Chapter 1 Physical Quantities & Units

Question 1

The Newton (N), the unit of force, is defined by the equation

Answer 1

• Force = mass × acceleration
• N = kg × m s–2 = kg m s–2
• Therefore, the Newton (N) in SI base units is kg m s–2

Question 2

The Joule (J), the unit of energy, is defined by the equation

Answer 2

• Energy = ½ × mass × velocity²
• J = kg × (m s–1)2 = kg m2 s–2
• Therefore, the Joule (J) in SI base units is kg m2 s–2

Question 3

The Pascal (Pa), the unit of pressure, is defined by the equation:

Answer 3

• Pressure = force ÷ area
• Pa = N ÷ m2 = (kg m s–2) ÷ m2 = kg m–1 s–2
• Therefore, the Pascal (Pa) in SI base units is kg m–1 s–2

Question 4

SI units table

Answer 4

Question 5

Powers of Ten Table

Answer 5

Question 6

Homogeneity of Physical Equations

Answer 6

• The units on either side of the equation should be the same
• to check the homogeneity of physical equations:

1. Check the units on both sides of an equation
2. Determine if they are equal
3. If they do not match, the equation will need to be adjusted

Question 7

A scalar

Answer 7

is a quantity which only has a magnitude (size)

Question 8

A vector

Answer 8

is a quantity which has both a magnitude and a direction

Question 9

Distance is a

Answer 9

scalar quantity because it describes how an object has travelled overall, but not the direction it has travelled in

Question 10

Displacement is a

Answer 10

vector quantity because it describes how far an object is from where it started and in what direction

Question 11

Scalars and Vectors Table

Answer 11

Question 12

Condition for Equilibrium

Answer 12

• Coplanar forces can be represented by vector triangles
• In equilibrium, these are closed vector triangles. The vectors, when joined together, form a closed path

Question 13

Resolving Vectors

Answer 13

• Two vectors can be represented by a single resultant vector that has the same effect
• A single resultant vector can be resolved and represented by two vectors, which in combination have the same effect as the original one
• When a single resultant vector is broken down into its parts, those parts are called components

For example, a force vector of magnitude F and an angle of θ to the horizontal is shown below

Question 14

Random error

Answer 14

• Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions
• This affects the precision of the measurements taken, causing a wider spread of results about the mean value
• To reduce random error: repeat measurements several times and calculate an average from them

Question 15

Systematic error

Answer 15

• Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method
• This type of error is repeated every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained
• To reduce systematic errors: instruments should be recalibrated or the technique being used should be corrected or adjusted

Question 16

Zero error

Answer 16

• This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero
• This introduces a fixed error into readings which must be accounted for when the results are recorded

Question 17

Precision of a measurement:

Answer 17

• this is how close the measured values are to each other; if a measurement is repeated several times, then they can be described as precise when the values are very similar to, or the same as, each other
• The precision of a measurement is reflected in the values recorded – measurements to a greater number of decimal places are said to be more precise than those to a whole number

Question 18

Accuracy:

Answer 18

this is how close a measured value is to the true value; the accuracy can be increased by repeating measurements and finding a mean average

Question 19

The difference between precise and accurate results

Answer 19

Question 20

These uncertainties can be represented in a number of ways:

Answer 20

• Absolute Uncertainty: where uncertainty is given as a fixed quantity
• Fractional Uncertainty: where uncertainty is given as a fraction of the measurement
• Percentage Uncertainty: where uncertainty is given as a percentage of the measurement

Question 21

To find uncertainties in different situations:

-The uncertainty in a reading:

Answer 21

± half the smallest division

Question 22

To find uncertainties in different situations:

-The uncertainty in a measurement:

Answer 22

at least ±1 smallest division

Question 23

To find uncertainties in different situations:

-The uncertainty in repeated data

Answer 23

half the range i.e. ± ½ (largest – smallest value)

Question 24

To find uncertainties in different situations:

-The uncertainty in digital readings:

Answer 24

± the last significant digit unless otherwise quoted

Question 25

Combining Uncertainties (adding and subtracting)

Answer 25

• Adding / subtracting data – add the absolute uncertainties
• difference between measurements are added or subtracted as well as the ± uncertainties

Question 26

Combining uncertainities: Multiplying / dividing data

Answer 26

add the percentage uncertainties

Question 27

combining uncertainties: Raising to a power

Answer 27

• multiply the uncertainty by the power