Sample Exam 2 Phys 106

SAMPLE EXAM 2 PHYS 106 ______

1 2 1 2  = I; work: W =  ; Wtot = K = I  I ; Angular momentum: L = I l = mvrsinφ I11 = I22 2 f 2 i 2 m m M  4  3 2R GM gravitation: F= G 1 2 ; G = 6.67x10-11 Nm2/ kg2, W = mg, g = G ; T2 =  r ; v  ; p 2 2   sat vsat  r r  GM  T R 24 6 Mearth = 5.98x10 kg, Rearth = 6.37 x10 m static equilibrium: F = 0; FX = 0 FY = 0 ;  = 0  = rFsin;

2 Oscillations: x = x cos(t+) v = -  x sin(t+) a = - 2 x cos(t+)  = 2f = F = -kx m m m T

m 1 2 k period: Tspring = 2 ; f = vmax = xm  amax = xm   = k T m

2 Wheel 1 1. One wheel of rotational inertia I1 = 2 kgm is rotating freely at 20 rad/sec in counterclockwise direction on a shaft. A second 2 wheel of rotational inertia I2 = 5 kgm , rotating freely at 15 rad/sec in the opposite direction, is suddenly coupled along the same shaft to the first wheel. Afterwards, the coupled wheel system rotates at A) 1.00 rad/s, counterclockwise Wheel 2 B) 2.25 rad/s , clockwise C) 4.50 rad/s , clockwise D) 5.00 rad/s , counterclockwise E) 5.00 rad/s , clockwise

2. A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg × m2 . It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:

A. 0.61 rad/s B. 0.73 rad/s C. 0.80 rad/s D. 0.89 rad/s E. 1.1 rad/s

3. In figure a 1.0 g bullet is fired into a 0.45 kg block that is mounted on the end of a 0.60 m uniform rod of mass 0.50 kg. The block–rod–bullet system then rotates about a fixed axis at point A. Assume the block is small enough to treat as a particle on the end of the rod. If the speed of the bullet just before the impact is 300 m/s, what is the angular speed of the block–rod–bullet system about A just after the bullet's impact?

A) 0. 5 rad/s B) 0.8 rad/s C) 2.5 rad/s D) 4.9 rad/s E) 6.6 rad/s

0 4. A 20 kg traffic lights are suspended from a cable as shown. Find the tension T1 if  = 25 . A) 120 N B) 165 N C) 196 N D) 220 N E) 420 N

A uniform 150-kg strut, which is 3.44 m long, is pinned at one end and supported at the other end by a horizontal cable..

5. The tension in the cable is closest to 2.8 A) 1000 N B) 1450N m C) 1600 N D) 2000 N 2.0 E) 2450 N m

6. Find the force from the pin on the beam. A) 1000 N B) 1450N C) 1800 N D) 2060 N E) 2450 N

1 7. A uniform ladder of mass 25 kg and length of 9.0 m is leaning against a smooth wall, making an angle θ with horizontal. If the ladder is just on the verge of slipping when the angle θ is 500 , what is the coefficient of the static friction between the ladder and the ground? ( Neglect friction between the ladder and the wall.)

A) 0.42 B) 0.85 C) 0.24 D) 0.71 E) 0.12

8. A uniform 400-N beam 6 m long rests on two supports, as shown. The force exerted on the beam by the left support A is closest to A B

A) 50 N B) 160 N C) 240 N 1 m 5 m D) 320 N E) 400 N

9. An uniform 720-N beam, 3 m long, is supported by a cable that makes 400 angle with horizontal. The tension in the cable is:

A) 350 N B) 460 N C) 560 N D) 670 N E) 736 N

0 10. A uniform beam of length 5.0 m and negligible mass is attached to the vertical wall and supports a 120 kg ball as shown in the figure. If θ 1 = 40 0 and θ2 = 60 what is the force that the wall exerts on the beam?

A) 1460 N B) 2920N C) 3420N D) 514 0N E) 7680 N

11. The mass of the moon is 7.4x1022 kg and its mean radius is 1.73x106 m . What is the gravitational acceleration at the surface of the moon?

A) 15.4 m/s2 B) 9. 8 m/s2 C) 3.4 m/s2 D) 1.6 m/s2 E) 0.8 m/s2

12. The earth has radius R. A satellite of mass 100 kg is at a point 2R from the surface of the earth. What is the satellite's weight?

A) 110 N B) 420 N C) 980 N D) 1310 N E) 1800 N

13. The period of earth's satellite is 185 min. What is its altitude?

A) 6541 km B) 4380 km C) 3980 km D) 1678 km E) 1240 km

2 14. A planet is in circular orbit around the Sun. Its distance from the Sun is 3.75 x1011m. and its period is 4 years. What is the mass of the sun ?

A. 1.09x1020 kg. B. 4.25x1024 kg. C. 5.41x1028 kg. D. 1.99x1030 kg. E. 2.39x1031 kg.

15. A satellite moves in a circular orbit around Earth at a speed of 5850 m/s? How much time does it take for the satellites to make one revolution? A) 3.5 h B) 5.5 h C) 8.0 h D) 12.0 h E) 17.5 h

16. The distance of Jupiter from the Sun is 5.2 times the average distance of Earth from the Sun. Calculate the number of years required for Jupiter to make one revolution about the Sun. A) 12 years B) 8 years C) 5 years D) 3 years E) 1 year

17. The motion of a piston in an auto engine is simple harmonic. The piston travels back and forth over a distance of 18 cm, and the piston has a mass of 1.6 kg. What is the maximum speed of the piston when the engine is running at 5000 rpm?

m A) 21 /s m B) 34 /s m C) 47 /s m D) 59 /s m E) 72 /s

18. A vertical spring stretches a distance d when a block of 0.350 kg is hung from its end. This block is then displaced from its equilibrium position and undergoes 100 periods of oscillations in 48.9 s. What is the stretch distance d? (Hint: assuming the oscillations are harmonic, find the spring constant first).

A) 2.35 cm B) 4.71 cm C) 5.94 cm D) 6.28 cm E) 7.52 cm

19. The position of simple harmonic oscillator along the x-axis is given by x = (12.4 cm) cos(6.35rad/s∙ t ). At what time after t = 0 is the mass first located at x = 8.47 cm?

A) 4.34 s B) 0.108 s C) 0.129 s D) 7.39 s E) 0.842 s