تكلم مع الذكاء الاصطناعي
Deck 9: Energy in Nonisolated Systems
ملء الشاشة (f)
سؤال
A 2.0-kg particle has an initial velocity of 
m/s. Some time later, its velocity is 
m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?
A)17 J
B)49 J
C)19 J
D)53 J
E)27 J
m/s. Some time later, its velocity is m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?A)17 J
B)49 J
C)19 J
D)53 J
E)27 J
سؤال
سؤال
A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B? 
A)27 J
B)20 J
C)24 J
D)17 J
E)37 J
A)27 J
B)20 J
C)24 J
D)17 J
E)37 J
سؤال
سؤال
سؤال
A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B? 
A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J
A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J
سؤال
An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m? 
A)−10 J
B)+10 J
C)+30 J
D)−30 J
E)+40 J
A)−10 J
B)+10 J
C)+30 J
D)−30 J
E)+40 J
سؤال
The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m? 
A)52 J
B)44 J
C)36 J
D)60 J
E)25 J
A)52 J
B)44 J
C)36 J
D)60 J
E)25 J
سؤال
If the resultant force acting on a 2.0-kg object is equal to 
N, what is the change in kinetic energy as the object moves from 
m to 
m?
A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J
N, what is the change in kinetic energy as the object moves from m to m?A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J
سؤال
A 4.0-kg block is lowered down a 37° incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B? 
A)−58 J
B)−53 J
C)−68 J
D)−63 J
E)−47 J
A)−58 J
B)−53 J
C)−68 J
D)−63 J
E)−47 J
سؤال
A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m? 
A)−2 J
B)−18 J
C)−10 J
D)−26 J
E)+18 J
A)−2 J
B)−18 J
C)−10 J
D)−26 J
E)+18 J
سؤال
A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B? 
A)−3.3 J
B)+1.3 J
C)+3.3 J
D)−1.3 J
E)+4.6 J
A)−3.3 J
B)+1.3 J
C)+3.3 J
D)−1.3 J
E)+4.6 J
سؤال
As a 2.0-kg object moves from 
m to 
m, the constant resultant force acting on it is equal to 
N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?
A)62 J
B)53 J
C)73 J
D)86 J
E)24 J
m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?A)62 J
B)53 J
C)73 J
D)86 J
E)24 J
سؤال
سؤال
سؤال
A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point 
m. How much work is done by the given force during this displacement?
A)+45 J
B)−45 J
C)+30 J
D)−30 J
E)+75 J
m. How much work is done by the given force during this displacement?A)+45 J
B)−45 J
C)+30 J
D)−30 J
E)+75 J
سؤال
A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m? 
A)18 J
B)21 J
C)23 J
D)26 J
E)8 J
A)18 J
B)21 J
C)23 J
D)26 J
E)8 J
سؤال
A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point 
m. How much work is done by the given force during this displacement?
A)+60 J
B)+84 J
C)+72 J
D)+48 J
E)+57 J
m. How much work is done by the given force during this displacement?A)+60 J
B)+84 J
C)+72 J
D)+48 J
E)+57 J
سؤال
سؤال
A 3.0-kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37° above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement? 
A)−34 J
B)−64 J
C)−30 J
D)−94 J
E)+64 J
A)−34 J
B)−64 J
C)−30 J
D)−94 J
E)+64 J
سؤال
سؤال
سؤال
سؤال
Each of two vectors, 
and 
, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is 
. Which possibility is correct?
A)
and 
both lie along the positive x axis.
B)
lies along the positive x axis. 
lies along the negative x axis.
C)
and 
both lie along the positive y axis.
D)
lies along the negative x axis. 
lies along the negative y axis.
E)
lies along the positive y axis. 
lies along the negative x axis.
and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?A)
and both lie along the positive x axis.B)
lies along the positive x axis. lies along the negative x axis.C)
and both lie along the positive y axis.D)
lies along the negative x axis. lies along the negative y axis.E)
lies along the positive y axis. lies along the negative x axis. سؤال
A conservative force on a particle moving along the x axis is given by 
. Which of the following is a potential that is associated with this force?
A)
B)
C)
D)
E)No answer given above is correct.
. Which of the following is a potential that is associated with this force?A)
B)
C)
D)
E)No answer given above is correct.
سؤال
The only force acting on a 2.0-kg body as it moves along the x axis is given by Fx = (12 − 2.0x) N, where x is in m. The velocity of the body at x = 2.0 m is 5.5 
m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?
