

. . . the weight of the fluid displaced.

For a flowing fluid, what quantity does Av represent, and why is this quantity the same everywhere in a flowing fluid?

Av is the volume flow rate. Fluid can't be created or destroyed; so, unless there's a source or a sink of fluid, total volume flowing past one point in a second must push the same amount of total volume past another downstream point in the same time interval.

Write the alternate expression for mass that is useful when dealing with fluids of known density.

mass = density · volume.

How do you determine the internal energy of a gas given the temperature of the gas? Define all variables in your equation.

U = 3/2 Nk B T . Internal energy is 3/2 times the number of molecules in the gas times Boltzmann's constant (which is on the constant sheet) times the absolute temperature, in kelvins. Or, U = 3/2 n RT is correct, too, because Nk B = nR . (Capital N represents the number of molecules; small n represents the number of moles.)

How do you determine the rms speed of molecules given the temperature of a gas? Define all variables in your equation.

Vrms=Root((3k(b)T)/m)

K(b) the ideal gas constant (8.314 kgm2/s2mol*K)

T temperature (Kelvin)

M molar mass (kg/mol)

State the equation for the first law of thermodynamics. What does each variable stand for? What are the units of each term?

ΔU = Q + W

Change in internal energy is equal to (say it in rhythm, now) "heat added to, plus work done on" a gas. Each term is a form of energy and so has units of joules.

Sketch two isotherms on the PV diagram below. Label which isotherm represents the higher temperature.

The isotherm labeled as "2" is at the higher temperature because it's farther from the origin.

PV graph with a higher aliti and more left. refer back to book.

Describe a situation in which heat is added to a gas, but the temperature of the gas does not increase.

Let's put the initially room-temperature gas into a boiling water bath, adding heat. But let's also make the piston on the gas cylinder expand, so that the gas does work. By the first law of thermodynamics, if the gas does as much or more work than the heat added to it, then ΔU will be zero or negative, meaning the gas's temperature stayed the same or went down.

Imagine you are given a labeled PV diagram for 1 mole of an ideal gas. Note that one of the following is a trick question!

(a) How do you use the graph to determine how much work is done on or by the gas?

(b) How do you use the graph to determine the change in the gas's internal energy?

(c) How do you use the graph to determine how much heat was added to or removed from the gas?

(a) Find the area under the graph. (b) Use PV = nRT to find the temperature at each point; then, use U = 3/2nRT to find the internal energy at each point; then subtract to find ΔU . (c) You can NOT use the graph to determine heat added or removed. The only way to find Q is to find ΔU and W .

How can we estimate absolute zero in a school lab?

An estimate for absolute zero can be found by plotting the relationship between gas pressure and its temperature while keeping the volume constant. For example, confine a gas in a container. While measuring the temperature and pressure, cool the gas. Plot the data and you will see that as temperature goes down, pressure goes down (a direct relationship). Draw a line through your data and extrapolate backward until you get to zero pressure, because you can't go any lower than no pressure. The temperature at zero pressure is absolute zero.

You can also find absolute zero by measuring gas volume as a function of temperature and repeating the extrapolation process to zero volume. The temperature at zero volume is absolute zero.

If the volume of a gas doubles while the temperature is held constant, what happens to the pressure of the gas?

The model for an ideal gas is PV = nRT . Temperature is being held constant, R is a constant, and assuming we don't gain or lose any gas in the process, the number of moles is a constant. Therefore: PV = a constant. So, if volume doubles, the pressure will be cut in half.

Heat is added to a gas in a closed container.

(a) Is there any work done by or on the gas?

(b) What happens to the temperature and pressure of the gas?

Heat is added (+Q ). The volume of the container does not appear to be changing (ΔV = 0):

(a) W donebygas = P ΔV = 0.

