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