IB Physics HL D 1 13 Hl Escape Speed Questions

Practise IB Physics HL D.1.13 by solving escape-speed, launch-energy, density and event-horizon problems.

Exam points

Derive and apply vₑₛc = √(2GM/r) from gravitational energy conservation.
Compare escape speed using mass, radius, density and multi-body gravitational data.
Analyse launch energy, maximum height, atmosphere retention and event-horizon implications.

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Study D.1.13 (HL)—Escape speed conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 2]

A uniform, spherical planet P has mass M and radius R.

A projectile of mass m is launched with kinetic energy $\frac{2 G M m}{3 R}$ from the surface of P.

Figure for Question IB Physics HL D 1 13 Hl Escape Speed Questions question 1 — IB Physics HL

Determine whether the projectile will escape the gravitational field of P.

ALTERNATE 1
$\begin{aligned} & E_{\mathrm{T}}=\lessdot \frac{2 G M m}{3 R}-\frac{G M m}{R}=»-\frac{1}{3} \frac{G M m}{R} & E_{\mathrm{T}}<0 \text { hence it will not escape } \end{aligned}$

ALTERNATE 2
$\frac{1}{2} m v^{2}=\frac{2 G M m}{3 R} \Rightarrow v=\sqrt{\frac{4 G M}{3 R}}$ $v<v_{\text {esc }}$ hence it will not escape

Argument necessary to get second MP. Do not accept a bald statement that it will not escape.

Allow ECF from MP1.

[2]

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IB Physics HL D 1 13 Hl Escape Speed Questions question 1