A)36 J
B)39 J
C)43 J
D)46 J
E)30 J
m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?A)36 J
B)39 J
C)43 J
D)46 J
E)30 J
سؤال
If 
, 
, and the angle between 
and 
(when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?
A)−13
B)+13
C)+37
D)−37
E)73
, , and the angle between and (when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?A)−13
B)+13
C)+37
D)−37
E)73
سؤال
If 
= 5.0, 
= 8.0, and α = 30°, determine the scalar product of the two vectors shown. 
A)−35
B)+35
C)−20
D)+20
E)+40
= 5.0, = 8.0, and α = 30°, determine the scalar product of the two vectors shown. A)−35
B)+35
C)−20
D)+20
E)+40
سؤال
If 
= 10, 
= 15, and α = 130°, determine the scalar product of the two vectors shown. 
A)+96
B)−96
C)+51
D)−51
E)−35
= 10, = 15, and α = 130°, determine the scalar product of the two vectors shown. A)+96
B)−96
C)+51
D)−51
E)−35
سؤال
Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct? 
A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.
A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.
سؤال
Each of two vectors, 
and 
, lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is 
. Which possibility is correct?
A)
and 
both lie along the positive x axis.
B)
lies along the positive x axis. 
lies along the negative x axis.
C)
and 
both lie along the positive y axis.
D)
lies along the negative x axis. 
lies along the negative y axis.
E)
lies along the positive y axis. 
lies along the negative y axis.
and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?A)
and both lie along the positive x axis.B)
lies along the positive x axis. lies along the negative x axis.C)
and both lie along the positive y axis.D)
lies along the negative x axis. lies along the negative y axis.E)
lies along the positive y axis. lies along the negative y axis. سؤال
Two vectors 
and 
are given by 
and 
. The scalar product of 
and a third vector 
is −16. The scalar product of 
and 
is +18. The z component of 
is 0. What is the magnitude of 
?
A)7.8
B)6.4
C)3.6
D)5.0
E)4.8
and are given by and . The scalar product of and a third vector is −16. The scalar product of and is +18. The z component of is 0. What is the magnitude of ?A)7.8
B)6.4
C)3.6
D)5.0
E)4.8
سؤال
سؤال
سؤال
سؤال
If 
= 6.0, 
= 5.0, and α = 40°, determine the scalar product of the two vectors shown. 
A)+19
B)+23
C)−19
D)−23
E)+30
= 6.0, = 5.0, and α = 40°, determine the scalar product of the two vectors shown. A)+19
B)+23
C)−19
D)−23
E)+30
سؤال
سؤال
سؤال
If the scalar product of two vectors, 
and 
, is equal to −3.5, if 
, and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of 
?
A)2.1
B)2.5
C)2.3
D)2.7
E)3.1
and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?A)2.1
B)2.5
C)2.3
D)2.7
E)3.1
سؤال
If the vectors 
and 
have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?
A)6.6
B)4.6
C)8.3
D)9.8
E)7.6
and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?A)6.6
B)4.6
C)8.3
D)9.8
E)7.6
سؤال
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العب
ملء الشاشة (f)
Deck 9: Energy in Nonisolated Systems
1
A 2.0-kg particle has an initial velocity of m/s. Some time later, its velocity is m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?
A)17 J
B)49 J
C)19 J
D)53 J
E)27 J
m/s. Some time later, its velocity is m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?A)17 J
B)49 J
C)19 J
D)53 J
E)27 J
17 J
2
A force acting on an object moving along the x axis is given by Fx = (14x − 3.0x2) N where x is in m. How much work is done by this force as the object moves from x = −1 m to x = +2 m?
A)+12 J
B)+28 J
C)+40 J
D)+42 J
E)−28 J
A)+12 J
B)+28 J
C)+40 J
D)+42 J
E)−28 J
+12 J
3
A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?
A)27 J
B)20 J
C)24 J
D)17 J
E)37 J
A)27 J
B)20 J
C)24 J
D)17 J
E)37 J
24 J
4
A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (−4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?
A)4.2 m
B)3.5 m
C)5.3 m
D)6.4 m
E)5.0 m
A)4.2 m
B)3.5 m
C)5.3 m
D)6.4 m
E)5.0 m
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5
How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?
