UPCAT Physics — Uncertainty in Measurement & VectorsFlash Cards

Calculate the number of significant figures in 0.0045200 g

Step 1: Identify the rules. Leading zeros are never significant. Trailing zeros after decimal are significant. Step 2: 0.0045200 → The first nonzero digit is 4. Step 3: Count from 4: 4, 5, 2, 0, 0 (all significant after first nonzero) Answer: 5 significant figures

What is the difference between accuracy and precision in measurements?

Accuracy: How close a measurement is to the actual/correct value. Precision: How close repeated measurements are to each other, regardless of the actual value. Example: A clock that consistently shows 3:05 PM when it's actually 3:00 PM is precise (consistent) but not accurate (wrong time).

Convert 2.5 hours to seconds using dimensional analysis

Setup: 2.5 hours × conversion factors Step 1: 2.5 hr × (60 min/1 hr) = 150 min Step 2: 150 min × (60 sec/1 min) = 9000 sec Alternatively: 2.5 hr × (3600 sec/1 hr) = 9000 sec Answer: 9000 seconds

Multiply (2.45 × 10³) × (3.2 × 10⁻²) and express in proper significant figures

Step 1: Multiply coefficients: 2.45 × 3.2 = 7.84 Step 2: Add exponents: 10³ × 10⁻² = 10¹ Step 3: Combine: 7.84 × 10¹ Step 4: Apply sig fig rules: 3.2 has 2 sig figs (fewest) Answer: 7.8 × 10¹ or 78

Why do we use scientific notation in physics measurements?

Scientific notation (N × 10ⁿ) serves three main purposes: 1. Avoids ambiguity about trailing zeros (230 vs 2.30 × 10²) 2. Makes very large/small numbers easier to read and calculate 3. Clearly shows the number of significant figures Example: 0.000045 becomes 4.5 × 10⁻⁵ (clearly 2 sig figs)

Calculate the displacement of a student who walks 30 m north, then 40 m east

Step 1: Draw vectors perpendicular to each other Step 2: Use Pythagorean theorem: R² = x² + y² Step 3: R² = (40 m)² + (30 m)² = 1600 + 900 = 2500 Step 4: R = √2500 = 50 m Step 5: Direction: θ = tan⁻¹(30/40) = 36.9° north of east Answer: 50 m at 36.9° north of east

What is the difference between distance and displacement?

Distance: Total ground covered during motion (scalar - magnitude only) Displacement: Change in position from start to end point (vector - magnitude and direction) Example: Walking around a 100m track and returning to start: - Distance = 100 m - Displacement = 0 m (no net change in position)

Two forces of 15 N and 20 N act on an object in the same direction. Find the resultant force.

Rule: Vectors in same direction → add magnitudes Step 1: Identify direction - both forces act in same direction Step 2: Add magnitudes: R = 15 N + 20 N = 35 N Step 3: Direction remains the same as both forces Answer: 35 N in the common direction

Add: 12.34 + 1.2 + 0.005. Apply significant figure rules for addition.

Rule for addition: Result determined by number with fewest decimal places Step 1: Identify decimal places: 12.34 (2), 1.2 (1), 0.005 (3) Step 2: Fewest decimal places = 1 (from 1.2) Step 3: Add normally: 12.34 + 1.2 + 0.005 = 13.545 Step 4: Round to 1 decimal place Answer: 13.5

List three examples each of scalar and vector quantities

Scalar Quantities (magnitude only): 1. Mass (50 kg) 2. Temperature (25°C) 3. Speed (60 km/h) Vector Quantities (magnitude + direction): 1. Velocity (60 km/h north) 2. Force (100 N downward) 3. Acceleration (9.8 m/s² downward)

Convert 45 km/h to m/s using dimensional analysis

Setup: 45 km/h × conversion factors Step 1: Convert km to m: 45 km/h × (1000 m/1 km) = 45000 m/h Step 2: Convert h to s: 45000 m/h × (1 h/3600 s) = 12.5 m/s Alternatively: 45 km/h × (1000 m/1 km) × (1 h/3600 s) = 12.5 m/s Answer: 12.5 m/s

Two forces of 8 N and 6 N act perpendicular to each other. Find the resultant.

Step 1: Apply Pythagorean theorem for perpendicular vectors Step 2: R² = (8 N)² + (6 N)² = 64 + 36 = 100 Step 3: R = √100 = 10 N Step 4: Find direction: θ = tan⁻¹(6/8) = tan⁻¹(0.75) = 36.9° Answer: 10 N at 36.9° from the 8 N force

How many significant figures are in the measurement 1200 m?

Problem: Trailing zeros without decimal point are ambiguous Step 1: Count definite significant figures: 1, 2 (definitely significant) Step 2: The zeros could be significant or just placeholders Step 3: Without additional information, assume minimum Answer: 2 significant figures (could be 3 or 4 if written as 1.200 × 10³ m)

What happens when two equal vectors act in opposite directions?

Rule: Opposite direction vectors → subtract magnitudes Result: The vectors cancel each other out completely Magnitude: |A| - |A| = 0 Example: 10 N east + 10 N west = 0 N (no net force) This creates equilibrium - no net effect on the object.

Give an example of direct and inverse proportionality in physics

Direct Proportionality (y = kx): Distance vs Time at constant speed: d = vt When time doubles, distance doubles Inverse Proportionality (y = k/x): Speed vs Time for constant distance: v = d/t When time doubles, speed halves Real example: For a 100m race, if time increases from 10s to 20s, speed decreases from 10 m/s to 5 m/s

Round 23.456 to 3 significant figures

Step 1: Identify first 3 significant figures: 2, 3, 4 Step 2: Look at the next digit: 5 Step 3: Since next digit ≥ 5, round up the last kept digit Step 4: 4 becomes 5 Answer: 23.5 (3 significant figures)

Why are vectors important in physics?

Vectors are crucial because many physical quantities have direction: 1. Force: Must know magnitude AND direction to predict motion 2. Velocity: Speed + direction determines where object goes 3. Electric field: Strength + direction affects charged particles 4. Momentum: Mass × velocity (includes direction) Without direction, we cannot fully describe or predict physical phenomena.

Express 0.000456 in scientific notation

Step 1: Move decimal point to get 1 ≤ |N| < 10 Step 2: 0.000456 → 4.56 (moved 4 places right) Step 3: Since we moved right, exponent is negative Step 4: Count places: 4 places = 10⁻⁴ Answer: 4.56 × 10⁻⁴

A car travels 60 km north, then 80 km south. Find distance and displacement.

Distance (scalar - total path): Step 1: Add all segments: 60 km + 80 km = 140 km Displacement (vector - net change): Step 2: Choose north as positive: +60 km - 80 km = -20 km Step 3: Negative means south direction Answer: Distance = 140 km, Displacement = 20 km south

What are the characteristics of exact vs inexact numbers? Give examples.

Exact Numbers: - No uncertainty - From definitions, counting, simple fractions - Infinite significant figures Examples: 12 items in a dozen, 100 cm in 1 m, 24 hours in a day Inexact Numbers: - Have uncertainty - From measurements - Limited significant figures Examples: height (1.75 m), temperature (25°C), mass of an apple (150 g)