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Figure 6 shows a rotating spacecraft that is proposed to carry astronauts to Mars - AQA - A-Level Physics - Question 4 - 2021 - Paper 1
Question 4
Figure 6 shows a rotating spacecraft that is proposed to carry astronauts to Mars. The spacecraft consists of two parts A and B connected by a rigid cylindrical rod... show full transcript
Worked Solution & Example Answer:Figure 6 shows a rotating spacecraft that is proposed to carry astronauts to Mars - AQA - A-Level Physics - Question 4 - 2021 - Paper 1
Step 1
Explain why the spacecraft imitates gravitational force.
Answer
As the spacecraft rotates, the centripetal force acts inward towards the center of rotation. This force is essential for maintaining circular motion. The astronauts experience this force as an equivalent to gravitational force pushing them against the floor. Thus, the rotation creates a sensation of weight, mimicking the effect of gravity on their bodies.
Step 2
Show that r_A is given by the formula.
Answer
To derive the formula, we analyze the forces acting on masses A and B:
The centripetal force for mass A is given by: F_{cA} = m_A rac{v_A^2}{r_A}
Where (the tangential speed of A) is related to its angular speed as . Hence,
F_{cA} = m_A rac{(r_A heta)^2}{r_A} = m_A r_A heta^2
Similarly, for mass B, we have: F_{cB} = m_B rac{v_B^2}{r_B} = m_B r_B heta^2
By balancing the forces acting on both masses and noting that:
It follows that:
Therefore: rac{r_A}{r_B} = rac{m_B}{m_A}
Working with the total distance :
Thus, we can express: r_A = rac{m_B}{m_A + m_B} L