An 8.0-kg object moving 4.0 m/s in the positive x direction has a one-dimensional collision with a 2.0-kg object moving 3.0 m/s in the opposite direction. The final velocity of the 8.0-kg object is 2.0 m/s in the positive x direction. What is the total kinetic energy of the two-mass system after the collision?
a. 32 J
b. 52 J
c. 41 J
d. 25 J
e. 29 J
[Ques. 2] A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnitude of the impulse exerted on the ball by the floor?
a. 9.6 N s
b. 2.4 N s
c. 6.4 N s
d. 1.6 N s
e. 1.0 N s
[Ques. 3] The value of the momentum of a system is the same at a later time as at an earlier time if there are no
a. collisions between particles within the system.
b. inelastic collisions between particles within the system.
c. changes of momentum of individual particles within the system.
d. internal forces acting between particles within the system.
e. external forces acting on particles of the system.
[Ques. 4] At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant?
a. 16 m/s
b. 45 m/s
c. 23 m/s
d. 20 m/s
e. 36 m/s
[Ques. 5] At an instant when a particle of mass 50 g has an acceleration of 80 m/s2 in the positive x direction, a 75-g particle has an acceleration of 40 m/s2 in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?
a. 60 m/s2
b. 56 m/s2
c. 40 m/s2
d. 50 m/s2
e. 46 m/s2
[Ques. 6] A 6.0-kg object moving 2.0 m/s in the positive x direction has a one-dimensional elastic collision with a 4.0-kg object moving 3.0 m/s in the opposite direction. What is the total kinetic energy of the two-mass system after the collision?
a. 30 J
b. 62 J
c. 20 J
d. 44 J
e. 24 J
[Ques. 7] Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m-high ladders. The center of mass of the Earth (mE = 5.90 1024 kg) is then displaced
a. 0 m.
b. 1.84 1023 m.
c. 1.84 1014 m.
d. 1.80 1013 m.
e. 2 m.
[Ques. 8] Two bodies with masses m1 and m2 are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2 . The magnitude of the velocity of the center of mass of this system of two bodies is
a. less than v1.
b. equal to v1.
c. equal to the average of v1 and v2.
d. greater than v1 and less than v2.
e. greater than v2.
[Ques. 9] At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system?
a. 3.8 m/s
b. 3.4 m/s
c. 5.0 m/s
d. 4.4 m/s
e. 4.6 m/s
[Ques. 10] Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (2, 2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin?
a. (3, 1) m
b. (+1, +3) m
c. (+3, 1) m
d. (1, 3) m
e. (0.5, 2) m
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