Kinetic and Potential Energy Quiz

Kinetic Energy

• Kinetic energy is the energy of motion, calculated using the formula: K.E. = ½ mv², where:
  • K.E. represents kinetic energy
  • m represents the mass of the object
  • v represents the object's velocity

Potential Energy

• Potential energy is stored energy due to an object's position or state.
• Gravitational potential energy (P.E.) depends on an object's height above the Earth's surface, calculated with: P.E. = mgh, where:
  • m represents the object's mass
  • g represents the Earth's gravitational acceleration (9.8 m/s²)
  • h represents the object's height above the Earth's surface

Elastic Potential Energy

• Elastic potential energy is energy stored in elastic materials when stretched or compressed.
• Hooke's Law states that if a spring is neither stretched nor compressed, it's at its equilibrium position and has no elastic potential energy.
• Elastic potential energy is calculated using: P.E.elastic = ½ kx², where:
  • k represents the spring constant (N/m²)
  • x represents the amount of compression or stretch (distance in meters)

Force

• A newton (N) is the force needed to accelerate a 1-kilogram mass by 1 meter per second squared.
• Tension forces are required to pull an object (opposite of compression).
• Spring force is exerted by a compressed or stretched spring.

Frictional Force

• Frictional force opposes motion between surfaces in contact, calculated using: F = μN, where:

  • F represents the frictional force
  • μ represents the coefficient of friction
  • N represents the normal force acting perpendicular to the surface

• Example: A 40-kg block of wood on a cement floor with a coefficient of friction of 0.6 experiences a frictional force of 235.2 N. This force must be overcome to move the block.

Force and Distance

• The relationship between force and distance is expressed as: F1D1 = F2D2, meaning the product of force and distance is constant.

Momentum

• Momentum (ρ) is the product of an object's mass and its velocity, calculated using: ρ = mv, where:
  • ρ represents momentum
  • m represents mass (kg)
  • v represents velocity (m/s)

Velocity

• Velocity is defined using the following formulas:

  • v = v₀ + at: This calculates final velocity (v), where:

    • v₀ represents the initial velocity
    • a represents acceleration
    • t represents time

  • S = v₀t + ½ at²: This calculates distance (S), where:

    • v₀ represents the initial velocity
    • a represents acceleration
    • t represents time

  • v² = v₀² + 2aS: This calculates final velocity (v), where:

    • v₀ represents the initial velocity
    • a represents acceleration
    • S represents distance

Work Done

• Work (W) is calculated using: W = FS, where:
  • W represents work done (in Joules)
  • F represents force (in Newtons)
  • S represents distance (in meters)

Newton's Second Law

• Newton's Second Law states: F = ma/g, where:

  • F represents force
  • m represents mass
  • a represents acceleration
  • g represents gravitational acceleration (9.8 or 32.2 (US units))

• Example: A force acting at 30 degrees with the horizontal on an object displaced 3 meters horizontally, with a normal force of 400 N and a coefficient of friction of 0.35, results in work done by the force of 363.7 N.

Statistics

• A histogram is a graphical representation of data distribution.

• Mean (average) is calculated by summing all data points and dividing by the number of data points: ΣXn/n

• Median is the middle value in a sorted dataset. If there are two middle values, the median is their average.

• Mode is the value that appears most frequently in a dataset.

• Skewness:

  • Negative Skew: Mean < Median < Mode, longer tail on the left side of the mean.
  • Positive Skew: Mode < Median < Mean, longer tail on the right side of the mean.
  • No Skew: Mean = Median = Mode, symmetrical distribution.

• Standard deviation measures the average distance of data points from the mean.

Temperature

• Conversion between temperature scales:

  • Celsius (C) to Fahrenheit (F): Tc = (Tf - 32) / 1.8
  • Celsius (C) to Kelvin (K): Tk = Tc + 273
  • Fahrenheit (F) to Rankine (R): F = 460 + R

• To convert to absolute temperature scales:

  • Rankine (R): oR = oF + 460
  • Kelvin (K): oK = oC + 273

Force

• 1 kilogram-force = 9.80665 newton [N]

Energy Unit

• 1 calorie = 4.186 Joule

Conversion

• 1 BTU (British thermal unit) = 1055 Joule
• 1 foot-pound = 1.356 Joule
• 1 joule = 1 kg · m/s²

Radiation

• 1 rad = 10⁻² gray
• 1 rem = 10⁻² sievert
• 1 curie = 3.7x10¹⁰ becquerel
• 1 becquerel = 1 disintegration/sec

Density of Water

• 1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)

Light

• 1 candela = 1 lumen/steradian
• 1 footcandle = 10.76 candela/m² = 10.76 lux

PHYSICAL CONSTANTS

• Acceleration of gravity: 32.2 ft/sec² = 9.8 m/sec²
• Velocity of light: 3.0 x 10⁸ m/sec
• Planck's constant: 6.626 x 10⁻³⁴ J·sec
• Avogadro's number: 6.024 x 10²³/ gram-mole

Area

• Rectangle: Area = length × width
• Square: Area = s², where 's' is the side length.
• Triangle: Area = (1/2) × base × height
• Circle: Area = π × r², where 'r' is the radius.

