23P2Q01

1a)

The surrounding water exerts pressure forces on all faces of the block.

Since pressure increases with depth,

the upward pressure force acting on the bottom surface is stronger than the downward pressure force acting on the top surface, resulting in a net upward force.

COMMENT: The horizontal pressure forces acting on all the other faces cancel out.

1bi)

Upthrust is equal to the weight of displaced fluid.

\displaystyle \begin{aligned}  (U&=\rho Vg) \\ U&=(1.0\times {{10}^{3}})(27.8\times {{10}^{-6}})(9.81) \\ &= 0.27\text{ N} \end{aligned}

COMMENT: For a “show” question, start with an explanatory sentence, and show all substitution values explicitly.

1bii)

Sum of CW moments = Sum of ACW moments

Fig. 1.1:           \displaystyle F\times 18.0=W\times 8.3\quad \cdots \cdots (1)

Fig. 1.2:           \displaystyle (F-0.27)\times 19.0=W\times 7.8\quad \cdots \cdots (2)

(1)÷ (2):           \displaystyle \begin{aligned}[t]  \frac{F}{F-0.27}\frac{18.0}{19.0}&=\frac{8.3}{7.8} \\ 140.4F&=157.7F-42.579 \\ F&=2.46\text{ N} \end{aligned}

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