Physical quantities, Units and Vectors Flashcards

Question

metre

Answer 1

the distance travelled by light in 1/299792458 sec0nd

Answer 2

the time interval of 9,192,631,770 periods or cycles of the duration of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom

Answer 3

is a constant current that will produce a force equal to 2 X 10^-7 newton per metre of length when maintained in two straight parallel conductors of infinite length of negligible circular cross section and placed one metre apart in the vaccum

Answer 4

the kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

Answer 5

the amount of a substance of a system which contains as many as there are carbon atoms in 0.012Kg of carbon-12

Answer 6

density {mass/volume}

Answer 7

Acceleration

Answer 8

force {mass X acceleration}

Answer 9

momentum {Kgms^-1}

Answer 10

joules per second{watts} {force x Velocity}

Answer 11

newton meter{force X distance}

Answer 12

NM^-2 {Force/Area}

Answer 13

an approximate measure of the size of a number equal to the logarithm(base 10) rounded to a whole number the smallest power of 10 required to represent a number

Answer 14

length mass and time

Answer 15

newton per metre

Answer 16

force X perpendicular distance

Answer 17

Angular velocity represents the rate of change of angular displacement and is measured in radians per second (rad/s). Radians are dimensionless, so angular velocity has the same dimension as frequency (1/time). The dimensional formula for angular velocity is: \text{[ω]} = \text{T}^{-1} Where T is time.

Answer 18

Viscous force is measured in the same units as force, typically in newtons (N). The dimensional formula for force is: F= MLT-2 Where: • M is mass, • L is length, and • T is time.

Answer 19

Viscous force is measured in the same units as force, typically in newtons (N). The dimensional formula for force is: F= MLT-2 Where: • M is mass, • L is length, and • T is time.

Answer 20

Viscous force is measured in the same units as force, typically in newtons (N). The dimensional formula for force is: \text{[F]} = \text{MLT}^{-2} Where: • M is mass, • L is length, and • T is time.

Answer 21

Viscous force is measured in the same units as force, typically in newtons (N). The dimensional formula for force is: \text{[F]} = \text{MLT}^{-2} Where: • M is mass, • L is length, and • T is time.

Answer 22

Viscosity (dynamic viscosity) is measured in pascal-seconds (Pa·s) or equivalently in units of N·s/m² or kg/(m·s). The dimensional formula for viscosity is: \text{[η]} = \text{ML}^{-1}\text{T}^{-1} Where: • M is mass, • L is length, and • T is time.

Answer 23

The vector product is anti–commutative: a × b = −b × a. Relations among the unit vectors for vector products are: i×j=k j×k=i k×i=j

Answer 24

can be described completely by their magnitudes

Answer 25

mass area volume density time temperature work energy power

Answer 26

can be described by their magnitude and direction

Answer 27

displacement velocity acceleration force weight momentum

Answer 28

c = absinφ where φ is the smallest angle between a and b. The direction of c is perpendicular to the plane containing a and b with its orientation given by the right–hand rule. One way of using the right–hand rule is to let the fingers of the right hand bend (in their natural direction!) from a to b; the direction of the thumb is the direction of c = a × b.

Answer 29

4.448221615260 newtons (exactly)

Answer 30

1u = 1.6605 × 10−27 kg

Answer 31

100 hectares

Answer 32

2.471 acres

Answer 33

A unit vector has a magnitude of 1 with no units.

Answer 34

a * b = |a| × |b| × cos(θ)

Answer 35

a · b = ab cos φ where a is the magnitude of a, b is the magnitude of b and φ is the angle between a and b.

Answer 36

a · b = ab cos φ where a is the magnitude of a, b is the magnitude of b and φ is the angle between a and b.

