Eduqas Physics for A Level Year 2: Student Bk

100 Eduqas A Level Physics Year 2: Component 2 7 The −20 µC charge in Q6 is now free to move. Its mass is 1.00 g . (a) Calculate its initial acceleration. (b) Describe its subsequent motion assuming no resistance to motion (c) Calculate the greatest speed. Questions 8–13 refer to a dwarf planet of radius 1000 km . The gravitational force on an object of mass 1.00 kg , due to the planet, is 1.00 N on the surface of the planet. Question 11 introduces a satellite (moon) of the dwarf planet with a radius of 100 km , of the same density as the planet and with an orbital radius of 20 000 km . 8 Calculate: (a) the mass and mean density of the dwarf planet (b) the acceleration due to gravity at the surface (c) the gravitational potential at the surface (d) the gravitational potential energy of a 100 kg object on its surface. 9 Calculate the gravitational potential and field strength: (a) 5 000 km from the centre and (b) 1000 km above the surface of the dwarf planet. 10 An object of mass 10 kg is raised 100 km from the surface. (a) Calculate the increase in gravitational potential energy using the uniform field approximation, Δ U = mg Δ h . (b) Calculate the increase in gravitational potential energy using the equation derived from Newton’s law of gravitation. (c) Calculate the percentage error obtained by using the uniform field approximation. 11 For the satellite: (a) Calculate the gravitational field strength at its surface. (b) Calculate the gravitational potential at its surface due to: (i) the satellite alone, and (ii) the two bodies (i.e. dwarf planet and satellite). (c) Discuss briefly to what extent the position on the satellite affects the answer to (b)(ii). 12 The satellite is in a circular orbit around the dwarf planet. (a) Determine the gravitational acceleration due to the dwarf planet at the position of the satellite. (b) By equating this to the centripetal acceleration of the satellite in its orbit, determine the period of the orbit. 13 Between the bodies on the line joining their centres, the gravitational forces due to the dwarf planet and satellite act in opposite directions. (a) Determine the distance from the satellite at which these two forces are equal and opposite. (b) State the significance of this point for the gravitational potential energy variation along the line.