(b) ΔU = Q + W . Since work is zero and heat is positive, the internal energy of the gas goes up. From the kinetic theory of gases, we know that the internal energy of a gas is directly related to the temperature of the gas. Therefore, as ΔU goes up, so does temperature. Finally, from the ideal gas law PV = nRT , we see that volume and the number of molecules aren't changing. Pressure is directly related to temperature. Therefore, the pressure increases as well.

Why does heat always flow from hot objects to cold objects?

Objects are made up of a bajillion atoms moving in a distribution of random speeds. Some fast, some slow. Temperature measures the average motion of these atoms. In hotter objects, on average, the atoms are moving faster. If you put a hot object in contact with a cold object, on average, the faster-moving atoms in the hot object will transfer energy to the slower-moving ones in the cold object by elastic collisions.

What are the three ways heat can be transferred? Explain each process.

Conduction is a process by which thermal energy is transferred by physical contact from atom to atom as we just discussed in #18. Convection is a process of thermal energy transfer through the movement of hot fluids as they rise due to changes in density. Radiation is the emission of electromagnetic radiation due to the random vibration of the charged particles. The higher the temperature of the object, the faster the particles vibrate and the more they radiate energy at higher frequencies.

Given the charge of a particle and the electric field experienced by that particle, give the equation to determine the electric force acting on the particle.

F = qE .

Given the charge of a particle and the magnetic field experienced by that particle, give the equation to determine the magnetic force acting on the particle.

F = qvB sin θ.

A wire carries a current to the left, as shown below. What is the direction and magnitude of the magnetic field produced by the wire at point P ?

Point your right thumb in the direction of the current, i.e., to the left. Your fingers point in the direction of the magnetic field. This field wraps around the wire, pointing into the page above the wire and out of the page below the wire. Since point P is below the wire, the field points out of the page.

When is the equation kQ /r 2 valid? What is this an equation for?

This equation is only valid when a point charge produces an electric field. (Careful—if you just said "point charge," you're not entirely correct. If a point charge experiences an electric field produced by something else, this equation is irrelevant.) It is an equation for the electric field produced by the point charge.

The electric field at point P is 100 N/C; the field at point Q , 1 meter away from point P , is 200 N/C. A point charge of +1 C is placed at point P . What is the magnitude of the electric force experienced by this charge?

Do not use E = kQ /r 2 here, because the electric field is known. So, the source of the electric field is irrelevant—just use F = qE to find that the force on the charge is (1 C)(100 N/C) = 100 N. (The charge is placed at point P , so anything happening at point Q is irrelevant.)

Can a current be induced in a wire if the flux through the wire is zero? Explain.

Yes! Induced emf depends on the change in flux. So, imagine that the flux is changing rapidly from one direction to the other. For a brief moment, flux will be zero; but flux is still changing at that moment. (And, of course, the induced current will be the emf divided by the resistance of the wire.)

True or false: In a uniform electric field pointing to the right, a negatively charged particle will move to the left. If true, justify with an equation; if false, explain the flaw in reasoning.

False. The negative particle will be forced to the left. But the particle could have entered the field while moving to the right . . . in that case, the particle would continue moving to the right, but would slow down.

Which is a vector and which is a scalar: electric field and electric potential?

Electric field is a vector, so fields produced in different directions can cancel. Electric potential is a scalar, so direction is irrelevant.

Fill in the blank with either "parallel" or "series":

(a) Voltage across resistors in ______ must be the same for each.

(b) Current through resistors in ______ must be the same for each.

(c) Voltage across capacitors in ______ must be the same for each.

(d) Charge stored on capacitors in ______ must be the same for each.

Voltage across resistors in parallel must be the same for each.

Current through resistors in series must be the same for each.

Voltage across capacitors in parallel must be the same for each.

Charge stored on capacitors in series must be the same for each.

A uniform electric field acts to the right. In which direction will each of these particles accelerate?

(a) proton

(b) positron (same mass as electron, but opposite charge)

(c) neutron

(d) anti-proton (same mass as proton, but opposite charge)

The positively charged proton will accelerate with the field, to the right.

