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A 4.00 kg4.00 \mathrm{~kg} object is moving at 5.00 m/s5.00 \mathrm{~m} / \mathrm{s} NORTHWEST. It strikes a 6.00 kg6.00 \mathrm{~kg} object that is moving SOUTHWEST at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} . The objects collide perfectly inelastically (stick together) . The velocity of the 6.00 kg6.00 \mathrm{~kg} object after the collision is


A) 3.89 m/s3.89 \mathrm{~m} / \mathrm{s} at an angle of 35.0 degrees NORTH of WEST.
B) 2.33 m/s2.33 \mathrm{~m} / \mathrm{s} at an angle of 35.0 degrees NORTH of WEST.
C) 2.33 m/s2.33 \mathrm{~m} / \mathrm{s} at an angle of 45.0 degrees NORTH of WEST.
D) 3.89 m/s3.89 \mathrm{~m} / \mathrm{s} at an angle of 14.0 degrees NORTH of WEST.
E) 2.33 m/s2.33 \mathrm{~m} / \mathrm{s} at an angle of 14.0 degrees NORTH of WEST.

F) B) and C)
G) A) and B)

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A 3.00 kg3.00 \mathrm{~kg} mass is located at x=2.0 cm\mathrm{x}=2.0 \mathrm{~cm} and y=4.0 cm\mathrm{y}=-4.0 \mathrm{~cm} . A 3.00 kg3.00 \mathrm{~kg} mass is located at x=5.0 cm\mathrm{x}=-5.0 \mathrm{~cm} and y=\mathrm{y}= 2.0 cm2.0 \mathrm{~cm} . A 4.00 kg4.00 \mathrm{~kg} mass is located at x=3.0 cm\mathrm{x}=-3.0 \mathrm{~cm} and y=3.0 cm\mathrm{y}=-3.0 \mathrm{~cm} . Where is the center of mass (x,y) (\mathrm{x}, \mathrm{y}) ?


A) (+2.1 cm,1.8 cm) (+2.1 \mathrm{~cm},-1.8 \mathrm{~cm})
B) (0.10 cm,0.50 cm) (-0.10 \mathrm{~cm},-0.50 \mathrm{~cm})
C) (2.1 cm,1.8 cm) (-2.1 \mathrm{~cm},-1.8 \mathrm{~cm})
D) (+1.1 cm,2.0 cm) (+1.1 \mathrm{~cm},-2.0 \mathrm{~cm})
E) (2.1 cm,+1.8 cm) (-2.1 \mathrm{~cm},+1.8 \mathrm{~cm})

F) A) and B)
G) B) and D)

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An 1800 kg1800 \mathrm{~kg} car traveling at 35.0 m/s35.0 \mathrm{~m} / \mathrm{s} strikes a wall. If the car comes to rest in 0.500 seconds, then the magnitude of the average force of the wall on the car is


A) 3.33×105 N3.33 \times 10^{5} \mathrm{~N} .
B) 1.26×105 N1.26 \times 10^{5} \mathrm{~N} .
C) 0.640×105 N0.640 \times 10^{5} \mathrm{~N} .
D) 0.330×105 N0.330 \times 10^{5} \mathrm{~N} .
E) 2.77×105 N2.77 \times 10^{5} \mathrm{~N} .

F) A) and E)
G) A) and D)

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Two objects of equal mass and velocity hit a wall. They both rebound with the same velocity in the opposite direction. Both objects experience the same momentum change but one experiences twice the average force as the other. Which of the following statements is true?


A) The change in the kinetic energy is different for the two objects.
B) The contact time between one of the object and the wall is one-fourth the contact time of the other.
C) The contact time between one of the objects and the wall is 1/31 / 3 the contact time of the other.
D) The contact times between the objects and the wall are equal.
E) The contact time between one of the objects and the wall is twice the contact time of the other.

F) B) and E)
G) A) and B)

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A 4.00 kg4.00 \mathrm{~kg} ball is moving at 3.00 m/s3.00 \mathrm{~m} / \mathrm{s} to the NORTH and a 5.00 kg5.00 \mathrm{~kg} ball is moving at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} to the NORTHEAST. The total momentum of the system is


A) 43.00 kg m/s43.00 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 45.0 degrees NORTH of EAST.
B) 26.1 kg m/s26.1 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 69.7 degrees SOUTH of EAST.
C) 20.3 kg m/s20.3 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 24.6 degrees SOUTH of EAST.
D) 26.1 kg m/s26.1 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 24.6 degrees NORTH of EAST.
E) 20.3 kg m/s20.3 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 69.7 degrees NORTH of EAST.