Answer 37

a·b=axbx +ayby +azbz

Answer 38

a·b=axbx +ayby +azbz

Answer 39

Why Work is a Scalar: 1. Dot Product: The dot product of two vectors (force and displacement) results in a scalar quantity. Since work is defined as a dot product, it is inherently scalar. 2. No Direction: Work represents a measure of energy transfer, and energy does not have direction—it’s only concerned with magnitude. Thus, work does not have components or direction associated with it, like vectors do. 3. Magnitude Only: When calculating work, we are only concerned with the amount of force applied and the distance moved in the direction of the force. There’s no need for directionality, so work is considered scalar. Clarifying Confusion: • Force and displacement are vector quantities, but work is the result of a dot product between these vectors, stripping the result of direction and leaving only magnitude. • You might encounter quantities like torque or momentum, which are vector quantities because they have direction, but work is specifically scalar because it measures the energy transferred, not how or in which direction.

Answer 40

Why Work is a Scalar: 1. Dot Product: The dot product of two vectors (force and displacement) results in a scalar quantity. Since work is defined as a dot product, it is inherently scalar. 2. No Direction: Work represents a measure of energy transfer, and energy does not have direction—it’s only concerned with magnitude. Thus, work does not have components or direction associated with it, like vectors do. 3. Magnitude Only: When calculating work, we are only concerned with the amount of force applied and the distance moved in the direction of the force. There’s no need for directionality, so work is considered scalar. Clarifying Confusion: • Force and displacement are vector quantities, but work is the result of a dot product between these vectors, stripping the result of direction and leaving only magnitude. • You might encounter quantities like torque or momentum, which are vector quantities because they have direction, but work is specifically scalar because it measures the energy transferred, not how or in which direction.

Answer 41

A dimensionless vector that has a magnitude of 1 Describes a direction in space and has no other physical significance

Answer 42

Yields a scalar quantity A•B = |A||B|cos £

Answer 43

Yields a vector product |AxB| = |A||B| sin £

Answer 44

When A and B are perpendicular Magnitude of the vector product will be maximum Sin 90 = 1

Answer 45

It is based on an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom (133Cs). When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to the other. One second (abbreviated s) is defined as the time required for 9,192,631,770 cycles of this microwave radiation

Answer 46

It is based on an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom (133Cs). When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to the other. One second (abbreviated s) is defined as the time required for 9,192,631,770 cycles of this microwave radiation

Answer 47

A cheap digital watch that gives the time as 10:35:17 a.m. is very precise (the time is given to the second), but if the watch runs several minutes slow, then this value isn’t very accurate. On the other hand, a grandfather clock might be very accurate (that is, display the correct time), but if the clock has no second hand, it isn’t very precise. A high-quality measurement is both precise and accurate.

Answer 48

A cheap digital watch that gives the time as 10:35:17 a.m. is very precise (the time is given to the second), but if the watch runs several minutes slow, then this value isn’t very accurate. On the other hand, a grandfather clock might be very accurate (that is, display the correct time), but if the clock has no second hand, it isn’t very precise. A high-quality measurement is both precise and accurate.

Answer 49

equal, no matter where they are located in space

Answer 50

equal, no matter where they are located in space

Answer 51

We define the negative of a vector as a vector having the same magnitude as the original vector but the opposite direction.

Answer 52

We define the negative of a vector as a vector having the same magnitude as the original vector but the opposite direction.

Answer 53

The magnitude of a vector quantity is a scalar quantity (a number) and is always positive. Note that a vector can never be equal to a scalar because they are different kinds of quantities. The expression ;AS = 6 m< is just as wrong as ;2 oranges = 3 apples

Answer 54

The magnitude of a vector quantity is a scalar quantity (a number) and is always positive. Note that a vector can never be equal to a scalar because they are different kinds of quantities. The expression ;AS = 6 m< is just as wrong as ;2 oranges = 3 apples

