Physics and Measurement Concepts

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Questions and Answers

What is the term used for the sum of two vectors?

  • Resultant vector (correct)
  • Magnitude vector
  • Vector sum
  • Direction vector

In a right triangle formed by two vectors, which side is referred to as the hypotenuse?

  • The longest side of the triangle (correct)
  • The adjacent side
  • The side opposite the right angle
  • The side along the direction of displacement

What is the correct trigonometric function to use in finding the magnitude of the resultant vector in this scenario?

  • Sine
  • Pythagorean theorem (correct)
  • Tangent
  • Cosine

What does the angle of direction (𝜃) represent in vector displacement?

<p>The angle between the resultant vector and the horizontal axis (D)</p> Signup and view all the answers

If Sheila ran 0.68 miles north and 1.09 miles east, which two vectors are being added?

<p>North and east vectors (C)</p> Signup and view all the answers

How would you denote the magnitude of the resultant vector mathematically?

<p>Sqrt(V1^2 + V2^2) (A)</p> Signup and view all the answers

To accurately graph vectors, which method is essential?

<p>Drawing the vectors with arrows (B)</p> Signup and view all the answers

What information is explicitly asked for in Sheila's displacement problem?

<p>Magnitude and angle of direction (A)</p> Signup and view all the answers

What is the converted temperature in Fahrenheit when the temperature is 25°C?

<p>77 °F (D)</p> Signup and view all the answers

When converting 25°C to Kelvin, what is the correct result?

<p>298.15 K (D)</p> Signup and view all the answers

Which conversion factor should be used to convert kilometers to miles?

<p>1 km = 0.6214 mi (D)</p> Signup and view all the answers

How many miles are there in 15 kilometers using the conversion factor?

<p>9.321 mi (D)</p> Signup and view all the answers

What is the formula for converting Celsius to Fahrenheit?

<p>°F = °C x 1.8 + 32 (A)</p> Signup and view all the answers

If Maria's hiking trip is 15 kilometers, which of the following might incorrectly describe the distance in miles?

<p>12.500 mi (D)</p> Signup and view all the answers

What is the average deviation in a dataset?

<p>The measure of how much individual data points differ from the mean (C)</p> Signup and view all the answers

In vector representation, what does the 'magnitude' refer to?

<p>The length or size of the vector (A)</p> Signup and view all the answers

What is the magnitude of the resultant vector calculated in the problem?

<p>1.2847 mi (C)</p> Signup and view all the answers

Using the given components, what is the value of $R^2$?

<p>1.6505 mi² (A)</p> Signup and view all the answers

Which trigonometric function is used to find the angle of displacement in this scenario?

<p>Sine (B)</p> Signup and view all the answers

What is the value of the sine of the angle $ heta$ calculated in the process?

<p>0.8484 (D)</p> Signup and view all the answers

What is the final result obtained when using the inverse sine function for finding $ heta$?

<p>58.0380° (A)</p> Signup and view all the answers

What step must be taken to find the magnitude of the resultant vector from $R^2$?

<p>Take the square root (C)</p> Signup and view all the answers

What should be the expression used to calculate the sine of the angle given the opposite and hypotenuse?

<p>$sin heta = \frac{O}{H}$ (D)</p> Signup and view all the answers

What represents the opposite side in the sine calculation in this scenario?

<p>1.09 mi (C)</p> Signup and view all the answers

What is the result of converting 15 km to miles using the equivalence factor 0.6214 mi/km?

<p>9.321 mi (C)</p> Signup and view all the answers

Which statement accurately describes average deviation?

<p>It measures how clustered measurements are around the mean. (B)</p> Signup and view all the answers

Which of the following is a scalar quantity?

<p>Distance (C)</p> Signup and view all the answers

What does a lower average deviation indicate about measurements?

<p>Measurements are closely clustered around the mean. (B)</p> Signup and view all the answers

What is an example of a vector quantity?

<p>Displacement (A)</p> Signup and view all the answers

In the conversion equation, why is 1 km in the denominator when converting km to miles?

<p>To ensure units cancel appropriately. (C)</p> Signup and view all the answers

Which of the following examples represents a scalar quantity?

<p>10 kg (A)</p> Signup and view all the answers

What type of measurement indicates lower precision based on average deviation?

<p>0.67 (D)</p> Signup and view all the answers

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Study Notes

Temperature Conversion

  • Convert Celsius (°C) to Fahrenheit (°F) using the formula: °F = °C x 1.8 + 32
  • Convert Celsius (°C) to Kelvin (K) using the formula: K = °C + 273.15

Units of Measurement Conversion

  • Use dimensional analysis to convert units
  • Ensure that the units you want to convert to appear in the numerator
  • To cancel units, place the same unit in the denominator

Average Deviation

  • Average deviation measures how spread out measurements are from the mean
  • Lower average deviation indicates higher precision, meaning measurements are closer to the mean
  • Higher average deviation indicates lower precision, suggesting measurements are more spread out

Vectors

  • Vectors have both magnitude and direction
  • Scalars have only magnitude
  • Vectors are represented by arrows, while scalars are represented by straight lines
  • The sum of two vectors is called the resultant vector (R)
  • Use trigonometric functions (SOH, CAH, TOA) to solve problems involving vectors

Resultant Vector and Angle of Direction

  • Calculate the magnitude of the resultant vector using the equation: R² = a² + b²
  • Determine the angle of direction using trigonometric functions like sine (SOH): sinθ = (opposite side) / (hypotenuse)

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