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

Test your knowledge on kinetic and potential energy concepts! This quiz covers the fundamental principles, formulas, and types of energy including gravitational and elastic potential energy. Perfect for students studying physics or energy topics.