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A student is using an elastic band to model the expansion of the Universe - Scottish Highers Physics - Question 5 - 2016

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A student is using an elastic band to model the expansion of the Universe. One end of the band is fixed in a clamp stand at V. Knots are tied in the band to represe... show full transcript

Worked Solution & Example Answer:A student is using an elastic band to model the expansion of the Universe - Scottish Highers Physics - Question 5 - 2016

Step 1

Complete the table to show the average speeds of the knots W and Y.

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Answer

To find the average speeds, we can use the formula:

extAveragespeed=DistanceTime ext{Average speed} = \frac{\text{Distance}}{\text{Time}}

For Knot W, the distance moved is 0.04 m over 2 seconds: Average speed of W=0.04 m2 s=0.02 ms−1\text{Average speed of W} = \frac{0.04 \, \text{m}}{2 \, \text{s}} = 0.02 \, \text{ms}^{-1}

For Knot Y, the distance moved is 0.06 m over the same time: Average speed of Y=0.06 m2 s=0.03 ms−1\text{Average speed of Y} = \frac{0.06 \, \text{m}}{2 \, \text{s}} = 0.03 \, \text{ms}^{-1}

Thus, the completed table is:

Knot Average speed (ms⁻¹) W 0.020 X
Y 0.030

Step 2

Explain why this model is a good simulation of the expansion of the Universe.

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Answer

This model effectively illustrates how galaxies, represented by the knots, are moving away from each other as the elastic band is stretched. Each knot moves at different speeds, which simulates the observation that more distant galaxies are receding faster. This behavior demonstrates Hubble's Law, which states that the recessional velocity of galaxies is directly proportional to their distance from us.

Step 3

Calculate the redshift of the light from the distant galaxy.

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Answer

The formula for redshift (z) is given by:

z=λobserved−λemittedλemittedz = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}}

Inserting the values: z=667 nm−656 nm656 nm=11 nm656 nm≈0.0168z = \frac{667 \, \text{nm} - 656 \, \text{nm}}{656 \, \text{nm}} = \frac{11 \, \text{nm}}{656 \, \text{nm}} \approx 0.0168

Thus, the redshift is approximately 0.0168.

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