IGCSE Physics: Measurement, Motion, Forces, and Density

Comprehensive practice flashcards covering measurement instruments, kinematics, mass and weight, density and flotation, vector addition, and Newton's laws of motion.

What is the distinction between base physical quantities and derived physical quantities, and what are their standard SI units?

Base quantities are fundamental properties measured directly: Length ($l$) in metres ($m$), Mass ($m$) in kilograms ($kg$), and Time ($t$) in seconds ($s$). Derived quantities are calculated from base units: Speed ($v$) in $m/s$, Volume ($V$) in $m^3$, and Density ($\rho$) in $kg/m^3$.

How do random errors differ from systematic errors in physical measurements, and how is each handled?

Random errors cause unpredictable scattering of readings (e.g., human reaction time or wind affecting a pendulum) and can be minimised by taking multiple readings and calculating an average. Systematic errors cause readings to deviate consistently in one direction (e.g., zero errors on a worn ruler or uncalibrated scales); averaging fails to eliminate them, so equipment must be recalibrated or zeroed.

How should a student measure length with a ruler and liquid volume with a measuring cylinder to avoid parallax error?

For length, position the eye directly perpendicular to the ruler mark, align the object precisely with the zero mark, and keep the ruler parallel and flush against the object. For liquid volume, position the eye at eye level and read from the bottom of the curved meniscus.

How is the multiple-measurement method used to determine the thickness of very thin objects, such as a single sheet of paper?

Stack a known number ($N$) of identical items together, measure the total thickness ($T$) using a ruler, and divide the total thickness by the count: $d = \frac{T}{N}$. For example, if $500$ sheets measure $45.0\,mm$, the average thickness of one sheet is $\frac{45.0\,mm}{500} = 0.090\,mm$.

Why is the period of a pendulum found by timing 20 oscillations rather than a single swing?

Human reaction time (~$0.2\,s$) introduces significant percentage error when timing a single fast event. Timing $20$ oscillations with a digital timer and dividing the total time ($t$) by $20$ ($T = \frac{t}{20}$) spreads the reaction time error over all swings, reducing uncertainty (e.g., down to $\pm 0.005\,s$ per swing).

Based on the provided micrometer diagram, what are the three steps to determine the total measurement, and what is the final reading shown?

1. Main Scale: Read the last visible sleeve mark ($16\,mm$).
2. Thimble Scale: Note the mark aligned with the datum line ($0.30\,mm$).
3. Combine: Add the sleeve and thimble readings ($16\,mm + 0.30\,mm = 16.30\,mm$).

What is the physical difference between distance and displacement?

Distance is a scalar quantity representing the total path length traversed by an object; it is always positive or zero. Displacement is a vector quantity representing the straight-line change in position from start to finish ($\Delta x = x_f - x_i$); it can be positive, negative, or zero depending on direction.

Why does a car moving around a circular roundabout at a steady 40 km/h have a changing velocity?

Speed is a scalar quantity that measures only how fast an object moves, whereas velocity is a vector that specifies both speed and direction. As the vehicle turns on the roundabout, its direction of travel continuously changes, which means its velocity continuously changes despite having constant speed.

How is acceleration defined, and what is its formula and SI unit?

Acceleration is the vector rate of change of velocity with respect to time: $a = \frac{v - u}{t}$, where $v$ is final velocity, $u$ is initial velocity, and $t$ is time. It is measured in $m/s^2$.

On a displacement-time ($s$-$t$) graph, what does the gradient represent, and how are stationary objects, steady velocities, and accelerations identified?

The gradient ($\frac{\Delta s}{\Delta t}$) equals velocity. A horizontal line (zero gradient) indicates a stationary object; a straight diagonal slope indicates a steady velocity (positive or negative); and a curved line indicates changing velocity (acceleration if getting steeper, deceleration if flattening).

On a curved displacement-time graph, how do instantaneous velocity and average velocity differ?

Instantaneous velocity is determined by calculating the gradient of the tangent line drawn to the curve at that specific single point in time. Average velocity across a time interval is determined by the gradient of the straight chord connecting the start and end points of that interval.

What two physical quantities can be derived directly from a velocity-time ($v$-$t$) graph, and how?

1. Acceleration: Found from the gradient of the line ($\frac{\Delta v}{\Delta t}$).
2. Displacement: Found from the geometric area bounded between the velocity curve and the time axis (using rectangles, triangles, or subtracting areas below the time axis).

What are the acceleration and peak velocity of an object in vertical free fall near Earth (ignoring air resistance)?

In free fall, all objects experience a constant downward acceleration due to gravity of $g = 9.81\,m/s^2$ (or $-9.81\,m/s^2$ when upward is positive). For an object projected vertically upward, its instantaneous velocity at the highest peak apex is exactly $0\,m/s$, while its acceleration remains $9.81\,m/s^2$ downwards.

What is the scientific difference between mass and weight?

Mass is a scalar measure of the quantity of matter in an object at rest relative to the observer (and its resistance to change in motion), measured in kilograms ($kg$). Weight is a vector force exerted on a mass due to a gravitational field ($W = mg$), measured in newtons ($N$).

How does the weight of a 42 kg astronaut differ between Earth ($g_E = 9.8\,N/kg$) and the Moon ($g_M = 1.6\,N/kg$)?

Mass remains $42\,kg$ in both locations. Weight on Earth is $W_E = 42 \times 9.8 = 411.6\,N \approx 410\,N$ ($2$ s.f.). Weight on the Moon is $W_M = 42 \times 1.6 = 67.2\,N \approx 67\,N$ ($2$ s.f.). Isabelle weighs about $6$ times less on the Moon because the Moon's gravitational field strength is much smaller.