Answer 55

we can apply the triangle inequality, which states that the magnitude of the difference between two vectors must fall within a specific range: ∣S−T∣≤∣S∣+∣T∣ and ∣S−T∣≥∣∣S∣−∣T∣∣. Given that ∣S∣=3m and ∣T∣=4m, we calculate the bounds as follows: The maximum possible magnitude occurs when the vectors are aligned in the same direction, yielding: ∣S−T∣=3+4=7m. The minimum possible magnitude occurs when the vectors are aligned in opposite directions, yielding: ∣S−T∣=∣3−4∣=1m. Thus, the magnitude of S−T must lie between 1 m and 7 m. Now, checking the options: (i) 9 m: Not possible, as it exceeds the maximum limit of 7 m. (ii) 7 m: Possible. (iii) 5 m: Possible, as it lies between 1 m and 7 m. (iv) 1 m: Possible, as it matches the minimum magnitude. (v) 0 m: Not possible, as the vectors are not equal in magnitude. (vi) -1 m: Not possible, as magnitude cannot be negative. Therefore, the correct answers are: (ii) 7 m, (iii) 5 m, (iv) 1 m.

Answer 56

When subtracting vectors 𝑆−𝑇, the result is a new vector. The magnitude of this new vector can vary depending on the directions of the original vectors 𝑆 and 𝑇 Vector Magnitude: The magnitude of a vector is its "length," and we denote the magnitude of a vector 𝐴 as ∣𝐴∣ Difference between vectors: When two vectors are subtracted, the magnitude of the result can range from the sum of their magnitudes to the absolute difference of their magnitudes, depending on the directions of the vectors. Step 2: Applying the Triangle Inequality Theorem The Triangle Inequality Theorem provides us with bounds for the magnitude of the difference of two vectors. This theorem tells us that: ∣𝑆−𝑇∣ ≤ ∣𝑆∣+∣𝑇∣ ∣S−T∣≤∣S∣+∣T∣ and ∣S−T∣≥∣∣S∣−∣T∣∣. The upper bound is the sum of the magnitudes of the vectors. The lower bound is the absolute value of the difference between the magnitudes. This theorem helps establish the range of possible values for the magnitude of S−T. Step 3: Finding the maximum magnitude To find the maximum magnitude of S−T, we consider the case when 𝑆 and 𝑇 are pointing in opposite directions. In that case, the result is just the sum of their magnitudes. ∣S∣=3m ∣T∣=4m The maximum possible magnitude occurs when the vectors are in opposite directions (effectively aligned along the same line but pointing opposite), so: ∣S−T∣=∣S∣+∣T∣=3+4=7m. This gives us the upper limit of the magnitude. Step 4: Finding the minimum magnitude The minimum magnitude occurs when the vectors are pointing in the same direction. In that case, the vectors "cancel out" part of each other, and the magnitude of the difference is the absolute value of the difference between their magnitudes. So, we calculate the difference in magnitudes: ∣S−T∣=∣∣S∣−∣T∣∣=∣3−4∣=1m. This gives us the lower limit of the magnitude. Step 5: Possible Magnitude Range From steps 3 and 4, we now know that the magnitude of S−T must lie between 1 m and 7 m. This means that the magnitude of the difference vector can take any value between 1 m and 7 m, inclusive.

Answer 57

When dealing with vectors, it's important to understand that vectors have both magnitude (size) and direction. When we subtract two vectors, the resulting vector's magnitude depends on both the magnitude and direction of the original vectors. Vectors 𝑆 and 𝑇 S has a magnitude of 3 meters (denoted as ∣S∣=3m). T has a magnitude of 4 meters (denoted as ∣T∣=4m). Vector subtraction: The vector S−T is the difference between the two vectors. The magnitude of this difference depends on the direction of both vectors. The Triangle Inequality Theorem: The magnitude of the difference vector is bounded by the triangle inequality theorem. This theorem gives us the range of possible magnitudes for ∣S−T∣≤∣S∣+∣T∣ and ∣S−T∣≥∣∣S∣−∣T∣∣. Step-by-step breakdown: Maximum magnitude: The largest possible magnitude of S−T occurs when the vectors point in opposite directions. In this case, the magnitude of the difference is the sum of the magnitudes: ∣S−T∣=3+4=7m. Minimum magnitude: The smallest possible magnitude of S−T occurs when the vectors point in the same direction. In this case, the magnitude of the difference is the absolute value of the difference between the magnitudes: ∣S−T∣=∣3−4∣=1m. Thus, the possible magnitudes of S−T lie between 1 m and 7 m.