A)0.22 kJ
B)0.20 kJ
C)0.24 kJ
D)0.27 kJ
E)0.31 kJ
A)0.22 kJ
B)0.20 kJ
C)0.24 kJ
D)0.27 kJ
E)0.31 kJ
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6
A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?
A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J
A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J
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7
An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?
A)−10 J
B)+10 J
C)+30 J
D)−30 J
E)+40 J
A)−10 J
B)+10 J
C)+30 J
D)−30 J
E)+40 J
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8
The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?
A)52 J
B)44 J
C)36 J
D)60 J
E)25 J
A)52 J
B)44 J
C)36 J
D)60 J
E)25 J
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9
If the resultant force acting on a 2.0-kg object is equal to N, what is the change in kinetic energy as the object moves from m to m?
A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J
N, what is the change in kinetic energy as the object moves from m to m?A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J
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10
A 4.0-kg block is lowered down a 37° incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?
A)−58 J
B)−53 J
C)−68 J
D)−63 J
E)−47 J
A)−58 J
B)−53 J
C)−68 J
D)−63 J
E)−47 J
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11
A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m?
A)−2 J
B)−18 J
C)−10 J
D)−26 J
E)+18 J
A)−2 J
B)−18 J
C)−10 J
D)−26 J
E)+18 J
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12
A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?
A)−3.3 J
B)+1.3 J
C)+3.3 J
D)−1.3 J
E)+4.6 J
A)−3.3 J
B)+1.3 J
C)+3.3 J
D)−1.3 J
E)+4.6 J
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13
As a 2.0-kg object moves from m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?
A)62 J
B)53 J
C)73 J
D)86 J
E)24 J
m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?A)62 J
B)53 J
C)73 J
D)86 J
E)24 J
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14
A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?
A)+0.29 kJ
B)−0.29 kJ
C)+30 J
D)−30 J
E)−50 J
A)+0.29 kJ
B)−0.29 kJ
C)+30 J
D)−30 J
E)−50 J
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15
A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm?
A)+2.0 J
B)+20 J
C)−2.0 J
D)−20 J
E)+40 J
A)+2.0 J
B)+20 J
C)−2.0 J
D)−20 J
E)+40 J
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16
A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point m. How much work is done by the given force during this displacement?
A)+45 J
B)−45 J
C)+30 J
D)−30 J
E)+75 J
m. How much work is done by the given force during this displacement?A)+45 J
B)−45 J
C)+30 J
D)−30 J
E)+75 J
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17
A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m?
A)18 J
B)21 J
C)23 J
D)26 J
E)8 J
A)18 J
B)21 J
C)23 J
D)26 J
E)8 J
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18
A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement?
A)+60 J
B)+84 J
C)+72 J
D)+48 J
E)+57 J
m. How much work is done by the given force during this displacement?A)+60 J
B)+84 J
C)+72 J
D)+48 J
E)+57 J
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19
A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20° above the horizontal. How much work is done by this force as the object moves 6.0 m?
A)78 J
B)82 J
C)85 J
D)74 J
E)43 J
A)78 J
B)82 J
C)85 J
D)74 J
E)43 J
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20
A 3.0-kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37° above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?
A)−34 J
B)−64 J
C)−30 J
D)−94 J
E)+64 J
A)−34 J
B)−64 J
C)−30 J
D)−94 J
E)+64 J
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21
The only force acting on a 2.0-kg body moving along the x axis is given by Fx = (2.0x) N, where x is in m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m?
A)4.2 m/s
B)3.6 m/s
C)5.0 m/s
D)5.8 m/s
E)2.8 m/s
A)4.2 m/s
B)3.6 m/s
C)5.0 m/s
D)5.8 m/s
E)2.8 m/s
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22
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
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
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23
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
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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24
Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
A) and both lie along the positive x axis.
B) lies along the positive x axis. lies along the negative x axis.
C) and both lie along the positive y axis.
D) lies along the negative x axis. lies along the negative y axis.
E) lies along the positive y axis. lies along the negative x axis.
and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?A)
and both lie along the positive x axis.B)
lies along the positive x axis. lies along the negative x axis.C)
and both lie along the positive y axis.D)
lies along the negative x axis. lies along the negative y axis.E)
lies along the positive y axis. lies along the negative x axis. فتح الحزمة
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25
A conservative force on a particle moving along the x axis is given by . Which of the following is a potential that is associated with this force?
A)
B)
C)
D)
E)No answer given above is correct.
