Week 1 Flashcards
What is accuracy in measurement?
What is precision in measurement?
What are significant digits?
The number of digits in a measurement or result indicates how accurate the number is.
27 has 2 SD
27.3 has 3 SD and implies more accuracy
When are trailing digits significant or insignificant?
Trailing zeros AFTER THE DECIMAL are significant if stated
Trailing zeros are not significant if there is no decimal point in the quoted number
Are leading zeros significant?
No. It doesn’t matter if they are before or after the decimal
0.0045 has 2 SD
1.0045 has 5 SD
What are significant digits?
Numbers with meaning
What is the convention for✖️ or➗
The result has the same number of significant digits as the LEAST accurate number used in the calculation
E.g 3.0 x 4.3574 the result will be rounded to 2 SD therefore it’ll be 13
What is precision?
The smallest order of tens. More numbers after the decimal. Think of it as fineness of a measurement
Which is precise which is accurate 7.123 and 17.1
Precise: 7.123
Accurate: 17.1
What is the convention for ➕ or ➖
When adding or subtracting numbers, the result has the same precision as the LEAST precise number used in the calculation.
E.g 57 + 0.045 = 57
As 57 is the least precise therefore 2SD is used and it’s rounded to the nearest full number
What is margin of error?
One half of the size of the last significant place
E.g measurement of 45kg is precise to the nearest 1kg
Margin of error is half of 1kg or 0.5kg
Margin of error acknowledges that rounding has occurred due to the limit of our measuring device
Why do significant digits matter?
As numerical values are information they must be communicated clearly
When we express clinical data with more digits than the values used in producing that data, we mislead the recipient regarding the level of accuracy
What is scientific notion?
An efficient method of representing numbers that have wide range of magnitude (sizes)
Expresses the value as a number between 1 and 10 that is multipled by 10 to some exponent
751 is expressed as 7.51 x 102(2 is a power)
0.00031 is expressed as 3.1 x 10-4 -4 is a power)
Conventions for Scientific Notation
It’s based on ‘a x 10 to the power of b’
a is the number between 1-10
B expresses the order of magnitudes (how many times 10 is multiplied by itself)
What communicates accuracy of a number?
The number of digits after the decimal place
E.g 6.000 has 4 SD
What are the steps to convert a number from standard notation to scientific notation?
Try 4769.0550
- How many SD’s? 8
- How many spots to shift the decimal place to get a number between 1-10? 3 to get 4.7690550, the value a
- Use that shift number as the exponent b
- if shift is to ur left b is positive, but if b is to ur right b is negative - Result: 4.7690550 x 10 to the power of 3
Are trailing zeros in scientific notation important?
E.g 2.0000
Yes. This means there are 5SD’s
What 2 things tell us the ‘order of magnitude’ of a value?
The size and sign
E.g 4.5 x 10 to the power of 17 is 3 x 10 (1000) times greater than 4.5 x 10 to the power of 14
That 3 x 10 means ‘3 orders of magnitude’ (where the order of magnitude is the number of powers of 10)
Hint:
A positive b exponent means the value is >1
A negative b exponent means the value is always smaller than <1
What are the base units (units for measurement) for length, mass and time?
Length: meter (m)
Mass: kilogram (kg)
Time: seconds (s)
What is SI?
System internationale units- Standard units for measurement
When using SI units what 2 options can I use?
- Use scientific notation and keep standard unit
- Convert value to a non-SI unit that is derived from the base unit and uses a prefix to relate the size to the base unit
E.g 7 x 10 to the power of -3 or 7 millimeters
What are prefixes?
The word for a value
E.g KILO = 1000 = 10 to the power of 3
What are variables?
Parameters that are not constant in magnitude
2 or more variables may have a ‘cause and effect’ relationship
- The causative variable is termed independent
- The affected variable is termed dependent
When does a proportional relationship exist?
When the causative (independent) variable’s magnitude impacts the affected (dependant) variable’s magnitude in a predictable way
What does the delta symbol (resembles a fish) mean?
Is proportional to
What are the 2 types of proportionality relationships?
Direct and Inverse
Explain direct and inverse relationships?
Direct: The dependant variables magnitude changes in the same direction (bigger or smaller) as the independent variables magnitude change
Inverse: The dependent variables magnitude changes in the opposite direction (bigger or smaller) to the independent variables magnitude change
Notation (way of writing very big/small numbers) for direct and inverse proportionality
Direct:
- Linear relationship A is proportional to B
If B gets x by a number, A will also be x’d by that same number
- Exponential relationship: A is proportional to Bx (power of x)
If B gets x’d by a number, then A will be x’d by that number to an exponent x
Inverse:
-Linear: A is proportional to 1/B
-Exponential: A is proportional to 1/Bx (power of x)
What is the difference between a proportionality statement and an equation?
A proportionality statement answers the question “how do these variables relate”
An equation answers the question “by how much do these variables relate”
- An equation is just a proportionality statement with a constant inserted to make the 2 sides of the equation balance
Where in physics is proportionality used?
As the statements communicate relationships between variables they can be used to predict what will happen to the size of 1 variable when the other’s size is changed, without having to do any actual calculations
Is A dependent or independent?
A is proportional to B
A is proportional to B squared
A is proportional to 1/Bsquared
Dependent
What is distance?
Describes the length between 2 locations following the actual path used to connect those 2 locations. (Not necessarily the fastest way)
What is displacement?
Describes the length between 2 locations measured along a straight line to connect those locations
- Displacement also has a direction
What is the formula for speed?
Speed = distance/time
SI units: meters/second
Speed doesn’t indicate direction just distance travelled vs time elapsed
What is instantaneous speed?
Speed during the instant (right now)
What is average speed?
