CAIE A-Level Physics A2 13.4.3 The Concept of Gravitational Potential Leads to the Gravitational Potential

[Maximum number: 4]

(a)

An isolated uniform spherical planet has gravitational potential $\phi$ at its surface.

A particle of mass m is projected vertically upwards from the surface. The particle is given just enough kinetic energy to travel to an infinite distance away from the planet, escaping from the gravitational pull of the planet, without any additional work being done on it.

[ 3 ]

(i)

Determine an expression, in terms of m and $\phi$ , for the gravitational potential energy $E_{\mathrm{P}}$ of the particle at the surface of the planet.

E_{P}=

[ 1 ]

$E_{\mathrm{P}}=m \phi$

(ii)

Show that the speed v at which the particle is projected upwards from the surface of the planet is given by

v=\sqrt{-2 \phi}

[ 2 ]

$1 / 2 m v^{2}+m \phi=0$
correct algebra leading to $v=\sqrt{ }(-2 \phi)$

(b)

A particle is moving upwards at the surface of the Moon.

Use your answer in (a)(ii) and the expression in (b)(ii) to determine the minimum speed of this particle that will result in it escaping from the gravitational pull of the Moon.
speed = $\mathrm{m} \mathrm{s}^{-1}$

[ 1 ]

$\begin{aligned} \text { speed } =\sqrt{ }\left(2 \times 2.9 \times 10^{6}\right) =2400 \mathrm{~m} \mathrm{~s}^{-1} \end{aligned}$

CAIE A-Level Physics A2 13.4.3 The Concept of Gravitational Potential Leads to the Gravitational Potential Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)