Units of Measurement and Conversions

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Questions and Answers

What is the relationship between force and distance as defined by the equation F1D1 = F2D2?

It establishes that force and distance are inversely proportional.

It indicates that the total work done is constant. (correct)

It shows that force and energy are equivalent.

It states that force increases with the square of distance.

If a force of 392 N is applied with a coefficient of friction of 0.6, what is the frictional force acting on the object?

196 N

352 N

235.2 N (correct)

260 N

Using the equation s = v0t + ½ at², what does the term 's' represent?

Distance from original position (correct)

Initial velocity

Acceleration

Final velocity

When considering a right-skewed distribution, which relationship holds true between mean, median, and mode?

Mode < Median < Mean Signup and view all the answers

What does the coefficient of friction determine in the equation Ffric = μN?

The resistance to motion between two surfaces Signup and view all the answers

If an object is undergoing acceleration, which formula correctly describes the final velocity?

v = vo + at Signup and view all the answers

In a central tendency analysis, how is the mean calculated?

Adding all values and dividing by the total count. Signup and view all the answers

What does the term 'work done' refer to in physics?

Force multiplied by distance moved in the direction of the force Signup and view all the answers

How many millimeters are there in one meter?

1000 mm Signup and view all the answers

What is the length of 1 mile in meters?

1609 m Signup and view all the answers

If a vehicle travels at 1 mile per hour, what is its speed in feet per second?

1.467 ft/s Signup and view all the answers

How many square centimeters are in one square inch?

6.452 cm² Signup and view all the answers

What is the equivalent of 1 foot in centimeters?

30.48 cm Signup and view all the answers

Convert 1 inch to microns.

25,400 microns Signup and view all the answers

How much energy is equivalent to 1 calorie in joules?

4.187 J Signup and view all the answers

What is the conversion factor from feet to meters?

1 ft = 0.305 m Signup and view all the answers

How many cubic centimeters are in one cubic inch?

16.39 cm³ Signup and view all the answers

1 knot is approximately equal to how many meters per second?

0.5148 m/s Signup and view all the answers

What is the equivalent value of 1 bar in Newtons per square meter?

105 N/m2 Signup and view all the answers

How many grams are in 1 ton (US)?

907,184 grams Signup and view all the answers

Which of the following conversions correctly represents 1 pound-force to Newtons?

4.45 Newtons Signup and view all the answers

How is 1 ppm expressed in terms of mass concentration?

1 mg/L Signup and view all the answers

What is the conversion of 1 cubic foot in terms of gallons?

7.5 gallons Signup and view all the answers

Which of the following best describes the relationship between Celsius and Kelvin?

K = °C + 273 Signup and view all the answers

Which of the following units is equivalent to 1 bar?

0.9869 atm Signup and view all the answers

What is the SI unit of luminous intensity?

Candela Signup and view all the answers

What does 1 kilowatt-hour equal in joules?

3.6 × 10^6 J Signup and view all the answers

How many milliliters are in 1 liter?

1000 mL Signup and view all the answers

What does a standard deviation of 1 correspond to in terms of the data set?

68% of the data set Signup and view all the answers

Which statement defines a Type I error in hypothesis testing?

Rejecting the null hypothesis when it's true Signup and view all the answers

What is the main purpose of the F-test in statistics?

To determine if there are significant differences between population means Signup and view all the answers

The coefficient of variation (CV) is defined as what ratio?

Standard deviation to mean Signup and view all the answers

What does a lower confidence limit (LCL) being greater than the permissible exposure limit (PEL) indicate?

Noncompliance with regulations Signup and view all the answers

What is the relationship between Celsius and Fahrenheit temperatures?

Tc = (Tf - 32) / 1.8 Signup and view all the answers

What is the formula for the volume of a cylinder?

V = πr^2h Signup and view all the answers

How is energy measured in terms of calories and Joules?

1 calorie = 4.186 Joules Signup and view all the answers

What is the formula for kinetic energy?

K.E. = ½ mv^2 Signup and view all the answers

What does 1 rad convert to in gray units?

1 rad = 0.01 gray Signup and view all the answers

How is the area of a triangle calculated?

Area = (1/2) * base * height Signup and view all the answers

What is the unit of force in terms of mass and acceleration?

1 N = 1 kg * m/s² Signup and view all the answers

Convert 1000 grams to slugs using the given density of water.

