AP Physics Trimester 2 Multiple Choice
The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2s. Length of one wave is 5 cm. What is the amplitude of the wave? A) 4 cm B) 5 cm C) 8 cm D) 10 cm
A) By inspection
A car of mass m slides across a patch of ice at a speed v with its brakes locked. It hits the dry pavement and skids to a stop in a distance d. The coefficient of kinetic friction between the tires and the dry road is u. If the car has a mass of 2m, it would have skidded a distance of: A) 0.5d B) d C) 1.41d D) 2d
C) This is a conservative situation so the total energy should stay the same the whole time. It should also start with max potential energy and min kinetic, which only occurs in choice C
The graph below was produced by a microphone in front of a turning fork. It shows the voltage produced from the microphone as a function of time. The function is a cosine wave. The frequency of the turning fork is approximately: A) 0.004s B) 0.020s C) 50 Hz D) 250 Hz
D) f = cycles/second
A standing wave of frequency 5 Hz is set up on a string 2 meters long with notes at both ends and in the center, as shown above: The speed at which waves propagate on the string is: A) 0.4 m/s B) 2.5 m/s C) 5 m/s D) 10 m/s
D) Based on the diagram, the wavelength is 2 meters Plug this into v = f(wavelength)
A pendulum is pulled to one side and released. It swings freely to the opposite side and stops. Which of the following might best represent graphs of kinetic energy (Ek), potential energy (Ep), and total mechanical energy (Et): A) A B) B C) C D) D
D) Double the velocity gives 4x the distance
A uniform meterstick is balanced at its midpoint with several forces applied as shown below. If the stick is in equilibrium, the magnitude of the force X in newtons (N) is (A) 50 N (B) 100 N (C) 200 N (D) 300 N
(A) 50 N Find the sum of all of the torques on the meter stick (with 0.5 as the center of gravity) and equal it to zero when solving for X
A uniform stick has length L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is: (A) Io + 1/4ML^2 (B) Io + 1/2ML^2 (C) Io + 3/4ML^2 (D) Io + ML^2
(A) I0 + 1/4ML^2 Use Inet = Io + Im = Io + (M(1/2L)^2)
A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown. A force F is applied at the other end, at an angle theta to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque? (A) Lsin (B) Lcos (C) L (D) Ltan
(A) Lsin (Fsin)(L) = FLsin To get the same torque with F applied perpendicular we would have to change the L to get F(Lsin)
A car travels forward with a constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road is: (A) Vertically upward (B) Horizontally forward (C) Horizontally backward (D) Upward and forward, at approximately 45º to the horizontal
(A) Vertically Upward
A light rigid rod with masses attached to its end is pivoted about a horizontal axis as shown above. When released from rest in a horizontal orientation, the rod begins to rotate with an angular acceleration of magnitude: (A) g/7l (B) g/5l (C) g4l (D) 5g/7l
(A) g/71 Use Tnet = Ia
A rod of length L and of negligible mass is pivoted at a point that is off-center with lengths shown in the figure below. The figures show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by the known mass, M1 or M2, so that the rod remains horizontal. What is the value of m in terms of the known masses? (A) radical(M1M2) (B) 1/2(M1+M2) (C) M1M2 (D) 1/2(M1M2)
(A) radica(M1M2) (mg)(L1) = (M1g)(L2) L1 = M1(L2)/m substitute the value of L1 into the following equation: (M2g)(1) = mg(L2) M2(L1) = m(L2)
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined place of height h as shown above. If the plane is frictionless, what is the speed v of the center of mass of the sphere at the bottom of the incline? (A) radical(2gh) (B) (2Mghr^2)/I (C) radical((2Mghr^2)/I) (D) radical((2Mghr^2)/(I+Mr^2)
(A) radical(2gh) Mgh = Ktot = Krot + Ktrans There is no torque to cause the sphere to rotate, so Krot = 0 Mgh = 1/2Mv^2
A block of mass m is placed against the inner wall of a hollow cylinder of radius R that rotates about a vertical axis with a constant angular velocity w, as shown above. In order for friction to prevent the mass from sliding down the wall, the coefficient of static friction u between the mass and the wall must satisfy which of the following inequalities? (A) u(g/R) (B) u(R/g) (C) u(g/R) (D) u(R/g)
(A) u(g/R) Solving for u gives u > g/w^2R
A 5-meter uniform plank of mass 100 kilograms rests on the top of a building with 2 meters extended over the edge as shown. How far can a 50-kilogram person venture past the edge of the building on the plank before the plank just begins to tip? (A) 0.5 m (B) 1 m (C) 1.5 m (D) 2 m
(B) 1 m (m1g)•r1 = (m2g)•r2 (100kg)(0.5m) = (50 kg)(r) r = 1m
A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown. The magnitude of the net torque on the system about the axis is: (A) Zero (B) 2FR (C) 5FR (D) 14FR
(B) 2FR Find the torques of each section and add them together Remember to consider the signs of the torques based off of their clockwise/counterclockwise direction F(3R) - (2F)(3R) + F(2R) + F(3R) = 2FR
A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it up vertically, such that the cylinder is suspended in midair for a brief time interval ∆t and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is 1/2MR^2. The linear acceleration of the person's hand during the time interval ∆t is: (A) Tmg/m (B) 2g (C) g/2 (D) T/m