Total distance covered/total time elapsed
What is speed?
Rate of distance change
What is velocity?
Speed in a specific direction
Why is velocity different to speed?
Speed is independent of direction so direction can change during the time
When does velocity change?
When either the speed or direction change
Note: Velocity must always be consider the straight line distance covered in a unit of time
What is acceleration?
When an object undergoes a change in its state of motion (whether speed, direction or both) the object is accelerated
- If the objects speed or direction change then velocity changes
Acceleration is the time rate of change in velocity
- Base unit is m/s2 (squared)
When does acceleration occur?
When you change direction
When the car’s speed changes can be + or - acceleration
Acceleration occurs whenever an object undergoes a change in velocity over a period of time
Change of velocity and acceleration
Change of velocity = (velocity at end of time interval - velocity at start of time interval)
What symbol is used to represent ‘a change of’
🔺(known as delta)
What is the change of velocity formula?
🔺v = vfinal - vinitial where vfinal is the velocity at the end of the time interval and vinitial is the velocity at the start of the time interval
What is Acceleration and what is the formula?
Acceleration is the change of velocity per time interval
A = 🔺v/🔺t
Velocity change formula
Velocity change = acceleration x time
What is the approximate acceleration rate on earth?
10m/s
What formula is used when trying to find the final velocity?
Vf = vi + 🔺V
What is the distance of free fall proportional to?
The square of time (d (fish) t2) 2 is squared
Distance with acceleration
Because acceleration due to gravity causes the object to continually increase in speed as time elapses, it stands to reason that the object experiences a bigger distance change with each passing second of time
The bigger the fall the MUCH bigger distance travelled
What does gravity do to acceleration?
The effect of gravity causes an upward velocity to be opposed by the downward ‘push’ of gravity. For example throwing a ball up in the air eventually comes down
What is inertia?
The tendency of an object to maintain its state of motion
It’s significant as it resists a change in motion (can be moving or not moving)
How is inertia overcome?
It requires a push, pull or force
What is a force?
An influence that tends to change the state of motion of an object
Forces are directional (like velocity)
SI unit of force is Newtons (N)
When can we add or subtract forces?
Add: when forces have the same direction
Subtract: when forces have different directions
- This is called ‘adding the inverse’
Forces in other angles are dealt with using vector math (not doing)
What is net force?
The sum of all the forces
The phrase ‘the vector sum of the forces’ can be abbreviated as (side ways MF)
What is mechanical equilibrium?
Mechanical: Motion. Forces
Equilibrium: Balance
Mechanical equilibrium refers to balance of forces
What are the 2 types of mechanical equilibrium?
Static: means stationary
Dynamic: object is in a steady straight line motion
What is friction? What’s its impact on net force?
An opposing or resistive force to the applied force causing motion
Friction also reduces the net force because its in the opposite direction to the force being applied to cause the motion
What causes friction?
The molecular clinginess between surfaces of objects
(As friction is a force its also measured in N)
How is equilibrium removed?
As forces cause motion we need net forces to be non zero in order to get rid of equilibrium
What is newtons first law of motion?
Every object continues in its state of motion (whether rest or steady velocity) unless acted upon by a non-zero net force
As acceleration depends on net force how is this written as an equation?
A (is proportional to/fish symbol) F
What is mass and what is the SI?
The quantity of matter in an object
- The more matter, the more inertia the object has
Kilogram (kg)
What’s the difference between mass and weight?
Weight is the force of an object due to gravity
- its a force, so MUST be measured in N
Although weight is proportional to mass, its not the same
- w (is proportional to) m
What is the relationship between mass and acceleration?
Mass resists acceleration
The larger the mass, the less acceleration results for the same size of push (or force)
Acceleration is INVERSELY proportional to mass
A (is proportional to) 1/m
What is Newton’s second law of motion?
The acceleration of an object is directly proportional to the net force acting on it, is in the same direction of the net force, and is inversely proportional to the mass of the object
A (is proportional to) Fnet/m
- This proportionality statement is the combination of the 2 independent variables to show their co-effect on the dependent variable
(Note: a and f are directional so must be the same for both)
What is Newton’s third law of motion?
For every action there is an equal and opposite reaction
When 1 object exerts a force on another,the 2nd object exerts and equal force on the 1st object
What are force pairs?
Force pairs are always:
Always opposite in direction to each other
Between 2 seperate interacting objects
One object is the ‘action’ the other is the ‘reaction’
E.g push against a wall and the wall pushes back against you
How do force pairs and acceleration relate?
We need a force to cause acceleration (change in the motion state) of an object
However the acceleration is relative and we must identify what its relative to
By defining the ‘system’ involved, we determine which forces in the force pair are internal vs external to the system
- Recall1st law: it is an external force cause a change in motion
Can an inside force move an object?
e.g a person sitting in a wagon
No, there has to be an force exerted from the outside of the wagon
What happens when 2 objects exert forces on each other?
There is acceleration of each object relative to the other
The size of the acceleration resulting from the interaction depends on the mass of each object
- Recall that a (is proportional to) F/m
- Since f is the same magnitude for both objects, the resulting acceleration (a) has a magnitude that depends on the size of mass (m)
What is the equation for the proportionality statement for acceleration?
A = F/m
Or
F = a x m
F1 = F2 (forces are the same)
The bigger the m value, the smaller the a value must be to balance the equation, and vis versa
Since F1=a1 x m1 and F2 = a2 x m2 its also true that a1 x m1 = a2 x m2
When is it called when 2 balls with the same force but different mass collide?
Acceleration for non-equal masses
Note: when mass is big acceleration is small and when mass is small acceleration is big
What is the significance of acceleration for non-equal masses?
When 2 objects interact, the difference in size of their masses determines the outcome of the interaction
