A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020. The rocket was headed for the International Space Station (ISS). (i) The rocket was visible in Irish skies 15 minutes after take-off. At that time it had travelled a distance of 6484 km. Calculate the rocket’s average speed during this part of the journey. (ii) The rocket later docked on the ISS. The ISS orbits the Earth every 93 minutes. How many full orbits of the Earth does the ISS complete each day? (iii) Newton’s law of universal gravitation describes the force of attraction between the ISS and the Earth. State Newton’s law of universal gravitation. (iv) The ISS is located 400 km above the Earth’s surface. At this altitude, the acceleration due to gravity is 90% as strong as it is on the Earth’s surface. Before travelling to the ISS, the mass of one of the astronauts was measured to be 85 kg. (v) Calculate the astronaut’s weight on Earth. (vi) What is the astronaut’s mass at the altitude of the ISS? (vii) Calculate the astronaut’s weight at the altitude of the ISS. (acceleration due to gravity on Earth’s surface = 9.8 m/s²)

Leaving Cert Physics Force, Mass & Momentum: A SpaceX Falcon 9 rocket carryin

A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020 - Leaving Cert Physics - Question a - 2021

Question a

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A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020. The rocket was headed for the International Spac... show full transcript

Worked Solution & Example Answer:A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020 - Leaving Cert Physics - Question a - 2021

Step 1

Calculate the rocket’s average speed during this part of the journey.

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Answer

To find the average speed of the rocket, we can use the formula:

v = \frac{d}{t}

Where:

$v$ is the average speed,
$d$ is the distance travelled (6484 km), and
$t$ is the time taken (15 minutes = 0.25 hours).

Substituting the values, we get:

v = \frac{6484 \text{ km}}{0.25 \text{ hours}} = 25936 \text{ km/h}

Step 2

How many full orbits of the Earth does the ISS complete each day?

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Answer

The ISS completes one orbit every 93 minutes. To find the number of orbits in a day:

\text{Number of orbits} = \frac{24 \text{ hours} \times 60 \text{ minutes/hour}}{93 \text{ minutes/orbit}} \approx 15.48

Since we are looking for whole orbits, the ISS completes 15 full orbits each day.

Step 3

State Newton’s law of universal gravitation.

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Answer

Newton’s law of universal gravitation states that every point mass attracts every single other point mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them:

F = G \frac{m_1 m_2}{r^2}

Where:

$F$ is the gravitational force,
$G$ is the gravitational constant,
$m_1$ and $m_2$ are the masses of the objects, and
$r$ is the distance between the centers of the two masses.

Step 4

Calculate the astronaut’s weight on Earth.

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Answer

The weight of the astronaut on Earth can be calculated using the formula:

W = m \cdot g

Where:

$W$ is the weight,
$m$ is the mass (85 kg), and
$g$ is the acceleration due to gravity on Earth (9.8 m/s²).

Thus, the astronaut’s weight is:

W = 85 \text{ kg} \times 9.8 \text{ m/s²} = 833 \text{ N}

Step 5

What is the astronaut’s mass at the altitude of the ISS?

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Answer

The astronaut’s mass remains constant regardless of altitude. Therefore, the astronaut's mass at the altitude of the ISS is still 85 kg.

Step 6

Calculate the astronaut’s weight at the altitude of the ISS.

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Answer

At the altitude of the ISS, the acceleration due to gravity is 90% of that on Earth's surface:

g_{ISS} = 0.9 \times 9.8 \, ext{m/s²} = 8.82 \, ext{m/s²}

Now we can find the astronaut's weight at the altitude of the ISS using:

W_{ISS} = m \cdot g_{ISS} = 85 \, ext{kg} \times 8.82 \, ext{m/s²} = 749.7 \, ext{N}

A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020 - Leaving Cert Physics - Question a - 2021

Worked Solution & Example Answer:A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020 - Leaving Cert Physics - Question a - 2021

Calculate the rocket’s average speed during this part of the journey.

How many full orbits of the Earth does the ISS complete each day?

State Newton’s law of universal gravitation.

Calculate the astronaut’s weight on Earth.

What is the astronaut’s mass at the altitude of the ISS?

Calculate the astronaut’s weight at the altitude of the ISS.

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