(B) 2g Net torque = TR = Ia = 1/2MR^2a => a = @t/MR Fnet = 0 => T = Mg => a = 2g/R a = aR = 2g
A uniform meter stick of mass 0.20 kg is pivoted at the 20 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44 cm (D) 46 cm
(B) 36 cm Mass of stick m1 = 0.20 kg at midpoint, Total length L = 1.0 m, Pivot at 0.40 m, attached mass m2 = 0.50 kg Tnet = 0 (M1g)•r1 = (m2g)•r2 (0.2)(0.1) = (0.5)(x) x = 0.04 from the 40 cm mark => position on the stick is 36 cm
A meterstick of negligible mass is placed on a fulcrum at the 0.60 m mark, with a 2.0 kg mass hung at the 0 m mark and a 1.0 kg mass hung at the 1.0 m mark. The meterstick is released from rest in a horizontal position. Immediately after release, the magnitude of the net torque on the meterstick about the fulcrum is most nearly: (A) 2.0 Nm (B) 8.0 Nm (C) 10 Nm (D) 16 Nm
(B) 8.0 Nm Tnet = (M1g)•r1 - (m2g)•r2 (2)(9.8)(0.6) - (1)(9.8)(0.4) = 0 => 8.0 Nm
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed w of the wheel is increased from zero to wf in a time interval T. What is the average power input to the wheel during the time interval? (A) Iwf/2T (B) Iwf^2/2T (C) Iwf^2/2T^2 (D) I^2wf/2T^2
(B) Iwf^2/2T P = (t)(w) = (∆K)/(T)
A massless rigid rod of length 3d is pivoted at a fixed point W, and two forces each of magnitude F are applied vertically upward as shown. A third vertical force of magnitude F may be applied, either upward or downward, at one of the labeled points. With the proper choice of direction at each point, t he rod can be in equilibrium if the third force of magnitude F is applied at point: (A) Y only (B) V or X only (C) V or Y only (D) V, W, or X
(B) V or X only On the left of the pivot T = Fr, on the right side of the pivot T = F(2r). So we either have to add 1(Fr) to the left side to balance out the torque or remove 1(Fr) on the right side to balance out the torque.
A particle of mass m moves with a constant speed v along the dashed line y = a. When the x-coordinate of the particle is x the magnitude of the angular momentum of the particle with respect to the origin of the system is: (A) Zero (B) mva (C) mvx (D) mv•radical(x^2 + a^2)
(B) mva
Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and moment of inertia I about its center. T1 and T2 are the tensions in the string on either side of the pulley and a is the angular acceleration of the pulley. Which of the following equations best describes the pulley's rotational motion during the time the blocks accelerate? (A) mgR = Ia (B) TR = Ia (C) (T2 - T1)R = Ia (D) (m2 - m1)gR = Ia
(C) (T2 - T1)R = Ia
To weigh a fish, a person hangs a tackle box of mass 3.5 kilograms and a cooler of mass 5 kilograms from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod's length from the tackle box. What is the mass of the fish? (A) 1.5 kg (B) 2 kg (C) 3 kg (D) 6 kg
(C) 3 kg (3.5)(9.8)(L/2) + (M)(9.8)(L/4) - (5)(9.8)(L/2) = 0 m = 4 kg
A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel as shown. If the system is in static equilibrium, what is the value of m in terms of M? (A) M/2 (B) M (C) 3M/2 (D) 5M/2
(C) 3M/2 mg(R) + Mg(Rcos60º) - 2Mg(R) = 0 Cos60º = 1/2 => 3M/2
A door has hinges on the left hand side. Which force produces the largest torque? The magnitudes of all forces are equal: (A) F perpendicular at pivot point (B) F diagonally outward away from door (C) F perpendicular to end of door (D) F diagonally inward to door
(C) F perpendicular to end of door Torque = (Fr), so if the entire force is maximized and the force applied is at the very end of the door (largest r), then this will be the greatest torque
An ant of mass m clings to the rim of a flywheel of radius r as shown above. The flywheel rotates clockwise on a horizontal shaft S with a constant angular velocity w. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? (A) I (B) II (C) III (D) IV
(C) III
An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected? Angular Momentum Kinetic Energy (A) Increases Increases (B) Increases Remains Constant (C) Remains Constant Increases (D) Remains Constant Remains Constant
(C) Remains Constant, Increases Li = Lf, so the increase in w is the in the same proportion as the decrease in I, and the kinetic energy is equal to Iw^2, so the increase in w results in an overall increase in the kinetic energy
A turntable that is initially at rest is set in motion with a constant angular acceleration a. What is the angular velocity of the turntable after it has made one complete revolution? (A) radical (2a) (B) radical (2pi(a)) (C) radical(4pi(a)) (D) 4(pi)a
(C) radical(4pi(a)) theta = 2(pi) w^2 = w^2 + 2a(theta)
The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed w. If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres? (A) 2/1 (B) 1/2 (C) 1/4 (D) 1/8
(D) 1/8 L = Iw Lupper/Llower => 2ml^2/2(2m)(2L)^2 => 1/8
A uniform meter stick has a 45.0 g mass placed at the 20 cm mark as shown in the figure. If a pivot is placed at 42.5 cm mark and the meter stick remains horizontal in static equilibrium, what is the mass of the meter stick? (A) 45.0 g (B) 72.0 g (C) 120.0 g (D) 135.0 g
(D) 135 g (m1g)•r1 = (m2g)•r2 (45)(22.5) = m(7.5) = 135 g
A bowling ball of mass M and radius R whose moment of inertia about its center is (2/5)MR^2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is: (A) v^2/5g (B) 2v^2/5g (C) v^2/2g (D) 7v^2/10g
(D) 7v^2/10g Ktot = Krot + Ktrans Replace the moment of inertia in Krot with (2/5)MR^2 and solve for H (the height of the inclined plane)