Volume

Trigonometric Functions

• Law of Cosines: C² = a² + b² - 2ab cos θC
• Law of Sines: A/SinA = b/Sinb = c/Sinc
• K.E. = ½ mv²

Units and Conversions

• 1 Newton (N) is equal to 1 kg * m/s².
• 1 kg is equal to 2.2 lb.
• 1 bar equals 14.5 PSI, 0.98 atm, or 760 mm Hg.
• 1 psia is equal to 51.72 mm Hg.
• 1 psig is 14.7 psia added to the pressure reading.
• 1 mm Hg (Torr) is equivalent to 0.01934 psia.

Force and Motion

• Force can be calculated using the formula: F = 40 * 9.8 = 392 N.
• Friction force can be calculated using the formula: F = μN = 0.6 x 392 = 235.2 N, where μ is the coefficient of friction and N is the normal force.
• Work done is calculated by multiplying force and distance: W = FS, where W is work done in Joules (J), F is force in Newtons (N), and S is distance in meters (m).
• Force can also be calculated using Newton's Second Law: F = ma/g, where m is mass, a is acceleration, and g is the acceleration due to gravity (9.8 m/s²).
• Momentum is calculated using the formula: ρ = mv, where ρ is momentum, m is mass in kg, and v is velocity in m/s.

Statistics

• A histogram is a visual representation of the frequency distribution of data.
• The mean is the average value of a data set and is calculated by summing all values and dividing by the number of values.
• The median is the central value in a data set, when it is ordered from smallest to largest.
• The mode is the value that appears most frequently in a data set.
• A left-skewed distribution has a longer tail on the lower end of the data, with the mean less than the median and mode.
• A right-skewed distribution has a longer tail on the higher end of the data, with the mode less than the median and mean.
• A symmetrical distribution has no skew, with the mean, median, and mode all equal.
• Standard deviation is a measure of the spread of data around the mean.
• One standard deviation encompasses approximately 68% of the data, two standard deviations encompass 95.45%, and three standard deviations encompass 99.73%.

Hypothesis Testing

• The null hypothesis states that there is no significant difference between the population means.
• A Type I error (false positive) occurs when the null hypothesis is rejected when it is actually true.
• A Type II error (false negative) occurs when the null hypothesis is accepted when it is actually false.

Coefficient of Variation

• The coefficient of variation (CV) is a measure of the dispersion of data relative to the mean.
• It is calculated as the standard deviation (S) divided by the mean (Xmean) and expressed as a percentage.
• A higher CV indicates a greater variability in the data.

Cumulative Error

• Cumulative error is used to determine the uncertainty in a measurement due to the accumulation of errors from various sources, such as calibration errors, lab errors, instrument measurement errors, and correction errors.
• As the sample size increases, the cumulative error decreases, leading to a more accurate assessment of the mean.

Precision and Accuracy

• Accuracy refers to how close a measured value is to the true or accepted value.
• Precision refers to the reproducibility of measurements, or how close repeated measurements are to each other.

Lower Confidence Limit (LCL)

• The LCL is used by OSHA to determine if a measured value exceeds permissible exposure limits (PELs).
• If the LCL is greater than the PEL, then the worker is considered to be overexposed.
• If the PEL is greater than the LCL, then the worker is considered to be compliant.
• If the time-weighted average (TWA) or PEL is over 1 and the LCL is also over 1, then the worker is overexposed.

Area and Volume Formulas

• Rectangle: Area = length * width
• Square: Area = s², where s is the side length.
• Triangle: Area = (1/2) base * height
• Circle: Area = π * r², where r is the radius.
• Rectangular Solid/Cuboid: Volume = length * width * height
• Cube: Volume = a³, where a is the side length.
• Cylinder: Volume = πr²h, where r is the radius and h is the height.
• Prism: Volume = B * h, where B is the area of the base and h is the height.
• Sphere: Volume = (4/3)πr³, where r is the radius.
• Pyramid: Volume = (1/3) * B * h, where B is the area of the base and h is the height.

