Physical Science: How Things Work — NYU CORE-UA 214 Equation Sheet PDF

Physical Science: How Things Work — NYU CORE-UA 214 Equation Sheet Mechanics Linear Motion Rotational Motion position ~x [m] angle θ~ (θ = x⊥ /...

Physical Science: How Things Work — NYU CORE-UA 214 Equation Sheet Mechanics Linear Motion Rotational Motion position ~x [m] angle θ~ (θ = x⊥ /r) [rad = 1] velocity ~v [m/s] angular velocity ω ~ (ω = v⊥ /r) [1/s] F~ ~τ acceleration ~a = [m/s2 ] angular acceleration α ~= (α = a⊥ /r) [1/s2 ] m I force F~ [N] torque ~τ (τ = F⊥ r) [N m] mass m [kg] moment of inertia I [kg m2 ] momentum p~ = m~v [kg m/s] angular momentum ~ = I~ L ω [kg m2 /s] impulse ∆~ p = F~ ∆t [N s] angular impulse ~ = ~τ ∆t ∆L [N m s] opposite reaction F~BA = −F~AB [N] opposite reaction ~τBA = −~τAB [N m] 1 1 kinetic energy K = mv 2 [J] rotational kinetic energy K = Iω 2 [J] 2 2 work W = Fk ∆x [J] rotational work W = τk ∆θ [J] W W power P = = F~ · ~v = Fk v [W] rotational power P = = ~τ · ω ~ = τk ω [W] ∆t ∆t Equations of Linear Motion Equations of Rotational Motion 1 1 ~xf = ~xi + ~vi ∆t + ~a(∆t)2 θ~f = θ~i + ω ~ i ∆t + α~ (∆t)2 2 2 ~vf = ~vi + ~a∆t ω ~f = ω~i + α~ ∆t Gravity force F~grav = m~g potential energy U = mgh g = 9.81 m/s2 ≈ 10 m/s2 Friction F~static friction = −F~push if Fpush ≤ µstatic Fsupport F~sliding friction = −v̂ µsliding Fsupport  2 Springs, Pendula, Waves restoring force F~restoring = −k~x 1 elastic potential energy Uelastic = kx2 2 r m period of oscillation (spring) T = 2π k s L period of oscillation (pendulum) T = 2π g 1 frequency f = [unit: Hz] T wave speed c = λf [unit: m/s] Trigonometry B c a θ A b C a b a a2 + b2 = c2 ; sin θ = ; cos θ = ; tan θ =. c c b small-angle approximation: if |θ|  1, then tan θ ' sin θ ' θ.  3 Electromagnetism q1 q2 electric force F~el = k 2 r̂ = q E ~ r qp = −qe = 1.6 · 10−19 C Coulomb’s constant k = 8.988 · 109 N m2 /C2 ; Uel voltage V = [V] q electric field E ~ = −∇V [V/m] V current I = [A] R V resistance R = [Ω] I electric power P = IV µ 0 p1 p2 magnetic force F~mag = ~ r̂ = q B 4π r2 µ0 = 4π · 10−7 N/A2 Nsecondary Vsecondary = Vprimary Nprimary Nsecondary Isecondary = Nprimary Iprimary  4 Physical Science: How Things Work — NYU CORE-UA 214 Practice Exam 2A Question 1 You and a friend are studying the electrostatic interaction of two charges. If the distance between two electric charges doubles, how does the force they exert on each other change? (a) 4 times as large (b) 2 times as large (c) 1 2 as large (d) 1 4 as large Question 2 You stick two pieces of tape on a window and pull them off. If you hold the pieces near each other, they: (a) repel because they have like charges. (b) repel because they have opposite charges. (c) attract because they have like charges. (d) attract because they have opposite charges. Question 3 After running a plastic comb through your hair, you hold it above a small scrap of paper. The paper sticks to the comb because the paper becomes: (a) magnetic. (b) electrically charged. (c) conducting. (d) electrically polarized. Question 4 A charged object is able to repel: (a) only charged objects (b) neutral objects and neutral particles (c) neutral objects but not neutral particles (d) only neutral particles  5 Question 5 Polarization: (a) maximizes the potential energy of a system. (b) minimizes the potential energy of a system. (c) does not change the potential energy of a system. (d) resets the potential energy of a system to zero. Question 6 A typical commercial jet has a sharpened metal rod projecting backward from the tip of each wing. These two rods prevent the airplane from accumulating a large net electric charge during flight by: (a) reducing sliding friction between the airplane and the passing air stream. (b) transferring any charge on the plane to the air behind the plane. (c) maintaining a steady electric current between the airplane’s wings. (d) generating high voltages while passing quickly through Earth’s magnetic field. Question 7 High voltage power lines are usually supported by glass insulators. An electric current cannot flow through a piece of glass because (a) glass contains only positively charged particles. (b) glass contains only negatively charged particles. (c) the electrons