A meterstick is supported at each side by a spring scale. A heavy mass is then hung on the meterstick so that the spring scale on the left hand side reads four times the value of the spring scale on the right hand side. If the mass of the meterstick is negligible compared to the hanging mass, how far from the right hand side is the large hanging mass? (A) 25 cm (B) 67 cm (C) 75 cm (D) 80 cm
(D) 80 cm 4F(1 - x) = (F)(x) 4F = 5Fx x = 4/5 = 0.80 m measured from right side
Two objects, of masses 6 and 8 kilograms, are hung from the ends of a stick that is 70 cm long and has marks every 10 cm, as shown. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord? (A) A (B) B (C) C (D) D
(D) D Two balance the torques on each side, we need to be closer to the heavier mass: (m1g)•r1 = (m2g)•r2 (6kg)(40cm) = (8kg)(30cm)
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed w of the wheel is increased from zero to wf in a time interval T. What is the average net torque on the wheel during the time interval? (A)wf/T (B) Iwf^2/T (C) Iwf/T^2 (D) Iwf/T
(D) Iwf/T t= = ∆L/∆t = (Iwf - 0)/T
A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs? (A) Linear momentum is converted to angular momentum (B) Rotational kinetic energy is conserved (C) Translational kinetic energy is conserved (D) Linear Momentum and Angular Momentum are both conserved
(D) Linear momentum and Angular momentum are both conserved Since it is a perfectly inelastic collision, KE is not conserved. As there are no external forces or torques, both linear and angular momentum are conserved
A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it up vertically, such that the cylinder is suspended in midair for a brief time interval ∆t and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is 1/2MR^2. The net force on the cylinder during the time interval ∆t is: (A) mg (B) T - mgr (C) mgr - T (D) Zero
(D) Zero If the cylinder is "suspended in midair" the the net force is zero
An ant of mass m clings to the rim of a flywheel of radius r as shown above. The flywheel rotates clockwise on a horizontal shaft S with a constant angular velocity w. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III? (A) mg (B) mw^2r (C) mw^2r - mg (D) mw^2r + mg
(D) mw^2r + mg Use Fnet = Fadhesion - mg
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined place of height h as shown above. If the plane has friction so that the sphere rolls without slipping, what is the speed v of the center of mass at the bottom of the incline? (A) radical(2gh) (B) (2Mghr^2)/I (C) radical((2Mghr^2)/I) (D) radical((2Mghr^2)/(I+Mr^2)
(D) radical((2Mghr^2)/(I+Mr^2) Mgh = Ktot = Krot + Ktrans Substitute v/r for w Solve for v
A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram. At what time t does the particle achieve its maximum positive acceleration? A) 1s B) 2s C) 3s D) 4 s
A Acceleration occurs when the mass is at negative displacements since the force will be acting in the opposite direction of the displacement to restore equilibrium. Based on F = k∆x, the most force, and therefore the acceleration, occurs where the most displacement is
A 0.1-kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t=0. What is the amplitude, in meters, of the resulting simple harmonic motion of the block? A) 1/40m B) 1/20m C) 1/4m D) 1/2m
A) At the current location all of the energy is gravitational potential. As the spring stretches to its max location all of that gravitational potential will become spring potential when it reaches its lowest point. When the box oscillates back up it will return to its original location converting all of its energy back to gravitational potential and will oscillate back and forth between these two positions. As such the maximum stretch bottom location represents twice the amplitude so simply halving the max ∆x will give the amplitude. Finding the max stretch: The initial height of the box h and the stretch ∆x have the same value (h=∆x)
A string is firmly attached to both ends. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. Assume the tension in the string and its mass per unit length do not change. Which of the following frequencies could NOT also produce a standing wave pattern in the string? A) 30 Hz B) 40 Hz C) 80 Hz D) 180 Hz
A) The given diagram is in the 3rd harmonic at 60 Hz. That means the fundamental is 20 Hz. The other possible standing waves should be multiples of 20
A pendulum with a period of 1s on Earth, where the acceleration due to gravity is g, is taken to another planet where its period is 2s. The acceleration due to gravity on the other planet is most nearly: A) g/4 B) g/2 C) 2g D) 4g
A) Based on T = (2pi)sqrt(L/g), 1/4 g would double the period
The simple pendulum consists of a 1.0 kilogram brass bob on a string about 1.0 meters long. It has a period of 2.0 seconds. The pendulum would have a period of 1.0 seconds if the: A) String were replaced by one about 0.25 meter long B) String were replaced by one about 2.0 meters long C) Bob were replaced by a 0.25 kg brass sphere D) Bob were replaced by a 4.0 kg brass sphere
A) Based on T = (2pi)sqrt(L/g), 1/4 the length equates to 1/2 the period
A force F at an angle theta above the horizontal is used to pull a heavy suitcase of weight mg a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is u. The work done by the frictional force is: A) -Fdcos(theta) B) -uFdcost(theta) C) -umgd D) -umgdcos(theta)
A) Constant velocity: Fnet = 0 f = Fx = Fcos(theta) W = -fD = -Fcos(theta)d
