14 Carbon monoxide gas is produced in a pond by the decay of organic matter - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 2

At steady speed, the buoyant force equals the viscous drag force acting on the bubble. We can use Stoke's law to find the drag force $F_d$:

$F_d = 6 imes au r v$

where:

• $au$ is the viscosity of the fluid,
• $r$ is the radius of the bubble,
• $v$ is the steady speed.

Setting the buoyant force equal to the drag force:

$F_b = F_d$

Substituting the known values:

$1.7 imes 10^{-5} = 6 imes (0.0011) imes (0.00075) imes v$

Now solve for $v$:

v = rac{1.7 imes 10^{-5}}{6 imes 0.0011 imes 0.00075}

Calculating this gives: $$v ext{ (approximately)} = 3.4 imes 10^{-3} ext{ m/s}.$

The increase in potential energy (U) when the distance between the two atoms changes can be calculated using the formula for potential energy stored in a spring:

U = rac{1}{2} k x^2

where:

• $k = 1195 ext{ N/m}$ is the stiffness constant,
• $x$ is the change in distance from equilibrium.

Given that the equilibrium distance $d$ is 12 mm and the new distance is 18 mm:

$x = 18 ext{ mm} - 12 ext{ mm} = 6 ext{ mm} = 0.006 ext{ m}$

Now substituting for $x$ into the potential energy equation:

U = rac{1}{2} imes 1195 imes (0.006)^2

This calculates to: $$U ext{ (approximately)} = 0.0214 ext{ J}.$