10. The speed of the blood in a blood vessel can indicate a person's health. A high speed may indicate a high stress on the walls of the blood vessel. (a) The speed $v$ of the blood in a blood vessel with a diameter $d$ is given by $v = \frac{kn}{\rho d}$ where $\eta$ is the viscosity of the blood $\rho$ is the density of the blood $k$ is a constant with no units. Show that the unit for $\eta$ is Pas. (b) As the speed of the blood changes, the wall of the blood vessel expands and contracts: The wall of a blood vessel consists of collagen fibres. The graph shows the stress-strain relationship up to the breaking stress of the collagen fibres. (i) Calculate the Young modulus of collagen fibres. (ii) Describe the behaviour of collagen fibres when the stress in the fibres is increased from the elastic limit until the fibres break.

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10. The speed of the blood in a blood vessel can indicate a person's health - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 2

Question 10

10. The speed of the blood in a blood vessel can indicate a person's health. A high speed may indicate a high stress on the walls of the blood vessel. (a) The speed... show full transcript

Worked Solution & Example Answer:10. The speed of the blood in a blood vessel can indicate a person's health - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 2

Step 1

Show that the unit for η is Pas.

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Answer

To determine the unit for viscosity ( $\eta$ ), we start with the equation:

$v = \frac{kn}{\rho d}$

Where:

$v$ (speed) has units of $m/s$ .
$k$ is dimensionless, hence has no units.
$n$ (viscosity) has units that we need to determine.
$\rho$ (density) has units of $kg/m^3$ .
$d$ (diameter) has units of $m$ .

Rearranging the formula for $\eta$ gives:

$\eta = \frac{v\rho d}{k}$

Substituting the units into the equation, we get:

$\text{Unit of } \eta = \frac{(m/s) (kg/m^3) (m)}{1}$

This simplifies to:

$\text{Unit of } \eta = \frac{kg}{m\cdot s}$

Therefore, the unit for viscosity is:
$\text{Pascal-second (Pa s)} = \text{Pas}.$

Step 2

Calculate the Young modulus of collagen fibres.

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Answer

To calculate the Young's modulus ( $E$ ) of the collagen fibres, we use the formula:

$E = \frac{\text{Stress}}{\text{Strain}}$

From the graph, select a point on the linear portion before the elastic limit. For instance, if stress is $2 \times 10^6 \text{ N/m}^2$ at a strain of $0.02$ , then:

Stress = $2 \times 10^6 \text{ N/m}^2$
Strain = $0.02$

Calculating Young's modulus:

$E = \frac{2 \times 10^6}{0.02} = 1 \times 10^8 \text{ N/m}^2$

Thus, the Young's modulus for collagen fibres is approximately $1 \times 10^8 \text{ N/m}^2$ .

Step 3

Describe the behaviour of collagen fibres when the stress in the fibres is increased from the elastic limit until the fibres break.

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Answer

As the stress in the collagen fibres increases from the elastic limit:

Elastic Region: Initially, the collagen fibres exhibit elastic behaviour, whereby they can return to their original shape once the stress is removed. The stress-strain relationship is linear in this region.
Yield Point: As the stress increases and approaches the limit, the fibres reach a yield point, where slight increases in stress result in significant changes in strain.
Plastic Deformation: Beyond the yield point, the fibres undergo plastic deformation, meaning they do not return fully to their original shape after the stress is removed.
Breaking Point: Finally, as stress continues to increase, the fibres reach their breaking point. At this stage, they can no longer withstand the applied stress and eventually break, resulting in the loss of structural integrity.

10. The speed of the blood in a blood vessel can indicate a person's health - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 2

Worked Solution & Example Answer:10. The speed of the blood in a blood vessel can indicate a person's health - Edexcel - A-Level Physics - Question 10 - 2023 - Paper 2

Show that the unit for η is Pas.

Calculate the Young modulus of collagen fibres.

Describe the behaviour of collagen fibres when the stress in the fibres is increased from the elastic limit until the fibres break.

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