Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A 4.8-kg block attached to a spring executes simple harmonic motion on a frictionless horizontalsurface. At time t = 0 s, the block has a displacement of -0.50 m, a velocity of -0.80 m/s, and anacceleration of +8.3 m/s2. The force constant of the spring is closest to:A) 56 N/m B) 62 N/m C) 73 N/m D) 80 N/m E) 67 N/m

1)

2) A 3.4-kg block attached to a spring executes simple harmonic motion on a frictionless horizontalsurface. At time t = 0 s, the block has a displacement of -0.50 m, a velocity of -0.80 m/s, and anacceleration of +3.8 m/s2. The amplitude of the motion is closest to:A) 0.80 m B) 3.8 m C) 0.88 m D) 0.58 m E) 0.72 m

2)

3) A 1.5-kg block on a horizontal frictionless surface is attached to a spring whose force constant is220 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacementx = +0.080 m and is released from rest. The block then executes simple harmonic motion alongthe x-axis (horizontal). The displacement of the block at time t = 0.70 s is closest to:A) 0.07 m B) -0.5 m C) 0.04 m D) -0.04 m E) -0.07 m

3)

4) A 1.6-kg block on a horizontal frictionless surface is attached to a spring whose force constant is190 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacementx = +0.080 m and is released from rest. The block then executes simple harmonic motion alongthe x-axis (horizontal). The velocity of the block at time t = 0.40 s is closest to:A) -0.8 m/s B) -0.3 m/s C) 0.8 m/s D) 0.3 m/s E) zero

4)

5) A 0.13-kg block on a horizontal frictionless surface is attached to a spring whose force constantis 500 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacementx = +0.080 m and is released from rest. The block then executes simple harmonic motion alongthe x-axis (horizontal). When the displacement is x = 0.018 m, the kinetic energy of the block isclosest to:A) 1.5 J B) 1.4 J C) 1.7 J D) 1.8 J E) 1.6 J

5)

6) A 0.028-kg block on a horizontal frictionless surface is attached to a spring whose force constantis 170 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacementx = +0.080 m and is released from rest. The block then executes simple harmonic motion alongthe x-axis (horizontal). When the displacement is x = -0.054 m, the acceleration of the block isclosest to:A) 250 m/s2 B) 970 m/s2 C) 160 m/s2 D) 820 m/s2 E) 330 m/s2

6)

7) A 0.068-kg block on a horizontal frictionless surface is attached to a spring whose force constantis 390 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacementx = +0.080 m and is released from rest. The block then executes simple harmonic motion alongthe x-axis (horizontal). The maximum elastic potential energy of the system is closest to:A) 1.1 J B) 1.2 J C) 1.4 J D) 1.5 J E) 1.6 J

7)

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Figure 13.1

8) In Fig. 13.1, two masses, M = 10 kg and m = 8 kg, are attached to a spring of spring constant100 N/m. The system is set into oscillation with an amplitude of 58 cm. At the instant when theacceleration is at maximum, the 10-kg mass separates from the 8-kg mass, which then remainsattached to the spring and continues to oscillate. The amplitude of oscillation of the 8-kg masswill be:A) 46 cm B) 58 cm C) 130 cm D) 73 cm E) 26 cm

8)

9) For an object undergoing simple harmonic motion,A) the acceleration is greatest when the speed is greatest.B) the acceleration is greatest when the displacement is greatest.C) the displacement is greatest when the speed is greatest.

D) the total energy oscillates at frequency f = 12π

km.

E) the maximum potential energy is larger than the maximum kinetic energy.

9)

10) A particle is in simple harmonic motion along the x-axis with a period of 1.4 s and an amplitudeof 0.78 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is atx = +0.47 m and it is moving in the negative x-direction. The magnitude of the velocity of theparticle, at time t = 0 s , is closest to:A) 2.8 m/s B) 4.6 m/s C) 4.1 m/s D) 5.5 m/s E) 3.5 m/s

10)

11) A particle is in simple harmonic motion along the x-axis with a period of 7.7 s and an amplitudeof 0.51 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is atx = +0.36 m and it is moving in the negative x-direction. The x-component of the acceleration,at time t = 0 , is closest to:A) -0.34 B) 0.34 C) -0.24 D) 0.24 E) zero

11)