A mass m, attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. Its maximum displacement from its equilibrium position is A. What is the mass's speed as it passes through its equilibrium position? A) A•sqrt(k/m) B) A•sqrt(m/k) C) 1/A•sqrt(k/m) D) 1/A•sqrt(m/k)
A) Energy conservation: Usp = K 1/2KA^2 = 1/2mv^2
Assume that wavelengths are propagating in a uniform medium. If the frequency of the wave source doubles then: A) The wavelength of the waves halves B) The wavelength of the waves doubles C) The speed of the waves halves D) The speed of the waves doubles
A) For a given medium, speed is constant. Doubling the frequency halves the wavelength
A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest A sphere of mass m2, which is suspended from a string of length L, is displaced to the right as shown above and released from rest so that it swings like a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. Which of the following is true for both spheres? A)The maximum kinetic energy is attained as the sphere passes through its equilibrium position B) The maximum kinetic energy is attained as the sphere reaches its point of release C) The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position D) The maximum gravitational potential energy is attained when the sphere reaches the point of release E) The maximum total energy is attained only as the sphere passes through its equilibrium position
A) For the spring, equilibrium is shown where the maximum transfer of kinetic energy has occurred and likewise for the pendulum the bottom equilibrium position has the maximum transfer of potential energy into spring energy
If the frequency of the sound wave is doubled, the wavelength: A) Halves and the speed remains unchanged B) Doubles and the speed remains unchanged C) Halves and the speed halves D) Doubles and the speed doubles
A) Frequency and wavelength are inverses
A person vibrates the end of a string sending transverse waves down the string. If the person then doubles the rate at which he vibrates the string while maintaining the same tension, the speed of the waves: A) Is unchanged while the wavelength is halved B) Is unchanged while the wavelength is doubled C) Doubles while the wavelength is doubled D) Doubles while the wavelength is halved
A) Since the medium stays the same the speed remains constant. Based on v = f(upsidedown v) for constant speed, f and upside down v change as inverses
A pendulum bob of mass m on a cord of length L is pulled sideways until the cord makes an angle theta with the vertical as shown in the figure to the right. The change in potential energy of the bob during the displacement is: A) mgL(1 - cos(theta)) B) mgL(1-sin(theta)) C) mgLsin(theta) D) mgLcos(theta)
A) The potential energy at the first position will be the amount "lost" as the ball falls and this will be the change in potential energy U = mgh = mg(L = Lcos(theta))
A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning fork makes one complete vibration, the emitted wave travels: A) One wavelength B) About 340 meters C) A distance directly proportional to the square root of the air density D) A distance inversely proportional to the square root of the pressure
A) The time to make 1 cycle, is also the time it takes the wave to travel one wavelength
A softball player catches a ball of mass m, which is moving towards her with horizontal speed V. While bringing the ball to rest, her hand moved back a distance d. Assuming constant deceleration, the horizontal force exerted on the ball by the hand is: A) mV^2/(2d) B) mV^2/d C) 2mV/d D) mV/d
A) The word done by the stopping force equals the loss of kinetic energy -W = ∆k -Fd = (1/2mv^2)f - (1/2mv^2)i vf = 0 F = mv^2/2d
The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q coincide? The figure has one wave, P, that is a square with an arrow to the right and the other is Q with an arrow to the left and a small box on top and another small box on the bottom. A) Large box to left B) One large one small box in middle C) One large box in middle D) One large box on top and another small box on bottom
A) Use superposition and overlap the waves to see the resultant
When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position. Which of the following is true of the values of its speed and the magnitude of the restoring force? SPEED RESTORING FORCE A) Zero Maximum B) Zero Zero C) Maximum 1/2 Maximum D) Maximum Zero
A) At T/4 the mass reaches maximum displacement where the restoring force is at a maximum and pulling in the opposite direction and hence creating a negative acceleration. At maximum displacement, the mass stops momentarily and has zero velocity
Multiple correct: A standing wave pattern is created on a guitar string as a person tunes the guitar by changing the tension in the string. Which of the following properties of the waves on the string will change as a result of adjusting only the tension in the string? Select two answers: A) The speed of the traveling wave that creates the pattern B) The wavelength of the standing wave C) The frequency of the standing wave D) The amplitude of the standing wave
A, C) Based on v = sqrt(F/(m/l)), the tension changes the speed. Then based on f = nv/2L, this resulting speed change will effect the frequency also. But since the frequency increases in direct proportion to the speed, and v = f(wavelength), the wavelength should remain unchanged. The equation of the wave speed is not required for this problem.