1.94 slugs Signup and view all the answers

What is the value of Avogadro's number?

6.022 x 10²³ / gram-mole Signup and view all the answers

Determine the formula for the area of a square.

Area = s^2 Signup and view all the answers

Study Notes

Units

1 Newton (N) = 1 kg*m/s²
1 kg = 2.2 lb
1 cal = 0.003968 Btu
1 cal = 4.187 J
1 Btu = 252 cal
1 ft/s = 0.3048 m/s
1 ft/s = 0.8618 mi/h
1 ft/s = 0.5921 knots
1 m/s = 3.281 ft/s
1 m/s = 2.237 mi/h
1 mi/h = 0.4470 m/s
1 mi/h = 1.467 ft/s
1 knot = 0.5148 m/s
1 knot = 1.151 mi/h
1 knot = 1.689 ft/s
1 lb/cu.ft = 0.01602 cu.cm
1 g/cu.cm = 62.42 lb/cu.ft
1 g/cu.cm = 1000 kg/cu.m
1 kg/cu.m = 0.001 g/cu.cm
1 psia = 6.895 kN/m²
1 psia = 0.0680 atm
1 psia = 27.67 in.H₂O
1 bar = 14.5 PSI = 0.98 atm = 760 mm Hg = 105 N/m²
1 psia = 51.72 mm Hg
1 psig = 14.7 psia
1 mm Hg (Torr) = 0.01934 psia
16 oz = 1 lb
1 g = 1000 mg
2.205 lb = 1kg
1 ton (US) = 2000 lb
1 tonne (Metric ton) = 1000 kg
1 dram = 1771.85 mg
1 bar = 100 kN/m²
1 kN/m² = 0.1450 psia
1 bar = 0.9869 atm
1 kN/m² = 0.009869 atm
1 bar = 1.020 kg/cm²
1 Btu/lb/°F = 1 cal/g/°C
1 Btu/lb/°F = 4187 J/kg·K
1 ppm = 1 mg/L
1 mg/m³ = 1 × 10−9 g/cm³
1 g/cm³ = 1 × 109 mg/m³
1 g/m³ = 62.42 lb/ft³
1 lb/ft³ = 0.01602 g/cm³
1 British Thermal Unit (Btu) = 1055 J
1 faraday = 9.65 × 10⁴ coulombs
1 g-cal = 4.19 J
1 g-mol at 0°C and 1 atm = 22.4 L
1 g-mol at 25°C and 1 atm = 24.45 L
1 ampere-hour = 3600 coulombs
1 W = 1 J/s = 1 A × 1 V
1 kwh = 3.6 × 10⁶ J
1 liter = 1000 cm³
1 liter = 1000 ml
1 m³ = 1000 liter
1 liter = 1.06 qt = 61.02 in³ = 0.03531 ft³
1 ml = 1 cm³
1% by volume = 10,000 part per million (ppm)
1 ft³ = 7.5 gallons
1 gallon of water = 8.34 lb
1 gallon = 3.78 liters
1 liter = 61.02 cu in
1 hour = 3600 seconds
1 kg = 2.2 lb
1 lb = 454 gram
1 ton (US) =2000 lb
1 atm = 14.7 psi = 760 mm Hg = 33.90 ft.H₂O = 760 torr = 101.3 kPa
1 calorie = 4.186 Joule
1 BTU (British thermal unit) = 1055 Joule
1 foot-pound=1.356 Joule
1 joule = 1 kg · m/s²
1 rad = 10⁻² gray
1 rem = 10⁻² sievert
1 curie = 3.7x10¹⁰ becquerel
1 becquerel = 1 disintegration/sec
1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)
1 candela = 1 lumen/steradian
1 footcandle = 10.76 candela/m² = 10.76 lux

Physics Formulas

F = ma/g, m = mass, a = acceleration, g = 9.8 or 32.2 (US)
F = μN, N = normal force, μ = coefficient of friction
F₁D₁ = F₂D₂, F = force, D = distance
ρ = mv, ρ = momentum, m = mass, v = velocity
v = v₀ + at, v = final velocity, v₀ = original velocity, a = acceleration, t = time
S = 𝐯₀𝐭 + ½ 𝐚𝐭², 𝐯² =𝐯₀² + 𝟐𝐚𝐬, S = distance, v₀ = initial velocity, a = acceleration, t = time
W = FS, W = work done, F = force, S = distance
C² = a² + b² – 2ab cos 0C
A/SinA = b/Sinb = c/Sinc
K.E. = ½ mv², K.E. = kinetic energy, m = mass, v = velocity