F) A) and B)
G) B) and D)

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A 4.00 kg4.00 \mathrm{~kg} object is moving at 5.00 m/s5.00 \mathrm{~m} / \mathrm{s} NORTH. It strikes a 6.00 kg6.00 \mathrm{~kg} object that is moving WEST at 2.00 m/s\mathrm{m} / \mathrm{s} . The objects undergo a perfectly inelastic (stick together) collision. The kinetic energy lost in the collision is


A) 28.7 J28.7 \mathrm{~J} .
B) 34.8 J34.8 \mathrm{~J} .
C) 14.9 J14.9 \mathrm{~J} .
D) 20.4 J20.4 \mathrm{~J} .
E) 18.7 J18.7 \mathrm{~J} .

F) D) and E)
G) B) and C)

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A 5.00 kg5.00 \mathrm{~kg} ball is moving at 4.0 m/s4.0 \mathrm{~m} / \mathrm{s} to the right and a 6.00 kg6.00 \mathrm{~kg} ball is moving at 3.00 m/s3.00 \mathrm{~m} / \mathrm{s} to the left. The total momentum of the system is


A) 20 kg m/s20 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the right.
B) 18 kg m/s18 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the left.
C) 2.0 kg m/s2.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the left.
D) 2.0 kg m/s2.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the right.
E) 38 kg m/s38 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the right.

F) A) and B)
G) C) and E)

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A 4.00 kg4.00 \mathrm{~kg} object is moving at 5.00 m/s5.00 \mathrm{~m} / \mathrm{s} EAST. It strikes a 6.00 kg6.00 \mathrm{~kg} object that is at rest. The objects collide elastically. The velocity of 4.00 kg4.00 \mathrm{~kg} object after the collision is in the SOUTHWEST direction. The speed of the 6.00 kg6.00 \mathrm{~kg} object after the collision is


A) 3.02 m/s3.02 \mathrm{~m} / \mathrm{s} .
B) 3.96 m/s3.96 \mathrm{~m} / \mathrm{s} .
C) 2.38 m/s2.38 \mathrm{~m} / \mathrm{s} .
D) 4.06 m/s4.06 \mathrm{~m} / \mathrm{s} .
E) 5.22 m/s5.22 \mathrm{~m} / \mathrm{s} .

F) B) and C)
G) B) and E)

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A 30.00 kg30.00 \mathrm{~kg} mass falls from a height of 2.000 m2.000 \mathrm{~m} . The magnitude of the momentum of the mass just before it hits the ground is


A) 320.0 kg m/s320.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} .
B) 442.4 kg m/s442.4 \mathrm{~kg} \mathrm{~m} / \mathrm{s} .
C) 187.8 kg m/s187.8 \mathrm{~kg} \mathrm{~m} / \mathrm{s} .
D) 502.1 kg m/s502.1 \mathrm{~kg} \mathrm{~m} / \mathrm{s} .
E) 144.2 kg m/s144.2 \mathrm{~kg} \mathrm{~m} / \mathrm{s} .

F) None of the above
G) B) and C)

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A 4.00 kg4.00 \mathrm{~kg} ball is moving at 4.0 m/s4.0 \mathrm{~m} / \mathrm{s} to the right and a 6.00 kg6.00 \mathrm{~kg} ball is moving at 3.00 m/s3.00 \mathrm{~m} / \mathrm{s} to the left. The total momentum of the system is


A) 34 kg m/s34 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the left.
B) 16 kg m/s16 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the right.
C) 2.0 kg m/s2.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the right.
D) 2.0 kg m/s2.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the left.
E) 18 kg m/s18 \mathrm{~kg} \mathrm{~m} / \mathrm{s} to the left.

F) B) and E)
G) A) and E)

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D

If a 5.00 kg5.00 \mathrm{~kg} mass is moving EAST at 10.0 m/s10.0 \mathrm{~m} / \mathrm{s} and a 15.0 kg15.0 \mathrm{~kg} mass is moving WEST at 10 m/s10 \mathrm{~m} / \mathrm{s} , what is the velocity of the center of mass of the pair?