Multiple Correct: Two fire trucks have sirens that emit waves of the same frequency. As the fire trucks approach a person, the person hears a higher frequency from truck X than from truck Y. Which of the following statements about truck X can be correctly inferred from this information? Select two answers: A) It is traveling faster than truck Y B) It is closer to the person than truck Y C) It is speeding up, and truck Y is slowing down D) Its wavefronts are closer together than truck Y
A, D) Based on the Doppler effect, only speed matters. The faster a vehicle is moving, the closer together the sound waves get compressed and the higher the frequency. Take the case of a very fast vehicle traveling at the speed of sound; the compressions are all right on top of each other. So faster speed means closer compressions and higher frequencies. Choice I must be true because X is a higher frequency so must be going faster. Distance to the person affects the volume but not the pitch so the choice II is wrong. III seems correct but its not. It doesn't matter whether you are speeding up or slowing down, it only matters who is going faster. For example, suppose truck X was going 5 mph and speeding up while truck Y was going 50 mps and slowing down, this is an example of choice III but would not meet the requirement that X has a higher frequency because only actual speed matters, not what is happening to that speed.
Multiple Correct: A disk sliding on a horizontal surface that has negligible friction collides with a rod that is free to move and rotate on the surface, as shown in the top view above. Which of the following quantities must be the same for the disk-rod system before and after the collision? Select two answers. (A) Linear Momentum (B) Angular Momentum (C) Kinetic Energy (D) Mechanical Energy
A/B KE or ME are not conserved because the collision is perfectly inelastic
Two wave pulses approach each other as seen in the figure. The wave pulses overlap at point P. Which diagram best represents that appearance of the wave pulses as they leave point P? There are two arrows in opposite directions, the boundary on the left has a square top and the boundary on the right has an upward down triangle. A) One arrow to the left, square, and triangle B) Two arrows both pointing outward with triangle on left square on right C) One arrow to the right, strange triangle on right D) One arrow to left, strange triangle on ledt
B) After waves interfere they move along as if they never met
A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along with the x-axis with simple harmonic motion of amplitude A. Which of the following statements about the block is correct? A) At x = 0, its acceleration is at a maximum B) At x = A, its displacement is at a maximum C) At x = A, its velocity is at a maximum D) At x = A, its acceleration is zero
B) Basic fact about SHM, amplitude is max displacement
A mass m attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. Its maximum displacement from its equilibrium position is A. What is the massless speed as it passes through equilibrium position? A) 0 B) A•sqrt(k/m) C) A•sqrt(m/k) D) 1/A•sqrt(k/m)
B) Conservation of Energy: Usp = K 1/2KA^2 = 1/2mv^2 Solve for v
Assume the speed of sound is 340 m/s. One stereo loudspeaker produces a sound with a wavelength of 0.68 meters while the other speaker produces sound with a wavelength of 0.65 meters. What would be the resulting beat frequency? A) 3 Hz B) 23 Hz C) 511.5 Hz D) 11,333 Hz
B) Determine each separate frequency using the speed of sound as 340 and v = f(upsidedown v) then subtract the two frequencies to get the beat frequency
Referring to a graph below of the displacement x versus time for a particle in simple harmonic motion (The graph is a positive sine function): Which of the following graphs shows the kinetic energy K of the particle as a function of time t for one cycle of motion? A) Upward Quadratic B) Positive Cosine C) Translated Sine D) Sine Function
B) Energy will never be negative. The max kinetic occurs at zero displacement and the kinetic energy became zero when at the maximum displacement
A ball is thrown vertically upwards with a velocity v and an initial kinetic energy Ek. When half way to the top of its flight, it has a velocity and kinetic energy respectively of: A) v/2, E/2 B) V/sqrt2, E/2 C) v/4, E/2 D) v/2, E/sqrt2
B) Halfway up you have gained half of the height so you gained 1/2 of potential energy. Therefore you must have lost 1/2 of the initial kinetic energy so E2 = (Ek/2)
The frequencies of the first two overtones (second and third harmonics) of a vibrating string are f and 3f/2. What is the fundamental frequency of this string? A) f/3 B) f/2 C) f D) 2f
B) Harmonics are multiples of the fundamental, so the fundamental must be f/2
A car of mass m slides across a patch of ice at a speed v with its brakes locked. It hits the dry pavement and skids to a stop in a distance d. The coefficient of kinetic friction between the tires and the dry road is u. If the car has a speed of 2v, it would have skidded a distance of: A) d B) 1.41d C) 2d D) 4d
B) Stopping distance is a work-energy relationship. Work done by friction to stop = loss of kinetic energy The mass cancels in the relationship, so changing the mass doesn't change the distance
