Physics 9702 · AS & A Level · Gravitational force between point masses

Gravitational force between point masses — practice question

Treat the Earth as a sphere with uniform density, radius $6.37 \times 10^3\,\text{km}$, and mass $5.98 \times 10^{24}\,\text{kg}$ all concentrated at the centre. The Earth rotates about its axis in a period of $24.0\,\text{hours}$.
(a(i))[2]

A stone with mass $2.50\,\text{kg}$ is at rest on the Earth’s surface at the Equator. 1. Using Newton's law of gravitation, calculate the gravitational force acting on the stone.

(a(i))[2]

2. Find the force needed to keep the stone moving along its circular path.

(a(ii))[2]

The stone is now suspended from a newton-meter. Use your answers in (i) to find the reading on the meter. Give your answer to three significant figures.

(a(i).1)[2]

Using Newton’s law of gravitation, calculate the gravitational force acting on the stone.

(a(i).2)[2]

Find the force needed to keep the stone moving along its circular path.

(b)[3]

A satellite is orbiting the Earth. For an astronaut inside it, his sensation of weight is produced by the contact force from his surroundings. The astronaut says that he is ‘weightless’, even though he is in Earth’s gravitational field. Explain what is meant by the astronaut saying he is ‘weightless’.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct application of Newton’s law of gravitation $F = G m_1 m_2 / x^2$, followed by suitable substitution, gives $F = 24.6\,\text{N}$ (allow 2 s.f. or better).

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