A) 5.0 m/sEAST5.0 \mathrm{~m} / \mathrm{s} \mathrm{EAST}
B) 5.0 m/sWEST5.0 \mathrm{~m} / \mathrm{s} \mathrm{WEST}
C) 10 m/s10 \mathrm{~m} / \mathrm{s} EAST
D) 10 m/s10 \mathrm{~m} / \mathrm{s} WEST

E) B) and C)
F) None of the above

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B

A 4.0 kg4.0 \mathrm{~kg} ball is traveling at 5.0 m/s5.0 \mathrm{~m} / \mathrm{s} to the right and strikes a wall. The ball bounces off the wall with a velocity of 4.0 m/s4.0 \mathrm{~m} / \mathrm{s} to the left. The change in momentum of the ball is


A) 4.0 kg m/s4.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} left.
B) 26 kg m/s26 \mathrm{~kg} \mathrm{~m} / \mathrm{s} left.
C) 36 kg m/sright.36 \mathrm{~kg} \mathrm{~m} / \mathrm{s} \mathrm{right.}
D) 36 kg m/s36 \mathrm{~kg} \mathrm{~m} / \mathrm{s} left.
E) 30 kg m/s30 \mathrm{~kg} \mathrm{~m} / \mathrm{s} right.

F) B) and E)
G) All of the above

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D

A 5.00 kg5.00 \mathrm{~kg} mass is moving at 4.00 m/s30.04.00 \mathrm{~m} / \mathrm{s} 30.0 degrees SOUTH of WEST and a 2.00 kg2.00 \mathrm{~kg} mass is moving at 3.00 m/s60.0\mathrm{m} / \mathrm{s} 60.0 degrees SOUTH of EAST. Find the velocity of the center of mass, letting (a) =(\mathrm{a}) = the east-west component, and (b) = the north-south component.


A) a=2.17 m/s,b=+2.05 m/s\mathrm{a}=-2.17 \mathrm{~m} / \mathrm{s}, \mathrm{b}=+2.05 \mathrm{~m} / \mathrm{s} .
B) a=+2.17 m/s,b=2.05 m/s\mathrm{a}=+2.17 \mathrm{~m} / \mathrm{s}, \mathrm{b}=-2.05 \mathrm{~m} / \mathrm{s} .
C) a=2.05 m/s,b=2.17 m/s\mathrm{a}=-2.05 \mathrm{~m} / \mathrm{s}, \mathrm{b}=-2.17 \mathrm{~m} / \mathrm{s} .
D) a=2.05 m/s,b=+2.17 m/s\mathrm{a}=-2.05 \mathrm{~m} / \mathrm{s}, \mathrm{b}=+2.17 \mathrm{~m} / \mathrm{s} .
E) a=+2.05 m/s,b=2.17 m/s\mathrm{a}=+2.05 \mathrm{~m} / \mathrm{s}, \mathrm{b}=-2.17 \mathrm{~m} / \mathrm{s} .

F) A) and C)
G) B) and E)

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A 2.0 kg2.0 \mathrm{~kg} ball is moving at 4.0 m/s4.0 \mathrm{~m} / \mathrm{s} WEST. The momentum of the ball is


A) 10 kg m/s10 \mathrm{~kg} \mathrm{~m} / \mathrm{s} WEST.
B) 6.00 kg m/s6.00 \mathrm{~kg} \mathrm{~m} / \mathrm{s} WEST.
C) 8.0 kg m/s8.0 \mathrm{~kg} \mathrm{~m} / \mathrm{s} WEST.
D) 12 kg m/s12 \mathrm{~kg} \mathrm{~m} / \mathrm{s} WEST.
E) 4.00 kg m/s4.00 \mathrm{~kg} \mathrm{~m} / \mathrm{s} WEST.

F) A) and C)
G) C) and E)

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An apple and an orange are connected by a straw of negligible mass. If the centers of the fruits are 26 cm26 \mathrm{~cm} apart and the center of mass of the pair is 11 cm11 \mathrm{~cm} from the apple, what is the ratio of mapple \mathrm{m}_{\text {apple }} to morange \mathrm{m}_{\text {orange }} ?


A) 26/1126 / 11
B) 15/1115 / 11
C) 15/2615 / 26
D) 26/1526 / 15
E) 11/1511 / 15
F) 11/2611 / 26

G) A) and B)
H) D) and E)

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A 3.00 kg3.00 \mathrm{~kg} object is moving at 5.00 m/s5.00 \mathrm{~m} / \mathrm{s} EAST. It catches up to and strikes a 6.00 kg6.00 \mathrm{~kg} that is moving EAST at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} . The objects undergo an elastic collision in the EAST-WEST direction. The velocity of the 3.00 kg3.00 \mathrm{~kg} object after the collision is


A) 4.00 m/s4.00 \mathrm{~m} / \mathrm{s} EAST.
B) 3.00 m/s3.00 \mathrm{~m} / \mathrm{s} EAST.
C) 1.00 m/s1.00 \mathrm{~m} / \mathrm{s} EAST.
D) 1.00 m/s1.00 \mathrm{~m} / \mathrm{s} WEST.
E) 4.00 m/s4.00 \mathrm{~m} / \mathrm{s} WEST.