Two wave pulses, each of wavelength v, are traveling toward each other along a rope as shown. When both pulses are in the region between points X and Y, which are a distance v apart, the shape of the rope is: A) Bump at right B) Straight C) Sinusoidal D) Bump at right downward
B) Superpose the two waves on top of each other to get the answer
A standing wave of frequency 5 Hz is set up on a string 2 meters long with notes at both ends and in the center, as shown above: The fundamental frequency of vibration of the string is: A) 1 Hz B) 2.5 Hz C) 5 Hz D) 10 Hz
B) The diagram shows the second harmonic in the string. Since harmonics are multiples, the first harmonic would be half of this
A small vibrating object S moves across the surface of a ripple tank producing the wave fronts shown above . The wave fronts move with speed v. The object is traveling in what direction and with what speed relative to the speed of the wave fronts produced? DIRECTION SPEED A) To the right Equal to v B) To the right Less than v C) To the left Less than v D) To the left Greater than v
B) The waves at the right are compressed because the object is moving right. However, the waves are moving faster than the object since they are out in front of where the object is
As sound travels from steel into air, both its speed and its: A) Wavelength increase B) Wavelength decrease C) Frequency increase D) Frequency remain unchanged
B) When sound travels into less dense medium, its speed decreases...however, like all waves when traveling between two mediums, the frequency remains constant. based on v = f(upsidedown v), if the speed decreases and the frequency is constant then the upsidedown v must decrease also
An object swings on the end of a cord as a simple pendulum with period T. Another object oscillates up and down on the end of a vertical spring also with period T. If the masses of both objects are doubled, what are the new values for the periods? PENDULUM MASS ON SPRING A) T/sqrt(2) T•sqrt(2) B) T T•sqrt(2) C) T•sqrt(2) T D) T•sqrt(2) T/sqrt(2)
B) The pendulum is unaffected by mass. Mass-spring system has mass causing the T to change proportional to the sqrt so since the mass is doubled the period is changing by sqrt(2)
The graph below was produced by a microphone in front of a turning fork. It shows the voltage produced from the microphone as a function of time. The function is a cosine wave. In order to calculate the speed of sound from the graph, you would also need to know: A) Pitch B) Wavelength C) Frequency D) Volume
B) To use v = (f)(upsidedownv) you also need the upside down v
Multiple correct: In the doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following? Select two answers: A) The loudness of the sound B) The speed of the source C) The speed of the observer D) The phase angle
B, C) A fact about the doppler effect. Can also be seen from the doppler equation
Multiple correct. The diagrams above represent 5 different standing sound waves set up inside of a set of organ pipes 1 meter long. Which of the following statements correctly relates the frequencies of the organ pipes shown? Select two answers. A) Cy is twice the frequency of Cx B) Cz is five times the frequency of Cx C) Oy is twice the frequency of Ox D) Ox is twice the frequency of Cx
B,C) Wavelengths of each are (dist/cycle) ... 4L, 4/3L, 4/5L, L, 2/3L Frequencies are f = v/(upsidedownv) v/4L, 3v/4L, 5v/4L, 3v/2L --- Oy is 2x Cy
Two objects of equal mass hang from independent springs of unequal spring constant and oscillate up and down. The spring of greater spring constant must have the: A) Smaller amplitude of oscillation B) Larger amplitude of oscillation C) Shorter period of oscillation D) Longer period of oscillation
C) Based on T = (2pi)sqrt(m/k) the larger spring constant makes a smaller period
The figure above shows a transverse wave traveling to the right at a particular instant of time. The period of the wave is 0.2s. Length of one wave is 5 cm. What is the speed of the wave? A) 4 cm/s B) 25 cm/s C) 50 cm/s D) 100 cm/s
C) By inspection, the wavelength is 10 cm f = 1/T = 5 Then use v = wavelength(f)
A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be the greatest? A) A B) B C) C D) D
C) Clearly at point C the waves are compressed so are more frequent
Referring to a graph below of the displacement x versus time for a particle in simple harmonic motion (The graph is a positive sine function): Which of the following graphs shows the kinetic energy K of the particle as a function of its displacement x? A) Upward Quadratic B) Positive Linear C) Downward Quadratic D) Downward Sine Funciton
C) Energy will never be negative. The max kinetic occurs at zero displacement and the kinetic energy became zero when at the maximum displacement
If the speed of sound in air is 430 m/s, the length of the organ pipe, open at both ends, that can resonate at the fundamental frequency of 136 Hz, would be: A) 0.40 m B) 0.80 m C) 1.25 m D) 2.5 m
C) For an open-open pipe the harmonic frequency is given by f = nv/2L with n=1
What would be the wavelength of the fundamental and first two overtones produced by an organ pipe of length L that is closed at one end and open at the other? A) L, 1/2L, 1/4L B) 1/2L, 1/4L, 1/6L C) 4L, 4/3L, 4/5L D) 4L, 2L, L