Answer 58

**(b) Point in the same direction** ### Explanation: When two vectors point in the same direction and you subtract them, their magnitudes subtract directly, which results in the smallest possible magnitude (or zero if they are equal). If they point in opposite directions, the magnitudes will add up, giving a larger resultant magnitude. If they are perpendicular, the magnitude of the resultant will be between the minimum and maximum possible values.

Answer 59

To find the smallest possible magnitude of the vector difference C - D, we can use the fact that the magnitude of the difference between two vectors depends on their relative direction. The smallest possible magnitude occurs when the two vectors are in the same direction. The formula for the magnitude of the difference between two vectors is: |C-D|=||C|-|D|| Substituting the magnitudes of C and D: |C-D|=5-9=|-4|=4m So, the smallest possible magnitude of C- D is 4 meters.

Answer 60

The maximum possible magnitude of \( E - F \) occurs when the vectors \( E \) and \( F \) are in opposite directions. In that case, the magnitudes add up, and the formula for the magnitude of the difference between the vectors becomes: \[ |E - F| = |E| + |F| \] is 9 meters.

Answer 61

**(c) The difference of the two magnitudes** ### Explanation: When two vectors are parallel and point in the same direction, their magnitudes simply subtract. The result of their difference will be the difference between their magnitudes. If the vectors are equal in magnitude, the result will be zero, but in general, it is just the difference between the magnitudes.

Answer 62

The maximum possible magnitude of A - B occurs when the two vectors A and B are in opposite directions. In that case, the magnitudes add up, and the formula for the magnitude of the difference between the vectors becomes: A-B= A + B Given that |A| = 4m and |B |= 4m, we can calculate: |A-B|=4m + 4m = 8 m Thus, the maximum possible magnitude is 8 m, and the correct answer is: (c) 8 m.

Answer 63

If two vectors have equal magnitudes but opposite directions, their sum results in a cancellation of their effects. In this case, the magnitude of their sum is: |A + (-A)| = 0 Therefore, the correct answer is: **(b) Zero**.

Answer 64

The magnitude of the difference vector X - Y is minimized when the vectors X and Y are in the same direction. This is because the difference in their magnitudes will be smallest when they are aligned in the same direction. So, the magnitude of the difference is minimized when the vectors X and Y are pointing in the same direction.

Answer 65

The smallest possible value of \( |A - B| \) occurs when the vectors \( A \) and \( B \) are in the same direction. In this case, the magnitude of the difference is: |A - B| = ||A| - |B|| = |10- 6| 4 Therefore, the correct answer is: **(a) 4 m**.

Answer 66

True components are not vectors The components Ax and Ay of a vector AS are numbers; they are not vectors themselves. This is why we print the symbols for compo- nents in lightface italic type with no arrow on top instead of in boldface italic with an arrow, which is reserved for vectors.

Answer 67

1. Dot product (A · B = 0): This occurs when the vectors are perpendicular (i.e., the angle between them is 90°). 2. Cross product (A × B = 0): This occurs when the vectors are parallel (i.e., the angle between them is 0° or 180°). It is impossible for both to be zero simultaneously for nonzero vectors. If the vectors are parallel, their dot product cannot be zero unless one of the vectors is zero, and if the vectors are perpendicular, their cross product cannot be zero. Conclusion: No, it is not possible for both A · B and A × B to be zero at the same time for nonzero vectors.