12) A particle is in simple harmonic motion along the x-axis with a period of 3.7 s and an amplitudeof 0.64 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is atx = +0.38 m and it is moving in the negative x-direction. The time interval required for theparticle to reach x = - 0.64 m from its initial position at t = 0 s is closest to:A) 2.6 s B) 1.3 s C) 2.0 s D) 2.3 s E) 1.6 s

12)

13) A particle is in simple harmonic motion along the x-axis with a period of 3.5 s and an amplitudeof 0.32 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is atx = +0.26 m and it is moving in the negative x-direction. At time t = 0, the ratio of the potentialenergy to the total mechanical energy is closest to:A) 0.72 B) 0.64 C) 0.80 D) 1.1 E) 1.4

13)

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Situation 13.1A 0.90-kg solid disk has a radius of 10 cm and a thickness of 1.0 cm. The disk is used as a balance wheel in a mechanismand the torsion constant is 0.020 N ∙ m/rad.

14) In Situation 13.1, the period of oscillation of the wheel is closest to:A) 4.2 s B) 1.5 s C) 2.1 s D) 3.0 s E) 1.1 s

14)

15) In Situation 13.1, the torque required to hold the wheel at a 90° angular displacement fromequilibrium is closest to:A) 0.05 N ∙ mB) 0.01 N ∙ mC) 0.04 N ∙ mD) 0.03 N ∙ mE) 0.02 N ∙ m

15)

Figure 13.2

16) In Fig. 13.2, a mass of 2 kg is attached to three springs of spring constants 1 N/m, 2 N/m, and3 N/m. When the mass is at rest the springs are unstretched. For this system:A) ω2 = 3/2 rad/s2

B) ω2 = 1 rad/s2

C) ω2 = 1/2 rad/s2

D) ω2 = 3 rad/s2

E) ω2 = 2 rad/s2

16)

17) It has been suggested that a possible transportation system to connect two cities such as Bostonand Washington, D.C., might function like this: Drill a tunnel straight from Boston toWashington. A car released in Boston would fall under the influence of gravity, gaining speed,and then finally coasting back to the surface at Washington. The only expenditure of energyrequired would be that to overcome friction, and this could be reduced by using an evacuatedtunnel or magnetic levitation of the train or other possible techniques. Assuming the density ofthe earth is constant (it isn't), and using only the value of the acceleration of gravity at the earth'ssurface (9.8 m/s2) and the radius of the earth (6380 km) determine how long it would take totravel between any two cities via a straight tunnel. The result, rather surprisingly, is about:A) 58 minutesB) 42 minutesC) 1 hour 23 minutesD) 2 hours 54 minutesE) 6 hours 33 minutes

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Situation 13.2The x-component of the velocity of an object vibrating along the x-axis obeys the equation vx(t) = (0.445 m/s) sin[(25.4rad/s)t + 0.223].

18) In Situation 13.2, the amplitude of the motion is closest to:A) 0.445 m B) 0.223 m C) 0.0175 m D) 0.247 m E) 25.4 m

18)

19) In Situation 13.2, the maximum acceleration of the vibrating object is closest to:A) 287 m/s2

B) 0.286 m/s2

C) 25.4 m/s2

D) 0.445 m/s2

E) 11.3 m/s2

19)

Situation 13.3The angle with the vertical of a swinging simple pendulum obeys the equationΘ(t) = (0.150 rad) cos[(2.85 rad/s)t + 1.66].

20) In Situation 13.3, the length of the pendulum is closest to:A) 3.44 m B) 0.15 m C) 1.21 m D) 0.83 m E) 2.02 m

20)

21) In Situation 13.3, the mass of the swinging bob at the end of the pendulum is closest to:A) 0.454 kgB) 2.85 kgC) 0.150 kgD) 1.66 kgE) It cannot be determined from the information given.

21)

22) A mass at the end of an ideal spring vibrates with period T. If you double the mass, by whatfactor must you change the force constant of the spring so that the period of vibration will nowbe 2T?A) Decrease it by a factor of 2.B) Decrease it by a factor of 2.C) Increase it by a factor of 2.D) Decrease it by a factor of 4.E) Increase it by a factor of 2.