Trigonometric Functions

• Law of Cosines: c² = a² + b² - 2ab cos θ_C
• Law of Sines: a/sin A = b/sin B = c/sin C

Energy

• Kinetic Energy: KE = ½ * mv² , where KE is kinetic energy, m is mass, and v is velocity.
• Potential Energy: PE = mgh, where PE is potential energy, m is mass, g is gravitational acceleration, and h is height.
• Elastic Potential Energy: PE_elastic = ½ * k * x², where PE_elastic is elastic potential energy, k is the spring constant, and x is the amount of compression or extension.

Force

• Newton (N): One Newton is the force required to accelerate a 1 kg mass at 1 m/s².
• Tension Forces: These forces are required to pull an object, opposite to compression forces.
• Spring Force: This force is exerted by a compressed or stretched spring.
• Frictional Force: F = μN, where μ is the coefficient of friction and N is the normal force.

Variance and Standard Deviation

• Variance: σ² = Σ(X - X_av)²/N, where σ² is the variance, X_av is the average value, N is the sample size, and Σ denotes summation.
• Standard Deviation: S = √(Σ(X - X_av)²/N), where S is the standard deviation, X_av is the average value, N is the sample size.

Statistics and Parameters

• Statistic: A numerical value that describes a sample, a subset of the population.
• Parameter: A value that describes the entire population. It summarizes the characteristics of the population.
• F-Test: A statistical test used to measure the accuracy of a statistic.

Types of Errors

• Type I Error (False Positive): Rejecting the null hypothesis when it is true.
• Type II Error (False Negative): Accepting the null hypothesis when it is false.

Correlation Coefficient (r)

• The correlation coefficient measures the strength and direction of the linear relationship between two variables.
• A value of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

### Force and Motion

• 1 Newton (N) is the force that gives a 1 kg mass an acceleration of 1 m/s2
• Force is the product of mass and acceleration: F = ma
• Work done is calculated as the product of force and distance: W = FS
• Momentum is the product of mass and velocity: ρ = mv
• Friction force is the product of the coefficient of friction and the normal force: F = μN
• If there is an angle in the force, then the horizontal component of the force is Nsin angle + μ *N cos angle

### Units of Measurement

• 1 kg = 2.2 lb
• 1 mile = 1.6 Km = 1609 meter
• 1 m/s = 3.281 ft/s
• 1 m = 100 cm
• 1 m = 1000 mm

### Statistics

• A histogram is a graph used to distribute data frequency.
• Mean is the average value of a data set
• Median is the central number in a data set
• Mode is the number that appears most frequently in a data set
• Right skewed data shows that the mean is larger than the median.
• Left skewed data shows that the mean is less than the median.
• Symmetrical distribution occurs when: Mean = Median = Mode

### Area

• Area of a rectangle: Area = length * width
• Area of a square: Area = s², where s = side
• Area of a triangle: Area = (1/2) b * h where b = base and h = height
• Area of a circle: Area = π * r², where r = radius

### Angles

• 1 radian = 180°/π

### Volume

• The volume of a rectangular solid or cuboid is calculated as: V=l×w×h; where:
  • l = Length
  • w = Width
  • h = Height
• The volume of a cube is: V=a³, where: a = Length of edge or side.
• The volume of a cylinder is: V = πr²h, where:
  • r = Radius of the circular base
  • h = Height
• The volume of a prism is calculated as: V=B×h; where:
  • B = Area of base, B = side2 or length.breadth)
  • h = Height
• The volume of a sphere is: V = (4⁄3)πr³ , where r = Radius of the sphere.
• Volume of a pyramid: V = (1⁄3) × B × h, where:
  • B = Area of the base
  • h = Height of the pyramid

### Energy

• Kinetic Energy is calculated as: K.E.= ½ mv² ; where:
  • K.E.= kinetic energy (N)
  • m = mass of the object
  • v = speed of the object (velocity)
• Potential energy is calculated as: P.E.= mgh; where:
  • m = mass of the object (kg)
  • g = gravitational acceleration of the earth (9.8 m/s2)
  • h = height above earth’s surface (m)
• Elastic Potential Energy: P.E._elastic = ½ kx², where:
  • k = spring constant (N/m2)
  • x = amount of compression (distance in m)

### Other

• 1 hour = 3600 seconds
• 1 ton (US) =2000 lb
• 1 liter = 1000 cm3 = 1000 ml
• 1 ft3 = 7.5 gallons
• 1 gallon = 3.78 liters
• 1 liter = 61.02 cu in
• 1 kg = 2.2 lb
• 1 lb = 454 gram
• 1 atm = 14.7 psi = 760 mm Hg
• 1% by volume = 10,000 parts per million (ppm)
• Tc=Tf-32/1.8
• Tk=Tc+273
• F=460 + R
• 1 cal = 4.186 J