C) Now the length of the tube remains constant and the wave is changing within the tube to make each successive waveform. Each upside down v is given by: upside down v = dist/cycle so: v1 = 4L v3 = 4/3 L v5 = 4/5L
A 0.1-kilogram block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as shown above. The block is released from rest at time t=0. What will the resulting period of oscillation be? A) pi/40s B) pi/20s C) pi/10s D) pi/4s
C) Plug into period for mass-spring system T = 2(pi)sqrt(m/k)
The diagram shows two transverse pulses moving along a string. One pulse is moving to the right and the second is moving to the left. Both pulses reach point x at the same instant. What would be the resulting motion of point x as the two pulses pass each other? The arrow pointing to the left is in top of a triangle and the arrow pointing to the right is on top of an upside down triangle. The point x is directly in the middle of the two points. A) Down, up, down B) Up then down C) Up, down, up D) There would be no motion, the pulses cancel one another
C) Step the two pulses through each other a little bit at a time and use superposition to see how the amplitudes add. At first the amplitude jumps up rapidly, then the amplitude moves down as the rightmost negative pulse continues to propagate. At the very end of their passing the amplitude would be all the wave down and then once they pass the point will jump back up to the equilibrium
A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, Xmin and Xmax. The graphs can represent quantities associated with the oscillation as functions of the lengths x of the spring. Which graph can represent the kinetic energy of the block as a function of x? A) A B) B C) C D) D
C) The block momentarily stops at Xmin and Xmas, so must have zero K at these points. The box accelerates most at the ends of the oscillation since the force is the greatest there. This changing acceleration means that the box gains speed quickly at first but not as quickly as it approaches equilibrium. This means that the KE gain starts off rapidly from the endpoints and gets less rapid as you approach equilibrium where there would be a maximum speed and maximum K, but zero force so less gain in speed. This results in a curved graph
A tube is open at both ends with the air oscillating in the 4th harmonic. How many displacement nodes are located within the tube? A) 2 B) 3 C) 4 D) 5
C) To produce pipe harmonics, the ends are always antinodes. The first (fundamental) harmonic is when there are tow antinodes on the end and one node in between. To move to each next harmonic, add another node in the middle and fill the necessary antinodes. (ex, 2nd harmonic is ANANA so the 4th harmonic is ANANANANA and have four notes
Multiple correct: One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown and is reflected at wall. Properties of the reflected pulse include which of the following? Select two answers: A) It has a greater speed than that of the incident pulse B) It has a greater amplitude than that of the incident pulse C) It is on the opposite side of the string from the incident pulse D) It has a smaller amplitude than that of the incident pulse
C, D) When hitting a fixed boundary, some of the wave is absorbed, some is reflected inverted. The reflected wave has less amplitude since some of the wave is absorbed, but since the string has not changed its properties the speed of the wave should remain unchanged
The standing wave pattern diagrammed to the right with a total length of 1.0 m is produced in a string fixed at both ends. The speed of waves in the string is 2 m/s. What is the frequency of the standing wave pattern? A) 0.25 Hz B) 1 Hz C) 2 Hz D) 4Hz
D) From diagram, wavelength = 0.5 m. Find the frequency with v = f(upsidedown v)
A simple pendulum and mass m hanging on a spring both have a period of 1s when setting into small oscillatory motion on Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth? A) Both are shorter B) Both are the same C) The period of the mass on the spring is shorter; that of the pendulum is the same D) The period of the pendulum is shorter; that of the mass on the spring is the same
D) In a mass-spring system, both mass and spring constant affect the period
The graph shown represents the potential energy U as a function of the displacement x for an object on the end of a spring moving back and forth with amplitude Xo. Which of the following graphs represents the kinetic energy K of the object as a function of displacement x? A) Upward Quadratic B) Upward Absolute Value Function C) Straight LIne Above and Parallel to the X-Axis D) Downward Quadratic
D) As the object oscillates, its total mechanical energy is conserved and transfers from U to K back and forth. The only graph that makes sense to have an equal switch throughout is D
An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following: A) v > 0, a > 0 B) v > 0, a < 0 C) v > 0, a = 0 D) v = 0, a < 0
D) At T/4 the mass reaches maximum displacement where the restoring force is at a maximum and pulling in the opposite direction and hence creating a negative acceleration. At maximum displacement the mass stops momentarily and has zero velocity
A ball is dropped from a height of 10 meters onto a hard surface so that the collision at the surface may be assumed elastic. Under such conditions the motion of the ball is: A) Simple harmonic with a period of about 1.4s B) Simple harmonic with a period of about 2.8s C) Simple harmonic with an amplitude of 5m D) Periodic with a period of about 2.8s but not simple harmonic