. Which of the following is a potential that is associated with this force?A)
B)
C)
D)
E)No answer given above is correct.
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26
The only force acting on a 2.0-kg body as it moves along the x axis is given by Fx = (12 − 2.0x) N, where x is in m. The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?
A)36 J
B)39 J
C)43 J
D)46 J
E)30 J
m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?A)36 J
B)39 J
C)43 J
D)46 J
E)30 J
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27
If , , and the angle between and (when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?
A)−13
B)+13
C)+37
D)−37
E)73
, , and the angle between and (when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?A)−13
B)+13
C)+37
D)−37
E)73
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28
If = 5.0, = 8.0, and α = 30°, determine the scalar product of the two vectors shown.
A)−35
B)+35
C)−20
D)+20
E)+40
= 5.0, = 8.0, and α = 30°, determine the scalar product of the two vectors shown. A)−35
B)+35
C)−20
D)+20
E)+40
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29
If = 10, = 15, and α = 130°, determine the scalar product of the two vectors shown.
A)+96
B)−96
C)+51
D)−51
E)−35
= 10, = 15, and α = 130°, determine the scalar product of the two vectors shown. A)+96
B)−96
C)+51
D)−51
E)−35
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30
Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct?
A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.
A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.
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31
Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
A) and both lie along the positive x axis.
B) lies along the positive x axis. lies along the negative x axis.
C) and both lie along the positive y axis.
D) lies along the negative x axis. lies along the negative y axis.
E) lies along the positive y axis. lies along the negative y axis.
and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?A)
and both lie along the positive x axis.B)
lies along the positive x axis. lies along the negative x axis.C)
and both lie along the positive y axis.D)
lies along the negative x axis. lies along the negative y axis.E)
lies along the positive y axis. lies along the negative y axis. فتح الحزمة
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32
Two vectors and are given by and . The scalar product of and a third vector is −16. The scalar product of and is +18. The z component of is 0. What is the magnitude of ?
A)7.8
B)6.4
C)3.6
D)5.0
E)4.8
and are given by and . The scalar product of and a third vector is −16. The scalar product of and is +18. The z component of is 0. What is the magnitude of ?A)7.8
B)6.4
C)3.6
D)5.0
E)4.8
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33
Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (−2, −6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin?
A)(−1, −3) m
B)(−1, 2) m
C)(−1, 12) m
D)(−1, 7) m
E)(−1, 3) m
A)(−1, −3) m
B)(−1, 2) m
C)(−1, 12) m
D)(−1, 7) m
E)(−1, 3) m
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34
If the scalar (dot) product of two vectors is negative, it means that
A)there was a calculator error.
B)the angle between the vectors is less than 90 degrees.
C)the angle between the vectors is 90 degrees.
D)the angle between the vectors is greater than 270 degrees.
E)the angle between the vectors is between 90 and 180 degrees.
A)there was a calculator error.
B)the angle between the vectors is less than 90 degrees.
C)the angle between the vectors is 90 degrees.
D)the angle between the vectors is greater than 270 degrees.
E)the angle between the vectors is between 90 and 180 degrees.
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35
A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.
A)1
B)460
C)500
D)1000
E)35,000
A)1
B)460
C)500
D)1000
E)35,000
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36
If = 6.0, = 5.0, and α = 40°, determine the scalar product of the two vectors shown.
A)+19
B)+23
C)−19
D)−23
E)+30
= 6.0, = 5.0, and α = 40°, determine the scalar product of the two vectors shown. A)+19
B)+23
C)−19
D)−23
E)+30
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37
A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete could ascend in one minute while expending one horsepower is
A)4.
B)7.
C)65.
D)408.
E)4567.
A)4.
B)7.
C)65.
D)408.
E)4567.
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38
A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy.
A)746
B)3.43 × 105
C)3.73 × 105
D)7.46 × 105
E)2.61 × 107
A)746
B)3.43 × 105
C)3.73 × 105
D)7.46 × 105
E)2.61 × 107
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39
If the scalar product of two vectors, and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?
A)2.1
B)2.5
C)2.3
D)2.7
E)3.1
and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?A)2.1
B)2.5
C)2.3
D)2.7
E)3.1
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40
If the vectors and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?
A)6.6
B)4.6
C)8.3
D)9.8
E)7.6
and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?A)6.6
B)4.6
C)8.3
D)9.8
E)7.6
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41
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.
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.
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