Statistics

Histogram: A graph representing the frequency distribution of data.
Mean: The average value of a data set (ΣXn/n).
Median: The central value of a data set.
Mode: The most frequent value in a data set
Left Skewed: Mean < Median < Mode (longer tails at lower values)
Right Skewed: Mode < Median < Mean (longer tails at higher values)
No Skew: Mean = Median = Mode (symmetrical distribution)
Standard Deviation: A measure of the average distance of data points from the mean.
Central Tendency: Refers to the mean, median, and mode.
Coefficient of Variation (CV): Ratio of the standard deviation to the mean (S/Xmean = %).

Hypothesis Testing

Null Hypothesis (H₀): There is no significant difference between populations, any observed difference is due to sampling or experimental error.
Type I Error (False Positive, α): Rejecting the null hypothesis when it is true.
- There is a difference between the means when there is none.
Type II Error (False Negative, β): Accepting the null hypothesis when it is false.
- No difference in means, when there is an actual difference.
F-test: Used to measure the accuracy of sample statistics when comparing them to population parameters.
Cumulative Error: Accounts for errors in calibration, laboratory procedures, instrument measurement, and correction during sampling.

Accuracy and Precision

Accuracy: How close a measurement is to the true or accepted value.
Precision: The consistency of repeated measurements using the same method.

Lower Confidence Limit (LCL)

Used by OSHA to determine if a measured value exceeds the Permissible Exposure Limit (PEL).
- If LCL > PEL: Non-compliance
- If LCL < PEL: Compliance

Area and Volume Formulas

Rectangle: Area = length * width
Square: Area = s², where s = side
Triangle: Area = (1/2) b * h, where b = base and h = height
Circle: Area = π * r², where r = radius
Rectangular Solid or Cuboid: V = l×w×h, l = length, w = width, h = height
Cube: V = a³, where a = length of edge or side
Cylinder: V = πr²h, r = radius of the circular base, h = height
Prism: V = B×h, B = area of base, h = height
Sphere: V = (4⁄3)πr³, r = radius of the sphere
Pyramid: V = (1⁄3) × B × h, B = area of the base, h = height of the pyramid

Standards

STP (Standard Temperature and Pressure)
- Physical Science: 0°C and 1 atm (273.15K and 101.325 kPa)
- Ventilation: 70°F and 1 atm (21.11°C and 101.325kPa)
- Industrial Hygiene: 25°C and 1 atm (298.15K and 101.325kPa)
Density of Water:
- 1 g/cm³ = 1.94 slugs/ft³
- Weight Density: 62.4 lb/ft³
- 1 US gallon of H2O = 8.345 lb
Angles: 1 radian = 180°/π

Light

1 candela = 1 lumen/steradian
1 foot-candle = 10.76 candela/m² = 10.76 lux

Magnetic Fields

1 tesla = 10,000 gauss

Physical Constants

Acceleration of gravity = 32.2 ft/s² = 9.8 m/s²
Velocity of light = 3.0 × 10⁸ m/s
Planck’s constant = 6.626 × 10⁻³⁴ J·s
Avogadro’s number = 6.024 × 10²³ /g-mol

Radiation

1 rad = 10⁻² gray
1 rem = 10⁻² sievert
1 curie = 3.7 × 10¹⁰ becquerel
1 becquerel = 1 disintegration/s

Key Facts From The Text

Force and Distance Formula: F₁D₁ = F₂D₂
Momentum Formula: ρ = mv
Force Applied at an Angle: F = Nsin angle + μ * N cos angle
Work Done Formula: W = FS
Kinetic Energy Variance: Σ(X-Xav)²/N
Standard Deviation: S = Square Root (X-Xav)²/N
- 1 std dev = 68% of the data set
- 2 std dev = 95.45% of the data set
- 3 std dev = 99.73% of the data set
Coefficient of Variation (CV): S/Xmean = %
Relative Standard Deviation (RSD): A measure of dispersion, often expressed as a percentage.
Cumulative Error: Accounts for various sources of error in air sampling.

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Test your knowledge on the various units of measurement and their conversions. This quiz covers everything from Newtons and kilograms to Btu and pressure measurements. Perfect for students in physics or engineering courses.