1. This question is about the planet Jupiter and one of the moons that orbits it, called lo.

   

    

   lo orbits Jupiter at a speed, v of 1.7 x 10⁴ m s^-1 at an orbital radius, r, of 4.2 x 10⁸m.

   a) Show that lo takes approximately 43 hours to orbit Jupiter once.

   (2 Marks)

   b) lo is held in its orbit by a centripetal force,, where m is the mass of lo. This force is the gravitational attraction between lo and Jupiter.

   i) Show thatwhere M is the mass of Jupiter.

   ii) Show that the mass of Jupiter is about 2.0 x 10²⁷ kg.

   (4 Marks)

   c) Show that the gravitational potential at the top of Jupiter's atmosphere, 7.1 x 10⁷ m from the centre of the planet, is about -2 x 10⁹ Jkg^-1.

   Assume that Jupiter is a sphere.

   (2 Marks)

   d) In July 1994, comet Shoemaker-Levy 9 crashed into Jupiter causing dramatic heating of the planet's atmosphere. During the approach to the planet, the comet broke up. One piece that struck the planet had a mass of about 4 x 10¹² kg.

   This fragment crossed the orbit of lo heading directly towards Jupiter with a velocity of 10 km s^-1.

   i) Show that kinetic energy of the fragment at that moment is 2 x 10²⁰ J.

   (1 Mark)

   ii) Explain why the fragment will enter the atmosphere of Jupiter with a velocity greater than 10km s^-1.

   (2 Marks)

   (Marks available: 11)

2. a) A cyclist goes round a circular track, of radius 10 m, at a constant speed of 8.0 m s^-1.

   What is the acceleration of the cyclist and what is its direction?

   (3 Marks)

   b) What is the resultant force on the cycle and the rider if together they have a mass of 90 kg?

   (2 Marks)

   (Marks available: 5)

Answer