in the glass are tightly bound to their atoms and are thus not able to transport charge through the glass. (d) glass does not contain any electrically charged particles. Question 8 You notice that a light at home keeps going out but you are certain that the bulb is good. Such behavior could result from (a) either an open circuit or a short. (b) an open circuit only. (c) a short circuit only. (d) the bulb’s resistance being cut in half.  6 Question 9 The principal advantage of sending electric power across long distances using low current is that (a) the charge can get from one point to another faster. (b) electric power lost in the wires is greatly reduced. (c) the transmission lines are less likely to get in the way than low voltage transmission lines—which are much closer to the ground. (d) low current means low resistance in the lines. Question 10 You remove the batteries from a working flashlight, turn both of them around as a pair, and reinsert them in the flashlight. They make good contact with the flashlight’s terminals at both ends, so that there is no mechanical problem preventing the flashlight from working. If you now switch on the flashlight, it will (a) not work because only electrons can actually move through a circuit. The positively charged atomic nuclei are immobile. (b) work properly, although current will now be flowing backward through its circuit. (c) not work because the batteries can’t send current backward through the flashlight’s circuit. (d) not work because the light bulb can only carry electric current in one direction. Question 11 Your flashlight has three identical 1.5 V batteries in it, arranged in a chain to give a total of 4.5 V. Current passes first through the first battery, then through the second battery, then through the third, on its way to the bulb. When you operate the flashlight, the batteries provide power to the flowing charges and they gradually use up their chemical potential energy. Which battery will run out of chemical potential energy first? (a) All three will run out at the same time. (b) The first battery will run out first. (c) The second battery will run out first. (d) The third battery will run out first. Question 12 You somehow damaged the cord of your desk lamp: one of the two wires in the cord is completely cut in half and cannot carry any current. However, the other wire still connects the lamp to the electric socket. If you turn on the lamp, (a) the normal amount of current will flow through both wires and the lamp will glow at its normal brightness. (b) the normal amount of current will flow through the one remaining wire and the bulb will glow at its normal brightness. (c) no current will flow through the bulb. (d) only half the normal current will flow through the bulb.  7 Question 13: BONUS! Your new toaster has two separate toasting units, each of which consumes 600 W of power when it is in use. When you operate one unit, a current of 5 A flows through the wiring in your home and the wires waste about 1 watt of power handling that current. If you operate both toasting units at once, your toaster consumes 1200 W and the current flowing through the wiring in your home doubles to 10 A. How much power will the wires in your home waste now? (a) about 0.5 W. (b) about 4 W. (c) about 2 W. (d) about 1 W. Question 14 A power line carries current 10 A and has resistance 2 Ω. What is the power loss as heat in the line? (a) 200 W (b) 20 W (c) 10 W (d) 5 W Question 15 A typical bar magnet has an ”N” stamped on its north pole end and an ”S” stamped on its south pole end. With the right tools, you might be able to change this bar magnet in one or more of the following ways: (1) remove its magnetic poles altogether, (2) reverse its magnetic poles so that it has a north pole at the end stamped ”S” and a south pole at the end stamped ”N”, (3) convert its north pole into a south pole so that it has south poles at both ends and no north poles. Which of those three options is physically possible? (a) Only (1) and (2) (b) None of them is possible. (c) Only (2) and (3) (d) All three are possible. Question 16 A magnet factory is making bar magnets, each about the size and shape of an ordinary ruler. After forming each