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IB SL/HL Physics I Briggs March 26, 2021 Name____________________________________________________________ Topic 6 - Gravitation and Circular Motion – TEST – SUMMATIVE [30 TOTAL MARKS] 1

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IB SL/HL Physics I Briggs March 26, 2021 Name____________________________________________________________ Topic 6 - Gravitation and Circular Motion – TEST – SUMMATIVE [30 TOTAL MARKS] 1. [1 mark] Scaled Score_____________ Raw Score____________ A motorcyclist is cornering on a curved race track. Which combination of changes of banking angle θ and coefficient of friction μ between the tyres and road allows the motorcyclist to travel around the corner at greater speed? 2. [1 mark] Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass. What is the ratio ? A. B. C. 2 D. 4 3. [1 mark] A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3 rad s-1. What is the magnitude and direction of the force responsible for this motion? 2 4. [1 mark] The mass at the end of a pendulum is made to move in a horizontal circle of radius r at constant speed. The magnitude of the net force on the mass is F. What is the direction of F and the work done by F during half a revolution? 5. [1 mark] An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω. What is the tension in the string when the object is at the bottom of the circle? A. m(ω2r + g) B. m(ω2r – g) C. mg(ω2r + 1) D. mg(ω2r – 1) 3 6. [1 mark] A mass at the end of a string is swung in a horizontal circle at increasing speed until the string breaks. The subsequent path taken by the mass is a A. line along a radius of the circle. B. horizontal circle. C. curve in a horizontal plane. D. curve in a vertical plane. 4 7. [1 mark] A mass attached to a string rotates in a gravitational field with a constant period in a vertical plane. How do the tension in the string and the kinetic energy of the mass compare at P and Q? 8. [1 mark] A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X? A. B. T C. D. 2T 5 9. [1 mark] A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc. Point X is a distance 2L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a. What is the linear speed and centripetal acceleration of point X? 10. [1 mark] Which single condition enables Newton’s universal law of gravitation to be used to predict the force between the Earth and the Sun? A. The Earth and the Sun both have a very large radius. B. The distance between the Earth and the Sun is approximately constant. C. The Earth and the Sun both have a very large mass. D. The Earth and the Sun behave as point masses. 6 11a. [2 marks] This question is about circular motion. The diagram shows a car moving at a constant speed over a curved bridge. At the position shown, the top surface of the bridge has a radius of curvature of 50 m. Explain why the car is accelerating even though it is moving with a constant speed. 11b. [2 marks] On the diagram, draw and label the vertical forces acting on the car in the position shown. 7 11c. [3 marks] Calculate the maximum speed at which the car will stay in contact with the bridge. 12a. [2 marks] State, in words, Newton’s universal law of gravitation. 8 12b. [3 marks] The diagram shows a satellite orbiting the Earth. The satellite is part of the network of globalpositioning satellites (GPS) that transmit radio signals used to locate the position of receivers that are located on the Earth. When the satellite is directly overhead, the microwave signal reaches the receiver 67ms after it leaves the satellite. (ii) Calculate the height of the satellite above the surface of the Earth 9 12c. [8 marks] (i) Explain why the satellite is accelerating towards the centre of the Earth even though its orbital speed is constant. (ii) Calculate the gravitational field strength due to the Earth at the position of the satellite. Mass of Earth = 6.0×1024kg Radius of Earth = 6.4×106m (iii) Determine the orbital speed of the satellite. (iv) Determine, in hours, the orbital period of the satellite. Printed for Clearwater Central Catholic High School © International Baccalaureate Organization 2020 10