The positively charged positron will accelerate with the field, to the right.

The uncharged neutron will not accelerate.

The negatively charged anti-proton will accelerate against the field, to the left.

A uniform magnetic field acts to the right. In which direction will each of these particles accelerate, assuming they enter the field moving toward the top of the page?

(a) proton

(b) positron (same mass as electron, but opposite charge)

(c) neutron

(d) anti-proton (same mass as proton, but opposite charge)

Use the right-hand rule for each:

The positively charged proton will accelerate into the page.

The positively charged positron will accelerate into the page.

The uncharged neutron will not accelerate.

The negatively charged anti-proton will accelerate out of the page.

How do you find the potential energy of an electric charge?

If you know the electric potential experienced by the charge, PE = qV .

Describe the processes of conduction, polarization, and induction.

Conduction is when a charged object is physically touched to another. The charge migrates between the objects, and the two share the original net charge. Polarization is when you bring a charged object close to, but not touching, something else. The charged object repels like charges and attracts opposite charges in the second object, causing it to have a charge separation, but not a net charge. One side becomes more positive, and the other side becomes more negative. Induction is one step beyond polarization. With induction, the charged object is brought close to, but does not touch, a second object. This creates a charge separation—polarization. Now an escape path, or "ground," is attached to the polarized object, which allows the repelled charge to escape. The ground is removed, and the object is now charged the opposite sign.

What is the smallest unit of charge that you will likely ever find? Why?

1.6 × 10-19 C. This is the charge of an electron/proton. Unless you have a particle accelerator in your classroom, this is the smallest unit of charged matter you will ever encounter. Everything else you will encounter is made up of protons and electrons, so 1.6 × 10-19 C is the smallest you will see.

What do the electric field and electric potential "look like" between two oppositely charged capacitor plates?

The electric field will be uniform in strength and direction, pointing away from the positive plate and toward the negative one. The electric potential will have isolines that are parallel to the capacitor plates (making them perpendicular to the E-Field lines). Near the edges of the capacitor plates, things begin to get "curvy" as E-Field and isolines of potential spill out.

The force between two charges is F . If the size of the charges is doubled and the charges are moved twice as far apart, what will be the new force?

Double both charges and double the radius and you get 4 on top and 4 on the bottom, which cancels. Thus the force stay the same. (Charge equaltion)

What are the similarities and differences between the electric force and gravitational force?

Gm1m2/r^2 and kQ1Q2/r^2

both have the same inverse squared relationship with the radius. Both exert a force on a line between the two objects. Both forces extend to infinity. Differences: mass is always positive, while charge can be negative or positive. Gravity only attracts, while electric force attracts and repels. Gravity is very weak in comparison to the electric force. Most objects have a net charge of zero, so the electric forces cancel out in most cases. This is not true with gravity; all objects with mass will have an attraction to all other masses.

Two identical metal spheres, one with a charge of +2 C and the other with a charge of −4 C, touch. What is the new charge of each sphere?

Since both are conductors, by contact, or conduction, the two spheres will share the net charge of −2 C. Since they are the same size, each sphere will end up with −1 C.

If you double the diameter of a wire, what happens to its resistance?

R=pl/A=pl/pir^2

So if you double the diameter of the wire, the new resistance is one-fourth the original (R /4).

How would you determine if a resistor is ohmic?

An ohmic resistor will have the same resistance even though the voltage and current are changing: R=Delta V/I = constant. So, all you have to do is connect the resistor to different voltages, measure the current in each case, and calculate the resistance in each case to see if it is constant. Better yet, plot voltage versus current on a graph and make sure the graph is linear. If it is curved, the resistor is nonohmic.

I want to increase the capacitance of a capacitor. How could I change the geometry of the capacitor to accomplish this?

C=kmuA/dHere are your options for increasing the capacitance: (1) κ —insert an insulator between the plate plates with a higher dielectric constant; (2) A —increase the area of the plates; and (3) d —decrease the distance between the plates.

