Pressure and fluids

A hiker stands still on soft snow. Why do wide snowshoes reduce how far the hiker sinks?

1. A

   They reduce the hiker's weight.

2. B

   They increase the force on the snow.

3. C

   They spread the same force over a larger area, reducing pressure.

4. D

   They make the snow denser.

1. a

   Select and explain Select the correct explanation and connect it to the pressure equation.

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   Correct choiceC

   1. 1

      Selects option C: the same force spread over a larger area produces lower pressure.

   2. 2

      States pressure = force ÷ area.

   3. 3

      Explains that weight is essentially unchanged while larger contact area produces lower pressure.

A pressure sensor measures gauge pressure below the surface of a liquid. Gauge pressure excludes atmospheric pressure. Use g = 10 N kg⁻¹.

1. a

   Describe Describe the pattern supported by the data.

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   1. 1

      States that gauge pressure is directly proportional to depth.

   2. 2

      Supports the statement, for example by noting that doubling depth doubles pressure.

2. b

   Determine Use p = ρgh to determine the liquid's density.

   3
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   1. 1

      Rearranges to ρ = p ÷ (gh).

   2. 2

      Substitutes a consistent pair, for example 1600 ÷ (10 × 0.20).

   3. 3

      Obtains density = 800 kg m⁻³.

3. c

   Predict Predict the gauge pressure at a depth of 0.35 m and state one model assumption.

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   1. 1

      Calculates p = 800 × 10 × 0.35 = 2800 Pa.

   2. 2

      States a relevant assumption such as constant liquid density, uniform gravitational field, or a stationary connected liquid.

A sealed rescue platform has external volume 0.60 m³ and mass 120 kg. It operates in fresh water of density 1000 kg m⁻³. Designers require no more than 80% of its volume to be submerged in calm water, leaving reserve buoyancy. Each person is represented by a mass of 65 kg.

1. a

   Determine Determine the maximum total supported mass at the 80% submergence limit.

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   1. 1

      Calculates displaced volume at the limit = 0.80 × 0.60 = 0.48 m³.

   2. 2

      Uses floating equilibrium so supported mass equals displaced-water mass.

   3. 3

      Obtains maximum total mass = 1000 × 0.48 = 480 kg.

2. b

   Calculate Calculate the maximum whole number of represented people that can board without exceeding the design limit.

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   1. 1

      Finds available payload mass = 480 − 120 = 360 kg.

   2. 2

      Calculates 360 ÷ 65 = 5.54 and therefore limits the platform to 5 whole people under this model.

3. c

   Evaluate Evaluate whether advertising a five-person capacity is justified from this calculation alone.

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   1. 1

      Recognises that the calculation uses a simplified fixed person mass and calm fresh water.

   2. 2

      Identifies a relevant real condition such as equipment mass, waves, uneven loading, leakage, dynamic boarding, or water density.

   3. 3

      Recommends safety-factor testing or a lower rated capacity until stability and worst-case loading are verified.