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A spaceship is used to take astronauts and equipment to the International Space Station - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 1
Question 16
A spaceship is used to take astronauts and equipment to the International Space Station. The spaceship consists of an orbital module, a descent module and a service ... show full transcript
Worked Solution & Example Answer:A spaceship is used to take astronauts and equipment to the International Space Station - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 1
Step 1
Determine the velocity v of the descent module after separation.
Answer
To determine the velocity of the descent module after separation, we use the principle of conservation of momentum.
Let:
- mass of the orbital module (O) = 1350 kg
- velocity of O = 0.82 m/s (away from D)
- mass of the descent module (D) = 2950 kg (to be determined)
- velocity of D = v
- mass of the service module (S) = 2100 kg
- velocity of S = -0.58 m/s (away from D)
According to the conservation of momentum, the total momentum before separation should equal the total momentum after separation:
Substituting in the values:
Calculating the left side:
This simplifies to:
From this, we find:
Therefore, the magnitude of the velocity of the descent module after separation is approximately 0.04 m/s, directed towards the left.
Step 2
Explain why the velocity of the descent module changes when the rocket motor is used.
Answer
When the rocket motor is fired, it expels hot gases at high velocity, creating a reaction force that propels the descent module in the opposite direction. This is explained by Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction.
As the gas is expelled backward, the descent module experiences a forward thrust, leading to an increase in its velocity. This change in motion illustrates Newton's first and second laws as well; the descent module accelerates due to the net unbalanced force acting on it, resulting in a change in its state of motion.
Step 3
Calculate the average force exerted on the hot gas during this time.
Answer
To calculate the average force exerted on the gas, we can use Newton’s second law, which relates force, mass, and acceleration. First, we need to find the acceleration (a) of the descent module.
Using the formula:
where ( \Delta v = 0.58 m/s ) and ( t = 5.0 s ), we calculate:
Next, we calculate the net force (F) using:
where ( m = 2950 kg ):
Therefore, the average force exerted on the hot gas during this time is approximately 342.2 N.