An uncharged capacitor is connected to a battery. Compare the current of an uncharged capacitor immediately after it is connected to a battery to its current after it has been connected for a long time. Explain.

When the uncharged capacitor is first connected to the battery, it has no potential difference between the plates and offers no resistance to current. Thus, at first, the capacitor behaves like a wire. After a long time, the capacitor fills with opposite charges on the plates and builds a potential difference equal to, but in the opposite direction of, the battery. No more charge can move to the capacitor and it is "full." Thus, in the end, the capacitor acts like a "disconnect" or "open switch" in the circuit and current flow stops.

Describe how ferromagnetic, paramagnetic, and diamagnetic materials behave when placed in an external magnetic field.

The magnetic domains in a ferromagnetic material line up with the external B-Field amplifying the field. The magnetic field in a paramagnetic material also lines up with the external B-Field, but the effect is weak. Diamagnetic materials generate a magnetic field that is opposite to the external B-Field, partially cancelling the field. Superconductors exhibit diamagnetism and can completely cancel out the magnetic field inside themselves.

Describe what each variable means in the equation d sin θ = m λ.

d is the distance between the slits in the case of a double slit interference pattern, or the width of the slit, in the case of a single slit interference pattern.

m is the "order" of the points of constructive or destructive interference. In the case of a double slit interference pattern, it represents the difference in path length from one source to a point on the screen, and the path length from the other source in terms of wavelengths.

θ is the angle between the central maximum "m " order maxima or minima.

λ is the wavelength of the wave traveling through the slits.

Describe how the interference pattern for a single slit is the same and different from an interference pattern for a double slit where the width of the single slit is the same as the distance between the centers of the double slits.

A double slit interference pattern has fairly evenly spaced maxima and minima in the interference pattern, while the single slit has a wide central maximum. If the distance between the double slits is the same as the width of the single slit, the maxima on the double slit will be minima for the single slit and vice versa. The wide central maximum of the single slit pattern will be twice as wide as that of the double slit pattern.

Explain how dark and light locations are created when light shines through a double slit.

The interference pattern is created because light behaves as a wave. Light passing through each slit must travel a distance toward the screen. This distance can be measured in wavelengths. When the difference in distance from the slits to the screen is in whole multiples of a wavelength, the waves line up crest to crest to form constructive interference. When the travel distance from the two slits to the screen is off by a ½ wavelength, the waves strike the screen crest to trough for destructive interference.

Describe the differences between electromagnetic and mechanical waves.

Both exhibit wave behaviors: interference, diffraction, refraction, reflection, Doppler effect, etc. However, electromagnetic waves do not require a medium to travel. They are a self-propagating electric and magnetic wave. The energy of a mechanical wave is dictated by its amplitude. The energy of an EM wave depends on its frequency E=hf=hc/wavelength . EM waves also exhibit the particle properties (photons).

Only 80% of the light that strikes a particular surface reflects from it. What happened to the rest of the light?

Well, it depends. For clear substances, the remaining 20% of the light energy could have passed through and refracted. For opaque substances, the remaining 20% of the light energy is mostly absorbed. The key idea here is conservation of energy. Some light energy may reflect, some may transmit, and some may be absorbed, but it all adds up to the original 100% of the light energy.

Why does light refract (bend) when it enters a new medium?

When light enters a new medium, the wave fronts move at a new speed. This new speed causes the light to change direction. The only way light can travel into a new medium and not change direction is if it enters directly into the medium perpendicular to the surface, or if the speed of light in the new medium is the same as in the old medium.

(a) When light travels from water (n = 1.3) to glass (n = 1.5), which way does it bend?

(b) When light travels from glass to water, which way does it bend?

(c) In which of the above cases may total internal reflection occur?

(d) Write (but don't solve) an equation for the critical angle for total internal reflection between water and glass.

