Question 1

Determine the scalar product of  = 6.0  + 4.0  - 2.0  and  = 5.0  - 6.0  - 3.0  .

Accepted Answer

C

Question 2

A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3)
B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3)
If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

Accepted Answer

A

Question 3

If two nonzero vectors point in the same direction, their dot product must be zero.

Accepted Answer

The dot product of two vectors pointing in the same direction is positive, not zero, as it is equal to the product of their magnitudes.

Question 4

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

Accepted Answer

A force acting perpendicular to the direction of motion does no work on the object, as work is the dot product of force and displacement. Since no work is done, the kinetic energy of the object remains unchanged.

Question 5

The angle between vector  = 2.00  + 3.00  and vector  is  The scalar product of vectors  and  is 3.00. If the x component of vector  is positive, what is vector  .

Accepted Answer

The answer of The angle between vector  = 2.00...

Question 6

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Accepted Answer

The dot product of two vectors is zero if and only if the vectors are perpendicular (orthogonal) to each other.

Question 7

Determine the angle between the directions of vector  = 3.00  + 1.00  and vector  = -3.00  + 3.00  .

Accepted Answer

The answer of Determine the angle between the directions of...

Question 8

A stock person at the local grocery store has a job consisting of the following five segments: (1) picking up boxes of tomatoes from the stockroom floor
(2) accelerating to a comfortable speed
(3) carrying the boxes to the tomato display at constant speed
(4) decelerating to a stop
(5) lowering the boxes slowly to the floor.
During which of the five segments of the job does the stock person do positive work on the boxes?

Accepted Answer

Positive work is done when the force applied to an object is in the direction of the object's displacement. In segment (1), lifting the boxes off the floor involves applying a force upward, which is in the direction of the boxes' displacement, thus doing positive work. In segment (2), accelerating to a comfortable speed also involves applying a force in the direction of the boxes' motion, doing positive work. Segments (3), (4), and (5) involve either no work in the case of constant speed (since there's no acceleration) or work that does not contribute to the boxes' displacement in the desired direction, such as decelerating or lowering the boxes.

Question 9

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground

Accepted Answer

The answer of Two objects, one of mass m and...

Question 10

Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be

Accepted Answer

The slope of the displacement vs. applied force plot for an ideal elastic spring is the reciprocal of the spring constant, according to Hooke's Law (F = kx), where k is the spring constant.

Question 11

If  = 3  -  + 4  and  = x  +  - 5  , find x so  will be perpendicular to  .

Accepted Answer

The answer of If  = 3  - ...

Question 12

What is the angle between the vector  = +3  - 2  - 3  and the +y-axis?

Accepted Answer

The answer of What is the angle between the vector...

Question 13

Which of the graphs in the figure illustrates Hooke's Law?

Accepted Answer

The answer of Which of the graphs in the figure...

Question 14

The value of the dot product of two vectors depends on the particular coordinate system being used.

Accepted Answer

The dot product of two vectors is a scalar quantity that depends only on the magnitudes of the vectors and the cosine of the angle between them, not on the coordinate system.

Question 15

Which of the graphs in the figure represents a spring that gets less stiff the more it is stretched?

Accepted Answer

The answer of Which of the graphs in the figure...

Question 16

A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping?

Accepted Answer

Both objects experience the same constant braking force and both lose all their kinetic energy. The distance travelled by an object under a constant force is directly proportional to the square of its initial velocity, and inversely proportional to its mass. Since the ratio of mass to initial velocity is the same for both objects, they will travel the same distance before stopping.

Question 17

Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

Accepted Answer

Work is defined as the product of force and displacement in the direction of the force. Since the wall does not move, there is no displacement, and therefore, no work is done by either Joel or Jerry, regardless of the time spent pushing.

Question 18

A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point

Accepted Answer

At the highest point of the swing, the ball is momentarily at rest and its kinetic energy is zero. Therefore, the work done on the ball by gravity must be equal to its potential energy at that point, which is mgh, where m is the mass of the ball (3.00 kg), g is the acceleration due to gravity (9.81 m/s^2) and h is the height above the lowest point (2.00 m). This gives us a value of -118 J. Since the work done on the ball by the tension in the string is in the opposite direction to the displacement of the ball at all points of its motion, it does negative work. However, at the highest point of the swing, the displacement of the ball is zero and so the work done by the tension in the string is zero. Therefore, the total work done on the ball by gravity and the tension in the string is -118 J at the highest point of the swing.

Question 19

The scalar product of vector  = 3.00  + 2.00  and vector  is 10.0. Which of the following vectors could be vector  ?

Accepted Answer

The answer of The scalar product of vector  =...

Question 20

Two boys searching for buried treasure are standing underneath the same tree. One boy walks  east and then  north. The other boy walks  west and then  north. Find the scalar product of their net displacements from the tree.

Accepted Answer

The answer of Two boys searching for buried treasure are...

Quiz 9: Work and Kinetic Energy

Determine the scalar product of = 6.0 + 4.0 - 2.0 and = 5.0 - 6.0 - 3.0 .

A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3) B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3) If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

If two nonzero vectors point in the same direction, their dot product must be zero.

If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.

The angle between vector = 2.00 + 3.00 and vector is The scalar product of vectors and is 3.00. If the x component of vector is positive, what is vector .

If the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other.

Determine the angle between the directions of vector = 3.00 + 1.00 and vector = -3.00 + 3.00 .

Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. When they hit the ground

Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would be

If = 3 - + 4 and = x + - 5 , find x so will be perpendicular to .

What is the angle between the vector = +3 - 2 - 3 and the +y-axis?