Answer 68

1. Dot product (A · B = 0): This occurs when the vectors are perpendicular (i.e., the angle between them is 90°). 2. Cross product (A × B = 0): This occurs when the vectors are parallel (i.e., the angle between them is 0° or 180°). It is impossible for both to be zero simultaneously for nonzero vectors. If the vectors are parallel, their dot product cannot be zero unless one of the vectors is zero, and if the vectors are perpendicular, their cross product cannot be zero. Conclusion: No, it is not possible for both A · B and A × B to be zero at the same time for nonzero vectors.

Answer 69

No, the magnitude of a vector cannot be less than the magnitude of any of its individual components. The magnitude of a vector is the resultant of all its components. Since the magnitude is based on the sum of the squares of the components, it is either equal to the largest component (in cases where one component dominates and the others are zero) or larger than each individual component (if multiple components are non-zero). Therefore, the magnitude of the vector will always be greater than or equal to the magnitude of any of its components.

Answer 70

No, the magnitude of a vector cannot be less than the magnitude of any of its individual components. The magnitude of a vector is the resultant of all its components. Since the magnitude is based on the sum of the squares of the components, it is either equal to the largest component (in cases where one component dominates and the others are zero) or larger than each individual component (if multiple components are non-zero). Therefore, the magnitude of the vector will always be greater than or equal to the magnitude of any of its components.

Answer 71

Disprove: Only one correct experiment is needed to disprove a theory, as one contradiction can invalidate the theory. • Prove: No number of experiments can definitively prove a theory; they can only provide evidence supporting it. Scientific theories remain open to revision with new data.

Answer 72

Disprove: Only one correct experiment is needed to disprove a theory, as one contradiction can invalidate the theory. • Prove: No number of experiments can definitively prove a theory; they can only provide evidence supporting it. Scientific theories remain open to revision with new data.

Answer 73

No, it is not possible to compute the tangent of 5.00 meters because the tangent function applies to angles, not lengths. A trigonometric function like tangent requires an angular input (in radians or degrees), not a distance.

Answer 74

• Height: This is a personal measurement; to convert height to centimeters, multiply meters by 100. • Weight: Weight in newtons can be calculated by multiplying mass (in kilograms) by the gravitational constant (9.81 m/s²).

Answer 75

• Yes, it is important because these mass standards are used to define and calibrate weights worldwide. Even small deviations could affect high-precision measurements in science, engineering, and industry.

Answer 76

• Yes, it is important because these mass standards are used to define and calibrate weights worldwide. Even small deviations could affect high-precision measurements in science, engineering, and industry.

Answer 77

• Radioactive decay, vibrations of quartz crystals (used in quartz clocks), or the orbital period of celestial bodies (like Earth’s rotation around the Sun) could define a time standard.

Answer 78

• Radioactive decay, vibrations of quartz crystals (used in quartz clocks), or the orbital period of celestial bodies (like Earth’s rotation around the Sun) could define a time standard.

Answer 79

• Stack a large number of sheets (e.g., 100), measure the total thickness with the ruler, and divide the measurement by the number of sheets to estimate the thickness of one sheet.

Answer 80

• Reynolds number (ratio of inertial forces to viscous forces), Strain (ratio of deformation to original length), and Coefficient of friction (ratio of frictional force to normal force) are examples of dimensionless quantities.

Answer 81

• Reynolds number (ratio of inertial forces to viscous forces), Strain (ratio of deformation to original length), and Coefficient of friction (ratio of frictional force to normal force) are examples of dimensionless quantities.

Answer 82

• If C = A + B = 0, A and B must have equal magnitudes but opposite directions, meaning they cancel each other out.

Answer 83

• No, it is not possible. If A · B = 0, the vectors are perpendicular. If A × B = 0, the vectors are parallel. They can’t be both at the same time unless one of the vectors is zero.