(a) Light bends toward the normal when going from low to high index of refraction.

(b) Light bends away from the normal when going from high to low index of refraction.

(c) Total internal reflection can occur only when light goes from high to low index of refraction.

(d) sin θ c = 1.3/1.5

Describe two principal rays drawn for a convex lens. Be careful to distinguish between the near and far focal points.

For a convex (converging) lens:

• The incident ray parallel to the principal axis refracts through the far focal point.

• The incident ray through the near focal point refracts parallel to the principal axis.

• The incident ray through the center of the lens is unbent.

(Note that you don't necessarily need to know this third ray for ray diagrams, but it's legitimate.)

Describe two principal rays drawn for a concave lens. Be careful to distinguish between the near and far focal points.

For a concave (diverging) lens:

• The incident ray parallel to the principal axis refracts as if it came from the near focal point.

• The incident ray toward the far focal point refracts parallel to the principal axis.

• The incident ray through the center of the lens is unbent.

(Note that you don't necessarily need to know this third ray for ray diagrams, but it's legitimate.)

After sitting on a shelf for 3 years, a radioactive sample has only one-eighth of its original beta particle emissions. What does this tell you about the sample?

One-eighth the original emission means it has gone through 3 half-lives (½ × ½ × ½ = ⅛) So the sample is 9 years old.

Green light shines on a photosensitive material, causing it to eject electrons.

(a) What can you do to cause more electrons to be ejected?

(b) What can you do to cause the ejected electrons to have more energy?

Photoelectric effect and photons

(a) If all you want is more electrons, just shine more green light on the surface.

(b) To get higher-energy electrons, you will need higher-energy light striking the surface. Use blue light, or UV light.

What conservation laws are obeyed in the nano-world?

Conservation of charge, conservation of momentum, conservation of mass/energy (remember that mass and energy are two aspects of the same thing: E = mc 2 ), conservation of nucleon number.

A photon collides with a stationary electron giving it a velocity. What has happened to the wavelength and frequency of the photon? Explain.

The photon has transferred energy and momentum from itself to the electron. The frequency decreases and the wavelength increases.

(E=hf=hc/wavelength)

Why does gas in a neon bulb emit only discrete wavelengths of light?

The electrons in the neon atom exhibit the wave properties of constructive and destructive interference. Thus, the elections can only exist in specific energy level locations. To jump up to the next energy level, the electron must absorb the specific amount of energy required to get there. It's kind of like walking up steps. When electrons fall downward from one energy level to another, they must emit a photon of the exact energy difference between the levels: hence the bands of light.

What does a wave function tell us?

The wave function of a particle is a probability distribution that tells us the likelihood of finding the particle at a specific location. The larger the positive or negative amplitude of the wave, at a specific location, the higher probability of finding the particle. If the amplitude is zero at a location, the particle will not be found at that location.

Uranium decays into thorium by ejecting an alpha particle. How does the mass of the uranium compare to the thorium and alpha particle? Explain.

The mass of the uranium is larger than the combined mass of the thorium and alpha particle. The loss in mass is due to the kinetic energy gained by the alpha particle in the decay (E = mc 2 ). Spontaneous nuclear reaction generate by-products that have less mass than the original.

We often use two different equations for wavelength:

wavelength=hc/deltaE and wavelength=h/mv.

When is each used?

(wavelength= hc/delta E) is used to find the wavelength of a photon only. You can remember this because of the c , meaning the speed of light—only the massless photon can move at the speed of light.

(wavelength=h/mv)is the de Broglie wavelength of a massive particle. You can remember this because of the m —a photon has no mass, so this equation can never be used for a photon.

Name the only decay process that affects neither the atomic number nor the atomic mass of the nucleus.

Gamma decay doesn't affect the atomic mass or atomic number. In gamma decay, a photon is emitted from the nucleus, but because the photon carries neither charge nor an atomic mass unit, the number of protons and neutrons remains the same.