YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS

YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS QUESTION 1 (1995 EXAM)

(a) State Newton's Universal Law of Gravitation in words

Name:

Between any two masses, there exists a mutual attractive force. This force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. This force acts along a line between the centres of the masses.

(3 marks)

(b) A satellite of mass (m) moves in orbit of a planet with mass (M). The satellite, m, is smaller in mass than the planet, M. Assume that the satellite moves around the planet in a circular orbit with a radius, R with a constant speed, v.

(i) Explain how it is possible for the gravitational force to cause the satellite to accelerate while its speed remains constant.

Its speed maybe constant in magnitude but the direction of this motion is constantly changing over time due to the gravitational force constantly pulling the satellite towards the central mass. Since this force is constant and the speed is constantly changing per unit time, the body is acceleration.

(2 marks)

(ii) If T is the period of the satellite in its orbit around the planet, show that the radius of the

orbit of the satellite is r = 34222 given that T2 =

423 Gm2

=

=

r

=

(2 marks)

(iii) Calculate the moon's orbital radius given that its period of rotation is approximately 27 days and 7 hours (2.3582 x 106 s)

r

=

r

=

. - .

(. )

r

=

.

r = .

(3 marks)

QUESTION 2 (1996 EXAM)

Whilst orbiting the Earth, the space shuttle Endeavour had a velocity of 7.8 x 103 ms-1 (a) Calculate the radius of its circular orbit

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. - .

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= .

(2 marks)

(b) Two isolated masses M and m are separated by a distance, r. The mass M is twice the mass of the smaller body, m.

On the diagram above, draw vector arrows to illustrate the gravitational force (F) on each mass (2 marks)

HINT: Despite one mass being larger, the gravitational force acting on each object is equal in magnitude but opposite in direction.

QUESTION 3 (1999 EXAM)

The uniform circular motion of a space vehicle in a circular orbit round a planet is caused by the gravitational force between the planet and the vehicle.

(a) Calculate the magnitude and direction of the gravitational force on a space vehicle of mass m= 1.00 x 103 kg at a distance r of 1.65 x 107 m from the centre of a planet of mass M = 2.00 x 1025 kg given the Universal Gravitation law ( = 122).

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. - . .

=

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= .

(3 marks)

(b) Show that the speed v of the space vehicle is given by the formula = 2

=

=

(Cancel out like terms)

=

(2 marks)

(c) Using the relationship for the speed of the space vehicle given in part (ii) and an expression for the

period T, showing that (T2 = 4Gm223)

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=

Squaring everything in equation one yields:

=

=

Cancelling gives

Rearranging this gives =

(3 marks)

QUESTION 4 (2000 EXAM)

(a) Calculate the magnitude of the gravitational force F on mass m = 20.0 kg, positioned at 1.00 x 106 m above the Earth's surface. The mass of the Earth ME = 5.98 x 1024 kg and the radius of the Earth RE = 6.38 x 106 m.

r = 1.00 x 106 + 6.38 x 106 = 7.38 x 106

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=

(3 marks)

(b) A space vehicle of mass m is moving at a constant speed v in a circular orbit of radius r round the Earth.

(i) Derive an expression for v in terms of the radius r and the mass of the Earth ME.

=

=

(Cancel out like terms)

=

(3 marks)

(ii) Explain why the space vehicle does not need to use rocket engines to maintain its uniform circular motion. Ignore air resistance.

As the gravitation al force is supplying the centripetal acceleration and this force is constant.

(2 marks)

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