Final Examination
Physics 103
15 December 1980

#1.  The angle between the vectors A = 6 i - 3 j + 2 k and B = 3 i + 4 j is most nearly equal to
Answer:

a) 80o     b)  30o    c)  10o     d)  0o     e)  60o    

#2.  The displacement vs time graph of  moving automobile is given as shown.  The average speed of the automobile between 0 sec and 3 sec is approximately


Answer:
a) l9.8 m/sec     b) 9.1 m/sec     c) 13.2 m/sec     d) 9.9 m/sec     e) 0 m/sec
#3. An el train accelerates from rest at one station at 1 m/sec2 for half the distance to the next station; then it decelerates at this same rate for the final half.  If the stations are 2 km apart, how long does it take the train to travel between stations?
Answer:
a) 63.2 sec b) 44.7 sec c) 28.2 sec d) 282 sec e) 89.4 sec

#4.  A gun shoots a dart at an angle of 60o above the horizontal.  The dart lands a horizontal distance 10 meters away from the gun muzzle.  What is the speed of the dart as it leaves the gun?
Answer:
a) 7.0 m/sec    b) 9.2 m/sec   c) 14.0 m/sec     d) 9.9 m/sec      e) 10.6 m/sec
#5.  The earth rotates once about its axis in about 24 hours.  The magnitude of  the centripetal acceleration of an object on the equator is most nearly equal to (Note:  Radius of the earth is 6.37 ´ 106 m.)


Answer:
a) 436600 m/sec2   b)  8.5 ´ 10-4 m/sec2  c)  0.03 m/sec2  d)  11060 m/sec2)   e) 0 m/sec2)
#6.  A block of mass M is at rest on a horizontal, frictionless surface.  It is attached to a massless cord which is passed over a frictionless, massless pulley to another mass, m, which is hanging freely.  See sketch.  The system is then released from rest.  The tension in the cord is

Answer:
a) (m + M )g b) m M g/(m + M ) c) (M - M) g/(m + M )
d) (M - m )g e) m  g (M + 2 m)/(m + M )
#7. A 50 kg box rests on a horizontal floor with coefficient of friction µ = 0.4 (Assume µs = µk.)  The horizontal force (in Nt) required to accelerate the box at 0.5 m/sec2 is about
Answer:
a) 25 b) 171 c) 221 d) 10 e) 196
#8. A block of mass m is moving on a rough horizontal surface in the direction of the positive x-axis, while somebody is pulling on it with a force of magnitude F, directed at an angle q with respect to the horizontal.  The coefficient of sliding friction is µ.  The total force of the table on the block is

Answer:
a) (-i µ + j) (m g - F sin q )   
b)-i µ m g   
c) i ( F sin  q - µ m g) +   j  m g
d) -i µ m g cos q  + j F cos q   
e) -i µ (m g cos q - F sin q ) + j (m g - F sin q )
#9. A box of mass m = 1.5 slugs compresses a spring (k = 3000 lb/ft) by 0.3 ft.  After it is released, the box slides for 8 ft on a rough level surface (µK = 0.3).  Its speed (in ft/sec) after sliding 8 ft is about

Answer:
a) 0     b) 26.4      c) 333.6     d) 5.1     e) 18.2
#10. (Note:  See figure for previous problem.)  Assuming the velocity of the mass is V0 as it leaves the surface, if the height h is known, then x (the horizontal distance the mass travels before hitting the ground)  is given by:

Answer:

a) V02 /( 2g)    b) - g h2/ (2V02)     c) V0Ö(2h/g)   d) Ö(V02  - 2g h)    e) V0 /( 2g h)  
#11. A toy gun is powered by a spring (spring constant k).  It is loaded with a dart (mass m) and the spring is compressed by an amount x.  The dart is then fired vertically upward from the gun.  Assuming that only conservative forces are present, the height to which the dart rises above its initial position is equal to
Answer:
a) 2g / a    b) 2k x / m    c) kx2/(2m g)   d) m g / (2 k x)   e) 2m g ) (k x)
#12. The loaded cab of an elevator has a mass of 3000 kg and moves 200 meters up the shaft in 20 sec.  The average power (in Watts) is most nearly equal to
Answer:
a) 294000   b) 30000   c) 1.3   d) 3\0.75   e) 7000
#13. A small particle of mass m is attached to the perimeter of a uniform disc of radius R and mass M.  The center of mass of the resulting combination is a distance from the center of the disc equal to
Answer:
a) m R / M    b) M R / ( m + M)    c) zero   d) R  e) m R / ( m + M)
#14. A 0.5 kg baseball travels toward a batter at 40 m/sec.  The batter hits the ball, imparting an average force of 900 Nt for 50 milliseconds to the ball.  If the ball reverses direction, its final speed (in m/sec) is most nearly equal to
Answer:
a) 50    b) 130    c) 100    d) 1800    e) 90
#15.  A stream of small balls strikes a wall normally and rebounds elastically.  If the balls have a mass of 0.25 ´ 10-3 kg each, a speed of 100 m/sec, and strike the wall at a rate of 100 per second, the magnitude of the average force imparted to the wall by the balls in one second is equal to
Answer:
a) 0.025 Nt    b) 0.50 Nt    c) 1.0 Nt     d) 2.5 Nt     e) 5.0 Nt    
#16. In a football game, a player weighting 256 lb runs toward the ball carrier at 20 ft/sec.  The ball carrier weight 192 lbs and is running toward the player with a speed of 30 ft/sec.  If the collide in a tackle which is perfectly inelastic, their final speed is about
Answer:
a) 130/7 ft/sec    b) 130/7 ft/sec      c) 130/7 ft/sec     d)130/7 ft/sec      e) 10/7 ft/sec 
#17.  An object of mass 1.0 kg, traveling North with a speed of 400 m/sec, explodes into two pieces of equal mass.  After the explosion, one piece travels due West with a speed of 600 m/sec.  The other piece will have a momentum of magnitude (in kg m/sec)
Answer:
a)  200    b) 300   c)  400    d) 500    e) 720
#18.  A railroad car (m = 30,000 kg) with an initial velocity of 5 m/sec collides elastically with another car of equal mass, initially at rest.  The velocity of the second car after the collision is
Answer:
a) 2.5 m/sec b) 5 m/sec c)  0 m/sec d) 10 m/sec e) 25 m/sec
#19. A straight uniform rod is constrained to rotate about a vertical axis through its midpoint.  Its moment of inertia about this axis is 0.5 kg m2.  It is observed to make 45 revolutions before coming to rest in 30 seconds, because of a constant frictional torque at the axis.  The value of the constant angular acceleration (in revolutions/sec2) is most nearly equal too
Answer:
a) -p/5      b) -0.1      c)  0      d) +0.1      e) + p/5   
#20.  Referring to Problem #19, the frictional torque (in Newton-meters) is most nearly equal to
Answer:
a) -1.0    b) -0.7    c) -0.5    d) -0.3    e) -0.1   
#21. A grinding wheel of radius 5 cm is accelerated at a constant angular acceleration of 15 rad/sec2.  the wheel starts from rest at time t = 0 sec.  At time t = 2 sec, a particle flies off the edge of the wheel.  The linear velocity with which the particle flies off (in meters/sec) is approximately
Answer:
a) 3.6    b) 1.5    c) 150    d) 30    e) 600   
#22. Two particles, each of mass 1 kg, are moving in the x-y plane as shown.  The first, located at (x = 1 meter, y = 1 meter), has a velocity of 1 meter/sec to the left.  The second, located at (-1 m, -1 m), has a velocity of 1 meter/sec to the right.  The angular momentum of the two particles about the origin (in SI units) is
Answer:
a) + 2.0 k    b) - 2.8 k    c) zero    d) + 28 k   e)  1.4 ( i   +  j  )
#23. Three equal masses, M, lie in a plane at the corners of an equilateral triangle of side L.  the rotational inertia (moment of inertia) of the three-mass system  about an axis perpendicular to the plane of the triangle and passing through the center of mass is
Answer:
a) M L2    b) 3M L2    c) 2M L2 /3   d) 3M L2 /4      e) 3 ML2 /2  
#24. A hollow ball (Icm = 2M R2 /3), initially traveling at a velocity vcm (without sliding),  rolls up an incline with angle q as measured from the horizontal.  Assuming R is small compared with H, the height H that the ball travels before coming to rest is given by
Answer:
a) vcm2 /2g    b) 5vcm2 /6g   c)    vcm2 /g R d) vcm2 sin q /6g   e)  5vcm sin  q /6g   
#25. On the evening of December 24, a man of mass m wishes to descend a chimney of height H.  In order to do so, he wraps a rope of negligible mass about the rim of a wheel of mass M and radius R,  With the wheel initially at rest, he grasps the rope and steps into the chimney.  Assume that the wheel is a uniform disk.  The speed of the man as he reaches the bottom of the chimney is
Answer:
a) Ö(2m g h)   b) Ö[4m g h/(m+2M)]   c) Ö( g h)  
d) Ö[2m g h/(m+M)]   e) Ö(4m g h/M)