#### Quantities, Mass, and Weight

**QUANTITIES**

- A physical quantity is made up of magnitude and unit.

__Base Units__

__Base Units__

- The following are base units:

- All units (not from the table above) can be broken to base units.
- Homogeneity can be used prove equations.
- An equation is homogeneous if the base units on the left hand side are the same as the base units on the right hand side.
- This may not work all the time due to the fact that it does not take pure numbers into account.

__Multiples and Sub-multiples__

__Multiples and Sub-multiples__

__Scalar and Vector__

__Scalar and Vector__

- A scalar has magnitude only, it cannot be -ve. E.g. Speed, energy, power, work, mass, distance, etc.
- A vector has magnitude and direction, it can be -ve. E.g. Displacement, acceleration, force, velocity, momentum, weight, electric field strength, etc.

Vectors

__Measurement Techniques__

__Measurement Techniques__

**Using a Cathode Ray Oscilloscope (C.R.O.)**

- A supply of peak value, 5.0 V, and of frequency 50 Hz, is connected to a c.r.o with time-base at 10 ms per division, and Y-gain at 5.0 V per division. Which trace is obtained?

- The maximum value is 5.0 V; therefore eliminate A and B
- F =
^{1}/_{T}and T = Time-base × Divisions - ∴ F =
^{1}/_{Time-base × Divisions} - Divisions =
^{1}/_{F × Time-base}=^{1}/_{50 × 10 × 10-3}= 2 - The trace must have a period of 2 divisions and a height of 1 division, therefore D.

**Systematic and Random Errors**

- Systematic Error:
- Constant error in one direction; too big or too small
- Cannot be eliminated by repeating or averaging
- If systematic error is small, the measurement is accurate.
refers to the degree of agreement between a result of measurement and the true value of the quantity.*Accuracy*

- Random Error:
- Random fluctuations or scatter about a true value
- Can be reduced by repeating and averaging
- When random errors are small, the measurement is precise
refers to the degree of agreement of repeated measurements of the same quantity (regardless of whether it is correct or not)**Precision**

**Calculations Involving Errors**

- For a quantity
*x = (2.0 ± 0.1) mm*- Absolute uncertainty = Δx = ± 0.1 mm
- Fractional uncertainty =
^{Δx}/_{x}= 0.05 - Percentage uncertainty =
^{Δx}/_{x}× 100% = 5%

- Combining errors:
- When values are added or subtracted, add the absolute error.
- If p =
^{2x + y}/_{3}or p =^{2x – y}/_{3}, then Δp =^{2Δx + Δy}/_{3} - When the values are multiplied or divided, add percentage errors
- When values are powered (e.g. squared), multiply the percentage error with the power.
- If r = 2xy
^{3}or r =^{2x}/_{y3}, then^{Δr}/_{r}=^{Δx}/_{x}+^{3Δy}/_{y}

- If r = 2xy

**Treatment of Significant Figures**

- Actual error is recorded to only 1 significant figure.
- The number of decimal places for a calculated quantity is equal to the number of decimal places in the actual error.
- During a practical, when calculating using a measured quantity, give answers to the same significant figure as the measurement or one less.

**Micrometer Screw Gauge**

- Measures objects up to 0.01 mm
- Place the object between the anvil and spindle
- Rotate thimble until the object is firmly held by the jaws.
- Add the values from the main scale and the rotating scale.

**Vernier Scale**

- Measures objects up to 0.1 mm
- Place the object on the rule
- Push the slide scale to the edge of the object
- The sliding scale is 0.9 mm long and is divided into 10 equal divisions
- Check which line division on the sliding scale matches with a line division on the rule
- Subtract the value from the sliding scale (0.09 × divisions) by the value from the rule

**MASS AND WEIGHT**

- Mass is the amount of matter an object contains, and is a property that ‘resists’ change in motion.
- Weight is the force of gravity acting on an object, measured in Newtons, and given by the formula:
*Weight*=*Mass*×*Gravity* - Weights (and hence masses) may be compared using a balance.