bar of metal, that bar must be magnetized. The bar is placed in a coil of wire and a huge pulse of current is sent through the coil. During the pulse, current is only sent in one direction through the coil: a pulse of direct current or DC. If, instead, the current reversed directions rapidly during the pulse—a pulse of alternating current or AC, then (a) the bar magnet would end up with two south poles and no north poles. (b) the poles of the bar magnet would also reverse rapidly and would end up with a magnetization that depends upon what the AC current was at the precise moment it was shut off.  8 (c) the bar would become overmagnetized because AC is much more magnetic than DC. (d) the bar magnet would end up with two north poles and no south poles. Question 17 You are working on an experiment involving a very strong permanent magnet, and your data suggests that your magnet’s field suddenly decreased during some interval in time. Such a decrease could have been caused by the magnet (a) having overheated substantially. (b) being hit hard. (c) both (A) and (B). (d) being grounded out. Question 18 A steel refrigerator door is not permanently magnetic because (a) All the magnetic domains are oriented randomly. (b) There are no magnetic domains. (c) The electrons are bound and cannot move around much. (d) The door is usually ground out and loses all its magnetism. Question 19 You are working in a laboratory over the summer and you measure the magnetic field in a coil to be 3 T. You insert a steel rod which has a pole strength of 500 A m. The amount of force on the rod is (a) 0 (b) 3 N (c) 1500 N (d) 1500 N m Question 17 When you drop a strong magnet through the center of a copper pipe, the magnet (a) descends slowly because it is attracted to the magnetic copper metal. (b) descends rapidly because its motion causes currents to flow in the pipe and those currents attract the magnet. (c) falls at the usual rate because copper metal is nonmagnetic. (d) descends slowly because its motion causes currents to flow in the pipe and those currents repel the magnet.  9 Question 18: BONUS! If you float an aluminum pie plate on the surface of a pond and move the north pole of a strong magnet in a clockwise circle just above that plate, the plate will (a) begin turning counter-clockwise, as though it were being twisted away from the magnet. (b) begin turning clockwise, as though it were being dragged along with the magnet. (c) remain stationary. (d) be lifted out of the water and will stick to the strong north pole above it. Question 19 Suppose you have a machine which has a very strong magnet inside. You have some computer disks in the room and, although you think they are far away enough from the magnet to be safe, you do not want to take any risks. What material would be appropriate for building a magnetic shielding enclosure? (a) Aluminum. (b) Plastic. (c) Iron. (d) Copper. Question 20 A step-up transformer has 20 primary turns and 400 secondary turns. If the primary current is 30 A, what is the secondary current? (a) 12000 A (b) 600 A (c) 30 A (d) 1.5 A Question 21 Electricity produced in a generating plant passes through a large step-up transformer. This step-up transformer produces the high voltages needed to send electric power long distances across the countryside. Which of the following is transferred from the transformer’s primary coil to its secondary coil while the transformer is operating? (a) Negative electric charges and power. (b) Positive electric charges, negative electric charges, and power. (c) Power alone. (d) Positive electric charges and power.  10 Question 22 A step-down transformer transfers power from the 120 V alternating current passing through its primary coil to the 12 V alternating current passing through its secondary coil. If you interchange the primary and secondary coil, and send the 120 V alternating current through the new primary coil, (a) a 12 V alternating current will pass through its new secondary coil. (b) a 12 V direct current will pass through its new secondary coil. (c) no current will pass through its new secondary coil. (d) a 1200 V alternating current will pass through its new secondary coil.  11 THIS PAGE INTENTIONALLY LEFT BLANK