Third Examination
Physics 103
25 November 1980

#1. Three masses are positioned as shown:

2 kg at (2, 0) meters
1 kg at (-1, 2) meters
3 kg at (-1,-1) meters
The coordinates of the center of mass of the system (in meters) are: :

a) (0, -1)    b) (8, 5)     c) (8/6, 5/6)    d) (0, -1/6)     e) (0, 1)

#2.  A 70 kg man on a 20 kg boat walks 3 meters forward, as measured on the boat.  How far backward does the boat move, relative to a nearby pier.

Note: Neglect drag effects of the water.

a)  meters b)  6/7 meters       c)7/3 meters    d)  10.5 meters     e) 3 meters

#3.  Two particles, each of mass m, are placed initially at rest along the x-axis, one at x = +L and the other at x= -L

A constant force Fj acts on the mass initially located at x = +L for a time T.  There is no force acting on the mass at x = -L.  At the end of time T the center of mass is located at
a) (i mL + j ML)/(2m) b) i L + F0/(2m)   c) F0T2/(2m) j   d) F0T2/(4m)  j   e)  the origin 

#4.   The thrust [thrust is a force] required to accelerate a 20,000 kg rocket upward at an acceleration of  10 m/sec2 on the moon, where g = 1.6 m/sec2, is most nearly equal to

a)  6,960 Nt     b)  168,000 Nt     c)  23,000 Nt     d)   16,800 Nt    e)  232,000 Nt

#5.  A modern aircraft cannon can fire 100 two-kilogram shells per second.  If the muzzle velocity is 500 meters/second, the average "recoil force" exerted on the gun mounting is approximately

a) 500 Nt   b) 100,000 Nt   c) 1000 Nt   d) 50,000 Nt   e) 200 Nt

#6.  A particle of mass 2 kilograms is subject to the time-varying force given in the graph.  If the velocity of the particle at time t = 0 is zero, the velocity after three seconds is equal to

a) 8 m/sec b) 4 m/sec    c) zero    d) 6 m/sec   e) 22 m/sec

#7. An object, initially at rest, explodes into three pieces.  Two pieces of equal mass travel along the x-axis and y-axis, respectively, with the same speed of 10 m/sec.  The speed of the third piece, having a mass twice that of each other pieces, is about

a) 3.5 m/sec     b) 10 m/sec      c) 7.1 m/sec     d) 5.0 m/sec       e) 14.1 m/sec 

#8. A block of mass mA traveling on a frictionless horizontal table with a speed vA collides elastically with a block of different mass mB.  the block of mass mB is initially at rest.  Note:  this is a one-dimensional collision The speed of mB after the collision  is equal to

a) mA vA /(mA + mB)     b) 2 mA vA /(mA + mB)       c) zero            d) vA        e) 2 mB vA /(mA + mB)

#9. Two objects of equal mass m are heading toward one another with equal speeds v.  A massless spring of spring constant k is attached to one of the objects as shown.  In the one dimensional elastic collision of the objects, the maximum distance by which the spring is compressed is:

a) v Ö(m/k)       b) v Ö(2m/k)          c) v Ö(m/2k)        d) 2v Ö(m/k)       e) zero 

#10. A 2 kg block hangs at rest from a wire attached to the ceiling.  It is hit by a 0.05 kg bullet traveling horizontally at 200 m/sec.  If the collision is perfectly inelastic, the vertical distance above the original position to which the block and bullet rise is about:

a) 2000 m        b) 1.2 m         c) 4.9 m      d) 9 m        e) 10 m 

#11. An auto (weight = 3200 lb) traveling East at 45 ft/sec collides with a truck (weight = 9600 lb) traveling North at 30 ft/sec.  If the collision is perfectly inelastic, the loss in kinetic energy of the system (in ft-lb) is approximately

a) 7,520,000    b) 1,250    c)  110,000    d) 0    e) 235,000

#12. As shown in the sketch, a large particle (mass 2m) moves along the +x-direction with a small particle (mass m) initially at rest.  After the collision, the small particle is found moving with a velocity Ö3 v0 at an angle of 30o with respect to the x-direction (see sketch). The velocity (magnitude; angle below x-axis) of the large particle after the collision equals

a) v0; 60o     b) v0; 90o        c) Ö3v0 / 2; 60o       d) 2 v0; 30o        e) v0 / 2;  60o

#13. A stereo turntable accelerates uniformly from rest to 33 rev/min in 1.5 seconds.  The number of revolutions the turntable makes in the 1.5 seconds is about

a) 0.83    b)  49.5     c)  2.3     d)11   e) 0.41 

14. The angular acceleration of a bicycle wheel is constant at -0.10 rad/sec2 (clockwise). If its initial angular speed is  4.0 rad/sec2 (counter-clockwise), the net number of (counter-clockwise) revolutions it will have made at the end of 30 seconds is most nearly equal  to
a) 75      b) 120    c) 19       d) 7.2       e) 12

#15. An automobile is traveling at 22 ft/sec(15 mph).  If the radius of a tire on this auto is 1 ft, what is the angular velocity of the tire in rad/sec?  (Assume that the tire rolls without slipping.)
a) 3.5     b)138.2      c) 22     d) 0.38      e) 1260