Paper 4 Forces Answers

Q1 Force-extension experiment

1. Measure the original length with no load, then the new length with each load, using a ruler fixed beside the spring and reading at eye level to avoid parallax. Extension is new length minus original length. [2]
2. The load has weight $mg$ [1]. Once it is at rest, its acceleration is zero, so the spring tension equals its weight; hence the stretching force is $F=mg$ [1].
3. Award axes/units [1], sensible scales [1], accurate plots [2], and a straight fit through the proportional region followed by a suitable curve/segment through the final point [1].

4. Use a large triangle on the initial straight-line fit [1]:

$$k=\frac{\Delta F}{\Delta x}\approx \frac{3.00}{0.050}=60.0\mathrm{N}{\mathrm{m}}^{-1}.$$

Value [1] and unit [1]. 5. The graph remains proportional to about $x=0.050\mathrm{m}$ [1]; accept a reasonable estimate justified from the point where the trend departs from the initial straight line [1]. 6. Do not exceed the chosen maximum load/elastic range; add and remove masses gently; wait for oscillations to stop; keep the spring vertical and read at eye level. Any two relevant precautions [2].

Q2 Upthrust measurement

1. Upthrust is loss of apparent weight:

$$U=3.20-2.45=0.75\mathrm{N}.$$

[2] 2. If the object touches the beaker, the beaker exerts an additional contact force, so the newton-meter reading no longer represents only weight minus upthrust. [2] 3. $U=\rho gV$, so

$$V=\frac{U}{\rho g}=\frac{0.75}{1000(9.81)}=7.65\times 10^{-5}{\mathrm{m}}^3.$$

[3] 4. Take repeated readings after the object is fully submerged and stationary; remove air bubbles; read the scale at eye level; use a more sensitive force sensor. [1]