Answer 84

• No, it is not possible. If A · B = 0, the vectors are perpendicular. If A × B = 0, the vectors are parallel. They can’t be both at the same time unless one of the vectors is zero.

Answer 85

• A · A gives the magnitude squared of A: |A|^2. • A × A is always zero because the cross product of a vector with itself is zero.

Answer 86

• A · A gives the magnitude squared of A: |A|^2. • A × A is always zero because the cross product of a vector with itself is zero.

Answer 87

• A / |A| is a unit vector because its magnitude is 1. Its direction is the same as the direction of vector A.

Answer 88

• A / |A| is a unit vector because its magnitude is 1. Its direction is the same as the direction of vector A.

Answer 89

• The percent error is calculated as (10.0 \, \text{m} / 890,000 \, \text{m}) \times 100 = 0.00112\%.

Answer 90

• Generally, A × (B × C) and (A × B) × C do not have the same magnitude or direction. They follow different vector product rules and are not equal unless specific conditions hold (e.g., parallel vectors).

Answer 91

• The cross product A × B is perpendicular to A by definition. The dot product of any vector with a perpendicular vector is zero.

Answer 92

No, it only means A and B are perpendicular. They can both be nonzero.

Answer 93

No, it only means A and B are perpendicular. They can both be nonzero.

Answer 94

• No, it means A and B are parallel or one of them is zero.

Answer 95

• No, it means A and B are parallel or one of them is zero.

Answer 96

No, it does not follow. If A = 0, then both Ax and Ay must be zero.

Answer 97

• From north to south: The displacement is the diameter of the circle, because displacement is the straight-line distance between starting and ending points, so it’s 1000 m (diameter = 2 × 500 m). • One complete circle: The displacement is zero because the bicyclist returns to the starting point.

Answer 98

• From north to south: The displacement is the diameter of the circle, because displacement is the straight-line distance between starting and ending points, so it’s 1000 m (diameter = 2 × 500 m). • One complete circle: The displacement is zero because the bicyclist returns to the starting point.

Answer 99

Two vectors with different lengths cannot sum to zero; they must have equal magnitudes and opposite directions to sum to zero. • For three vectors, the sum can be zero if they form a closed triangle, meaning the vectors must have lengths that allow them to satisfy the triangle inequality theorem.

Answer 100

Two vectors with different lengths cannot sum to zero; they must have equal magnitudes and opposite directions to sum to zero. • For three vectors, the sum can be zero if they form a closed triangle, meaning the vectors must have lengths that allow them to satisfy the triangle inequality theorem.

Answer 101

No, time is not a vector quantity. Even though it has a direction (from past to future), it lacks the other essential feature of a vector: multiple components and the ability to operate in different directions. Time is considered a scalar.

Answer 102

No, time is not a vector quantity. Even though it has a direction (from past to future), it lacks the other essential feature of a vector: multiple components and the ability to operate in different directions. Time is considered a scalar.

Answer 103

• Yes, the name is correctly used because the instructions involve both direction and magnitude (such as speed or velocity), which are characteristics of vectors.

Answer 104

• No, a vector itself cannot be “negative.” However, the direction of a vector can be reversed, and we can describe one vector as the negative of another if they have the same magnitude but opposite directions.

Answer 105

• Yes, if two vectors have the same magnitude but opposite directions, one can be called the negative of the other. Would you like me to continue answering further questions in this series?

Answer 106

• Yes, if two vectors have the same magnitude but opposite directions, one can be called the negative of the other. Would you like me to continue answering further questions in this series?

Answer 107

• No, if the magnitude of a vector is zero, all of its components must be zero. • No, the magnitude of a vector is the result of the combination of its components, so it cannot be less than the magnitude of any individual component.

Answer 108

• No, if the magnitude of a vector is zero, all of its components must be zero. • No, the magnitude of a vector is the result of the combination of its components, so it cannot be less than the magnitude of any individual component.

Physical quantities, Units and Vectors Flashcards

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