A LevelPhysicsOCRExam Questions5. Newtonian World & Astrophysics5.9 Gravitational Potential & Energy

Gravitational Potential & Energy (OCR A Level Physics)

Exam Questions

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5.9 Gravitational Potential & Energy

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5.9 Gravitational Potential & Energy

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1a1 mark
a)
Write an expression for the gravitational potential Vg at the surface of a planet of mass M and radius r.

[1]

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1b6 marks
b)
The table below shows some data for Mercury and Pluto.

  Mass / kg Radius / m Mean distance from Sun / m
Mercury 3.30 × 1023 2.44 × 106 57.9 × 109
Pluto 0.131 × 1023  1.19 × 106 5910 × 109

  

i)
Show that the escape velocity v of a gas molecule on the surface of Pluto is given by the equation

v equals square root of fraction numerator 2 G M over denominator r end fraction end root

where M is the mass of Pluto and r is its radius.

[2]

ii)
Calculate the escape velocity v of gas molecules on the surface of Pluto.



v = ................................. m s−1 [1]

iii)
Explain why Mercury has no atmosphere whilst Pluto still has a thin atmosphere. Use data from the table to support your explanation.

[3]

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1a3 marks

In June 2018, the spacecraft Hayabusa2 arrived at an asteroid called Ryugu.

a)
The asteroid orbits the Sun in an elliptical orbit as shown below.

q23a-paper-1-nov-2020-ocr-a-level-physics

The diagram is not drawn to scale.

i)
Indicate with a letter X on the orbit where the asteroid would be moving at maximum speed.

[1]

ii)
Use Kepler’s second law to explain your answer to (a)(i).

[2]

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1b4 marks
b)
The gravitational potential at a distance r from the centre of the asteroid Ryugu is Vg. The graph of Vg against begin mathsize 14px style 1 over r end style for the asteroid is shown below.

q23b-paper-1-nov-2020-ocr-a-level-physics

i)
Define gravitational potential.

[1]

ii)
Show that the magnitude of the gradient of the graph is equal to GM, where M is the mass of the asteroid and G is the gravitational constant.

[1]

iii)
Use the gradient of the graph to show that the mass M of the asteroid is about 4.6 × 1011 kg.




M = ...................................... kg [2]

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1c3 marks
c)
In October 2018, the probe Mobile Asteroid Surface Scout (MASCOT) was released from rest from the Hayabusa2 spacecraft from a distance of 600 m from the centre of the asteroid.

Assume that the spacecraft was stationary relative to the asteroid when MASCOT was dropped.

Use information from (b) to calculate the speed of the impact v when MASCOT landed on the surface of the asteroid.





v = ................................................ m s–1 [3]

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2a1 mark

This question is about a space probe which is in orbit around the Sun.

a)
Define the gravitational potential of an object at a point in a gravitational field.

[1]

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2b5 marks
b)
The space probe has mass 810 kg. The orbital radius of the space probe is 1.5 × 1011 m. The orbital period of the space probe around the Sun is 3.16 × 107 s.
The mass of the Sun is 2.0 × 1030 kg.

i)
Show that the magnitude of the gravitational potential energy of the space probe is about 7 × 1011 J.

[2]

ii)
Show that the kinetic energy of the space probe is half the value of your answer to (b)(i).

[3]

iii)
Calculate the total energy of the space probe.



total energy = ....................................................... J [1]

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2c6 marks
c)
The power source for the instrumentation on board the space probe is plutonium-238, which
provides 470 W initially.

Plutonium-238 decays by α-particle emission with a half-life of 88 years.
The kinetic energy of each α-particle is 8.8 × 10–13 J.

i)
Calculate the number N of plutonium-238 nuclei needed to provide the power of 470 W.





N = ......................................................... [3]

ii)
Calculate the power P still available from the plutonium-238 source 100 years later.





P = ..................................................... W [3]

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