22)

23) A 2.00-kg mass is attached to an ideal horizontal spring of force constant 100.0 N/m and is atrest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to a pegin the table. Suddenly this mass is struck by another 2.00-kg mass traveling along the x-axis at3.00 m/s, and the two masses stick together. For the oscillations that result from this collision,the amplitude and period are closest to:A) 0.424 m, 1.26 sB) 0.300 m, 1.26 sC) 0.300 m, 0.889 sD) 0.424 m, 0.889 sE) 0.424 m, 5.00 s

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24) A meter stick is freely pivoted about the 20-cm mark. The frequency of small amplitudeoscillations is closest to:A) 1.5 Hz B) 0.7 Hz C) 0.5 Hz D) 1.2 Hz E) 0.9 Hz

24)

25) A coin is placed on a platform attached to a spring that oscillates vertically in simple harmonicmotion. The amplitude of the displacement is 1.20 cm. What is the maximum frequency forwhich the coin will always remain in contact with the platform?A) 6.89 Hz B) 8.75 Hz C) 12.2 Hz D) 4.55 Hz E) 2.25 Hz

25)

26) If both the mass of a simple pendulum and its length are doubled, the period willA) be unchanged.B) increase by a factor of 2.C) increase by a factor of 0.71.D) increase by a factor of 4.E) increase by a factor of 1.4

26)

27) What happens when a periodic driving force is applied to a vibrating system?A) The system will vibrate at the frequency of the driving force.B) The system will stop vibrating and finally come to a stop.C) It will vibrate at some multiple of the driving frequency (called a harmonic or "overtone").D) The system will vibrate at its natural frequency.E) The system will exhibit chaotic motion.

27)

Situation 13.4A 5.0-kg block is attached to a spring whose force constant is 125 N/m. The block is pulled from its equilibrium positionat x = 0 m to a position at x = +0.687 m and is released from rest. The block then executes damped oscillation along thex-axis. The damping force is proportional to the velocity. When the block first returns to x = 0 m, its x-component ofvelocity is -2.0 m/s and its x-component of acceleration is +5.6 m/s2.

28) In Situation 13.4, the magnitude of the acceleration of the block upon release at x = +0.687 m isclosest to:A) 16.4 m/s2

B) 19.6 m/s2

C) 18.0 m/s2

D) 18.8 m/s2

E) 17.2 m/s2

28)

29) In Situation 13.4, the damping coefficient b is closest to:A) 14 kg/s2 B) 22 kg/s2 C) 16 kg/s2 D) 18 kg/s2 E) 20 kg/s2

29)

30) In Situation 13.4, the work done by the damping force during the travel of the block fromx = +0.687 m to x = 0 m is closest to:A) -20 J B) -30 J C) -25 J D) -15 J E) -10 J

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

31) An object of mass 6.8 kg is attached to a spring of force constant 1780 N/m. The object isset into simple harmonic motion, with an initial velocity of ν o = 3.2 m/s and an initialdisplacement of x o = 0.14 m. Calculate the maximum velocity the object has during itsmotion.

31)

32) An object is undergoing simple harmonic motion with frequency f = 9.7 Hz andamplitude A = 0.12 m. At t = 0 the object is at x = 0. How long does it take the object togo from x = 0 to x = 0.024 m?

32)

33) A large stick is pivoted about one end and allowed to swing back and forth as a physicalpendulum. The mass of the stick is 5.20 kg and its center of gravity (found by finding itsbalance point) is 2.00 m from the pivot. If the period of the swinging stick is4.10 seconds, what is its moment of inertia, about an axis through the pivot?

33)

34) A 4.50-kg weight hangs from a vertical massless ideal spring. When set in verticalmotion, the weight obeys the equation y(t) = (6.20 cm) cos[(2.74 rad/s)t - 1.40]. Find: (a)the time for this weight to vibrate one complete cycle, (b) the maximum speed andmaximum acceleration of the weight, (c) the total distance the weight moves through inone cycle, (d) the maximum kinetic energy of the weight, and (e) the force constant ofthe spring.

34)

Figure 13.3

35) In Fig. 13.3, a 0.24-kg ball is suspended from a string 9.79 m long and is pulled slightlyto the left. As the ball swings through the lowest part of its motion it encounters a springattached to the wall. The spring pushes against the ball and eventually the ball isreturned to its original starting position. Find the time for one complete cycle of thismotion if the spring constant is 21 N/m. (Assume that once the pendulum ball hits thespring there is no effect due to the vertical movement of the ball.)

35)

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