F) B) and C)
G) None of the above

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A 30.0 g30.0 \mathrm{~g} mass is located at the origin. Where must a mass of 10.0 g10.0 \mathrm{~g} be located if the coordinates of the center of mass are (0.00 cm,10.0 cm) (0.00 \mathrm{~cm}, 10.0 \mathrm{~cm}) ?


A) (0.00 cm,5.00 cm) (0.00 \mathrm{~cm}, 5.00 \mathrm{~cm})
B) (0.00 cm,40.0 cm) (0.00 \mathrm{~cm}, 40.0 \mathrm{~cm})
C) (0.00 cm,20.0 cm) (0.00 \mathrm{~cm}, 20.0 \mathrm{~cm})
D) (0.00 cm,10.0 cm) (0.00 \mathrm{~cm}, 10.0 \mathrm{~cm})
E) (0.00 cm,7.50 cm) (0.00 \mathrm{~cm}, 7.50 \mathrm{~cm})

F) A) and B)
G) A) and E)

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A 3.00 kg3.00 \mathrm{~kg} mass is located at x=2.0 cm\mathrm{x}=2.0 \mathrm{~cm} and y=0.0 cm\mathrm{y}=0.0 \mathrm{~cm} . A 3.00 kg3.00 \mathrm{~kg} mass is located at x=0.0 cm\mathrm{x}=0.0 \mathrm{~cm} and y=\mathrm{y}= 2.0 cm2.0 \mathrm{~cm} . A 4.00 kg4.00 \mathrm{~kg} mass is located at x=3.0 cmx=3.0 \mathrm{~cm} and y=3.0 cmy=-3.0 \mathrm{~cm} . Where is the location of the center of mass?


A) (3.5 cm,0.6 cm) (3.5 \mathrm{~cm},-0.6 \mathrm{~cm})
B) (0.60 cm,1.8 cm) (0.60 \mathrm{~cm},-1.8 \mathrm{~cm})
C) (1.8 cm,0.60 cm) (1.8 \mathrm{~cm}, 0.60 \mathrm{~cm})
D) (1.8 cm,0.60 cm) (1.8 \mathrm{~cm},-0.60 \mathrm{~cm})
E) (1.8 cm,1.6 cm) (1.8 \mathrm{~cm}, 1.6 \mathrm{~cm})

F) A) and E)
G) A) and D)

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A 4.00 kg4.00 \mathrm{~kg} object is moving at 3.00 m/s3.00 \mathrm{~m} / \mathrm{s} WEST. It catches up to and strikes a 6.00 kg6.00 \mathrm{~kg} that is moving WEST at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} . The objects undergo an elastic collision in the EAST-WEST direction. The velocity of the 4.00 kg\mathrm{kg} object after the collision is


A) 1.80 m/s1.80 \mathrm{~m} / \mathrm{s} EAST.
B) 1.80 m/s1.80 \mathrm{~m} / \mathrm{s} WEST.
C) 1.00 m/s1.00 \mathrm{~m} / \mathrm{s} WEST.
D) 2.80 m/s2.80 \mathrm{~m} / \mathrm{s} WEST.
E) 2.80 m/s2.80 \mathrm{~m} / \mathrm{s} EAST.

F) All of the above
G) A) and E)

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A 4.00 kg4.00 \mathrm{~kg} ball is moving at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} to the WEST and a 6.00 kg6.00 \mathrm{~kg} ball is moving at 2.00 m/s2.00 \mathrm{~m} / \mathrm{s} to the NORTH. The total momentum of the system is


A) 21.6 kg m/s21.6 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 17.7 degrees NORTH of WEST.
B) 21.6 kg m/s21.6 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 56.3 degrees NORTH of WEST.
C) 21.6 kg m/s21.6 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 45.2 degrees SOUTH of WEST.
D) 14.4 kg m/s14.4 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 45.2 degrees SOUTH of WEST.
E) 14.4 kg m/s14.4 \mathrm{~kg} \mathrm{~m} / \mathrm{s} at an angle of 56.3 degrees NORTH of WEST.

F) A) and B)
G) C) and E)

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