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Forces and Motion - Measurement in Science

Grade 9IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Measurement in science relies on the International System of Units (SI). The base units for Forces and Motion are the meter (mm) for length, kilogram (kgkg) for mass, and second (ss) for time.

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Derived units are combinations of base units. For example, the unit for velocity is meters per second (m/sm/s) and the unit for force is the Newton (NN), where 1 N=1 kg⋅m/s21\ N = 1\ kg \cdot m/s^2.

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Scalar quantities have only magnitude (e.g., speed, distance, mass), while Vector quantities have both magnitude and direction (e.g., velocity, displacement, force, acceleration).

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Accuracy refers to how close a measurement is to the true value, while Precision refers to the consistency of repeated measurements.

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Significant figures (SF) are used to express the uncertainty in a measurement. When multiplying or dividing, the result should have the same number of SF as the value with the fewest SF used in the calculation.

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Systematic errors are consistent inaccuracies (like a scale that isn't zeroed), whereas random errors are unpredictable fluctuations in measurements.

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Scientific notation is used to express very large or very small numbers in the form a×10na \times 10^n, where 1≤a<101 \le a < 10.

📐Formulae

Speed(v)=Distance(d)Time(t)\text{Speed} (v) = \frac{\text{Distance} (d)}{\text{Time} (t)}

Velocity(v⃗)=Displacement(Δs⃗)Time(t)\text{Velocity} (\vec{v}) = \frac{\text{Displacement} (\Delta \vec{s})}{\text{Time} (t)}

Acceleration(a)=v−ut\text{Acceleration} (a) = \frac{v - u}{t}

Force(F)=m×a\text{Force} (F) = m \times a

Density(ρ)=mV\text{Density} (\rho) = \frac{m}{V}

Weight(W)=m×g\text{Weight} (W) = m \times g

💡Examples

Problem 1:

A car moves a distance of 120 km120\ \text{km} in 1.5 hours1.5\ \text{hours}. Calculate its average speed in meters per second (m/sm/s).

Solution:

First, convert distance to meters: 120 km×1000=120,000 m120\ \text{km} \times 1000 = 120,000\ m Next, convert time to seconds: 1.5 hours×3600=5,400 s1.5\ \text{hours} \times 3600 = 5,400\ s Now, apply the formula: v=dtv = \frac{d}{t} v=120,0005,400v = \frac{120,000}{5,400} v≈22.22 m/sv \approx 22.22\ m/s

Explanation:

To find speed in SI units, we must ensure distance is in meters (mm) and time is in seconds (ss) before dividing.

Problem 2:

An object has a mass of 5.0 kg5.0\ kg and is acted upon by a net force of 25 N25\ N. Determine the acceleration produced.

Solution:

Using Newton's Second Law: F=m×aF = m \times a Rearrange for aa: a=Fma = \frac{F}{m} Substitute the values: a=25 N5.0 kga = \frac{25\ N}{5.0\ kg} a=5.0 m/s2a = 5.0\ m/s^2

Explanation:

Acceleration is directly proportional to the force applied and inversely proportional to the mass of the object.

Problem 3:

Calculate the volume of a block of wood that has a mass of 450 g450\ g and a density of 0.60 g/cm30.60\ g/cm^3.

Solution:

Use the density formula: ρ=mV\rho = \frac{m}{V} Rearrange to solve for Volume (VV): V=mρV = \frac{m}{\rho} Substitute the values: V=4500.60V = \frac{450}{0.60} V=750 cm3V = 750\ cm^3

Explanation:

Density measurement relates mass to the space occupied. The units must be consistent (both in grams and centimeters cubed).