CAIE A-Level Physics 4.3.6 Calculating Upthrust

Practise calculating upthrust from F = rho gV, rearranging for unknowns and applying Archimedes’ principle to floating, suspended or apparent-weight problems.

Exam points

calculate upthrust using F = ρgV from the density of the displaced fluid and the displaced volume
rearrange F = ρgV to determine displaced volume, fluid density or gravitational field strength
apply Archimedes’ principle with a force balance and consistent units to explain floating, suspension or apparent weight in a fluid

[Maximum number: 2]

A cylinder is suspended from the end of a string. The cylinder is stationary in water with the axis of the cylinder vertical, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

The cylinder has weight 0.84 N , height h and a circular cross-section of diameter 0.031 m . The density of the water is $1.0 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ . The difference between the pressures on the top and bottom faces of the cylinder is 520 Pa .

Show that the upthrust acting on the cylinder is 0.39 N .

$\begin{aligned} (\text { upthrust } =)(\Delta) p \times A =(\Delta) p \times \pi(d / 2)^{2} \text { or }(\Delta) p \times \pi r^{2} \end{aligned}$

C1

$=520 \times \pi(0.031 / 2)^{2}=0.39(\mathrm{~N})$

A1

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4.3.6—The upthrust acting on an object in a fluid using the equation F = ρgV question 1