What instruments are used to measure mass versus weight in a laboratory?

Mass is measured using a balance (digital top-pan balance or beam balance) giving readings in $kg$ or $g$. Weight is measured using a force meter or newtonmeter (containing a calibrated spring and hook) giving readings in $N$.

What is the definition of density, what is its mathematical formula, and how do you convert between $g/cm^3$ and $kg/m^3$?

Density ($\rho$) is the mass per unit volume of a material: $\rho = \frac{m}{V}$. To convert from $g/cm^3$ to $kg/m^3$, multiply by $1000$ (e.g., $1.0\,g/cm^3 = 1000\,kg/m^3$). To convert from $kg/m^3$ to $g/cm^3$, divide by $1000$.

How is the density of an irregular solid found using the water displacement method?

1. Measure the mass ($m$) of the dry solid using a digital balance.
2. Fill a measuring cylinder or Eureka (displacement) can with water to an initial level ($V_1$).
3. Carefully submerge the solid on a thin thread, recording the new raised water level ($V_2$).
4. Calculate the solid's volume: $V = V_2 - V_1$.
5. Calculate density using $\rho = \frac{m}{V}$.

What are four common sources of experimental error when measuring density, and how can they be avoided?

1. Parallax error: Read the meniscus directly at eye level.
2. Zero / Tare error: Ensure the balance is zeroed/tared before placing items on it.
3. Water splashing: Lower solids gently on a thread so water is not lost.
4. Trapped air bubbles: Tap or shake the submerged object gently to remove bubbles clinging to its surface.

What is the fundamental condition for an object or immiscible liquid to float in a fluid?

An object or immiscible liquid floats if its density is lower than the density of the surrounding fluid ($\rho_{\text{object}} < \rho_{\text{fluid}}$), which allows the upward upthrust force to balance its downward weight force. If its density exceeds the fluid's density, it sinks.

How does average density explain why a 100,000-tonne steel cargo ship floats while a small steel coin sinks?

A solid steel coin consists purely of steel ($\rho \approx 7.8\,g/cm^3$ to $7.9\,g/cm^3$), which is denser than water ($1.0\,g/cm^3$) and sinks. A large cargo ship is hollow and encloses vast volumes of trapped air; its average density (total mass divided by total displaced volume) is significantly lower than water, allowing it to float.

Why do traditional dhows and cargo vessels float higher in the Arabian Gulf than in freshwater rivers?

Due to high evaporation rates in the UAE climate, the Arabian Gulf has higher salinity, raising seawater density to roughly $1.03\,g/cm^3$ compared to freshwater at $1.00\,g/cm^3$. Because the denser liquid provides greater upthrust per unit volume displaced, ships float higher in Gulf saltwater.

What are the rules for graphically adding vectors using the tip-to-tail method?

1. Choose and state a suitable scale factor (ensuring the drawing fills at least half the page).
2. Draw the first vector from an origin with its scaled length and direction.
3. Position the tail of the second vector at the tip (arrowhead) of the first vector.
4. Draw the resultant vector from the tail of the first vector directly to the tip of the final vector, ensuring it has an arrowhead pointing from start to finish.

If two perpendicular forces of 30 N North and 40 N East act on an object, what is the magnitude of the resultant force?

Using Pythagoras theorem: $R = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50\,N$.

What are the four main physical effects that an unbalanced force can have on an object?

Forces can change an object's:

1. Speed (speeding up or slowing down)
2. Direction of motion
3. Shape (squashing, bending, or stretching)
4. Size

What does Newton's First Law of motion state?

Objects will remain at rest, or continue to move with a constant velocity in a straight line, unless acted upon by a non-zero resultant force.

Why is the Moon orbiting Earth at a constant speed of 2000 mph NOT an example of Newton's First Law?

Although the Moon moves at a constant speed, its direction of travel is constantly changing as it orbits Earth. Because velocity is a vector quantity involving direction, its velocity is continuously changing, which requires a non-zero resultant gravitational pull from Earth.

What does Newton's Second Law of motion state, and what is its equation?

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass: $F = ma$, where $F$ is the resultant force in newtons ($N$), $m$ is the mass in kilograms ($kg$), and $a$ is acceleration in $m/s^2$.

What is Hooke's Law, and under what condition does it apply?

Hooke's Law states that the extension ($x$) of an elastic object is directly proportional to the applied force ($F$), provided it has not exceeded the limit of proportionality: $F = kx$, where $k$ is the spring constant measured in $N/m$.

What do the linear region, the marked point 'X', and the curved region represent on this force-extension graph?

The linear region represents where force is directly proportional to extension obeying Hooke's Law (gradient equals spring constant $k$); the point 'X' represents the limit of proportionality; and the curved non-linear region represents where Hooke's Law no longer applies.

What force causes an object to move in circular motion, in which direction does it act, and what three factors determine its magnitude?

It requires a centripetal force acting perpendicularly to the motion, directed continuously toward the centre of the circle. The magnitude of the force required increases with: greater mass of the object, higher speed of the object, and a smaller radius of the circular path.

What causes friction in solids versus fluids, and how can each be reduced?

Solid friction is caused by microscopic imperfections on surfaces sliding over each other; it reduces speed, transfers energy by heating, and is reduced by smoothing or lubricating surfaces. Fluid friction (drag/air resistance) is caused by colliding particles of gas or liquid; it increases with speed and is reduced by streamlining the shape of the moving object.