CIE iGCSE Co-Ordinated Science P1.4 Density Exam Style Questions Paper 4

(a)(i)

The original (unloaded) length of the spring is read from where the graph line meets the y-axis (zero force).
Original length = 2.0 cm.
This is the length of the spring before any force is applied.

(a)(ii)

From the linear portion of the graph, using \( F = k \times x \) where \(x\) = extension (not total length).
Taking two points on the straight line, e.g. at \(F = 0\text{ N}\), length = 2.0 cm and at \(F = 5.0\text{ N}\), length = 12.0 cm, so extension = 10.0 cm.
Spring constant \( k = \frac{F}{x} = \frac{5.0}{10.0} = \mathbf{0.5} \) N/cm.

(a)(iii)

Point X is called the limit of proportionality.
Beyond this point, the extension is no longer proportional to the applied force (Hooke’s Law no longer applies).
The spring may become permanently deformed if stretched beyond the elastic limit.

(b)

Measurement 1: Measure the volume of the slotted mass using a displacement method (e.g. submerge it in a measuring cylinder or eureka can and record the volume of water displaced).
Measurement 2: Measure the mass of the slotted mass using a balance/scales.
Calculation: Calculate density using \( \rho = \frac{m}{V} \) (density = mass ÷ volume).

(c)(i)

The amplitude should be marked with a double-headed vertical arrow (\(\updownarrow\)) from the equilibrium (rest) position to the peak (crest) or trough of the wave.
Amplitude is the maximum displacement of a point on the wave from its equilibrium position.
It must be drawn from the centre dashed line to either the top or bottom of the wave.

(c)(ii)

Transverse waves are made by oscillations which act perpendicular / at right angles / 90° to the direction of energy transfer.
In the spring demonstration, the coils move up and down while the wave energy travels horizontally along the spring.
Examples of transverse waves include light waves and water waves.