D) Based on free fall, the time to fall down would be 1.4 seconds. Since the collision with the ground is elastic, all of the energy will be returned to the ball and it will rise back up to its initial height completing 1 cycle in a total time of 2.8 seconds. It will continue doing this oscillating up and down. However, this is not simple harmonic because to be simple harmonic the force should vary directly proportional to the displacement but that is not the case in this situation
A block on a horizontal frictionless plane is attached to a spring, as shown above. The block oscillates along with the x-axis with simple harmonic motion of amplitude A. Which of the following statements about the energy is correct? A) he potential energy of the spring is at a maximum at x = 0 B) The potential energy of the spring is at a minimum at x = A C) The kinetic energy of the block is at a minimum at x = 0 D) The kinetic energy of the block is at a maximum at x = A
D) Basic fact about SHM, spring potential energy is a min at x=0 with no spring stretch
A mass m is attached to a spring with a spring constant K. If the mass is set into simple harmonic motion by a displacement d from its equilibrium position, what would be the speed, v, of the mass when it returns to the equilibrium position? A) v = sqrt(md/k) B) v = sqrt(kd/m) C) v = sqrtkd/mg) D) v = d•sqrt(k/m)
D) Energy Conservation: Esp = K e/skd^2 = 1/2mv^2
A mass m is attached to a vertical spring stretching it distance d. Then, the mass is set oscillating on a spring with an amplitude of A, the period of oscillation is proportional to: A) sqrt(d/g) B) sqrt(g/d) C) sqrt(d/mg) D) sqrt(m^2g/d)
D) First use the initial stretch to find the spring constant Fsp = mg = k∆x k = mg/d Plug into: T = 2(pi)sqrt(m/k)
A 2 kg ball is attached to a 0.80 m string and whirled in a horizontal circle at a constant speed of 6 m/s. The work done on the ball during each revolution is: A) 90 J B) 72 J C) 16 J D) Zero
D) In a circle moving at a constant speed, the work done is zero since the force is always perpendicular to the distance moved as you move incrementally around the circle
A pipe that is closed at one end and open at the other resonates at a fundamental frequency of 240 Hz. The next lowest/highest frequency it resonates at is most nearly: A) 80 Hz B) 120 Hz C) 480 Hz D) 720 Hz
D) Open-closed pipes only have odd multiples of harmonic so next f is 3x f1
A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shown above left and released from rest. A sphere of mass m2, which is suspended from a string of length L, is displaced to the right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude. Assume that both spheres undergo simple harmonic motion. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant: A) L/m1g B) g/m2L C) m2g/L D) m1g/L
D) Set period formulas equal to each other and rearrange for k
For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20 cm. Waves travel on this string at a speed of 1200 cm/s. At what frequency is the string vibrated to produce this standing wave? A) 120 Hz B) 60 Hz C) 40 Hz D) 30 Hz
D) Two antinodes by definition will be 1/2upside down v apart. So 20 cm = 1/2(upsidedown v) and the upsidedown v = 40 cm. Then using v = f(upsidedownv) we have: 1200 = f(40)
An ideal massless spring is fixed to the wall at one end, as shown above. A block of mass M attached to the other end of the spring oscillates with amplitude A on a frictionless, horizontal surface. The maximums peed of the block is Vm. The force constant of the spring is: A) mg/A B) MgVm/2A C) MVm^2/2A D)MVm^2/A^2
D) Using energy conservation: Usp = K 1/2kA^2 = 1/2mVm^2 Solve for k
A tube of length L1 is open at both ends. A second tube of length L2 is closed at one end and open at the other end. This second tube resonates at the same fundamental frequency as the first tube. What is the value of L2? A) 4L1 B) 2L1 C) L1 D) 1/2L1
D) We should look at the harmonic shapes open-open vs open-closed Comparing the fundamental harmonic of the open-open pipe to the closed-open pipe. The closed-open pipe should be half as long as the open-open pipe in order to fit the proper number of wavelengths of the same waveform to produce the given harmonic in each
Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring? A) The kinetic and potential energies are equal to each other at all times B) The kinetic and potential energies are both constant C) The maximum potential energy is achieved when the mass passes through its equilibrium position D) The maximum kinetic energy and maximum potential energy are equal, but occur at different times
D) Energy is conserved here and switches between kinetic and potential which have maximums at different locations
A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are, respectively, Xmin and Xmas. The graphs can represent quantities associated with the oscillation as functions of the length x and the spring. Which graph can represent the total mechanical energy of the block spring system as a function of x? A) A B) B C) C D) D
D) Only conservative forces are acting which means mechanical energy must be conserved so it stays constant as the mass oscillates