Textbook Chap 4 Gravitational force and fields answers

Student book answers 4.1 What is gravity? Pages 116–117 Check your learning 4.1 Describe and explain 1 Explain how Aristotle’s explanation for the motion of heavy objects was discredited. Aristotle argued that every object has a natural place and need to go there, and that the heavier an object is the quicker it will fall. Galileo proved that this is not the case with a series of experiments. 2 Describe how the word ‘gravity’ changed meanings in Newton’s writings . Gravity originally meant ‘heavy’ but Newton began using it to refer to a force between objects. Apply, analyse and interpret 3 In his treatise on motion, Newton compared the gravitational force to the electrostatic and magnetic forces. He said that gravity was an attractive force only. Deduce how this differs from the electrostatic and magnetic forces. Electrostatic and magnetic forces can also be attractive (for electrostatics a + and – charge will attract; for magnets a N-pole and a S-pole will attract). We say ‘unlike poles/charges attract’, but for mass, like masses attract. (If there was an anti-mass it may repel a mass). Investigate, evaluate and communicate 4 It is said that gravity was invented by Newton, whereas others say he discovered it. Evaluate these two claims. Newton gave the name ‘gravity’ to the natural phenomenon, whereby objects are attracted to each other. It could be said that he invented a model or laws that explain falling bodies, and the attraction between planets. Astronomers before Newton had discovered the orbits of planets, but he was the first to use the term ‘the force of gravity’ in his model of the universe. 5 Propose , with reasons, whether or not this statement is true: Gravitational waves didn’t exist until they were discovered in 2015. Something seems to happen when massive bodies like black holes collide and this phenomena has always existed. Signals are detected on Earth and these are said to be proof of gravitational waves. It is a good model and has supporting evidence, but the notion of gravitational waves being an explanation for this effect has been around for a 100 years. So, we could say the theory or model of gravitational waves was invented 100 years ago. 1 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

Student book answers 4.2 Newton’s law of universal gravitation Pages 118–124 Check your learning 4.2 Describe and explain 1 Newton’s law of gravitation is said to be an inverse square law. Explain what that means. The gravitational force is inversely proportional to the square of the distance between the two objects. 2 Determine what happens to the gravitationalforce when: a one of the masses is doubled The force is doubled b the distance between the objects is halved. One-quarter the force 3 Explain why Earth’s radius needs to be taken into account for objects near the surface, whencalculating gravitational forces. When using Newton’s law of gravitational attraction the objects should be treated as point masses (without size) so if the object is on the surface of the Earth it is the Earth radius away from the centre. 4 Calculate the force between the Sun ( m = 2.0 × 10 30 kg) and Earth ( m = 5.97 × 10 24 kg) assuming their centres are 1.5 × 10 8 km apart. 5 A 10 kg rock rests on the ground. Calculate the gravitational force acting on it, using Newton’s law of universal gravitation. 2 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

Student book answers 4.3 Gravitational fields Pages 125–131 Check your learning 4.3 Describe and explain 1 Explain how the unit symbol N kg –1 is equivalent to m s –2 . 2 Describe a gravitational field. A gravitational field is a region of space where a gravitational force is experienced. 3 Define ‘gravitational field strength’ and state its units. Gravitational field strength is the gravitational force per unit of mass. Units: Newtons per kilogram (N kg -1 ) 4 Explain what is meant by ‘the gravitational field strength does not depend on the mass of the object in the field’. Gravitational field strength is a measure of the force per unit of mass. The force depends on the mass but gravitational field strength is the factor that relates mass to strength. 5 Calculate the gravitational field strength at a point 100 000 km above Earth’s centre. 6 Clarify how the direction of a gravitational field is defined. It is the direction that a mass would fall freely in the field. 4 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

Apply, analyse and interpret 7 Determine the gravitational field strength at a point whose distance from Earth’s surface is equal to three Earth radii. 8 Determine the altitude above Earth’s surface where the gravitational field strength is one-eighth the value on the surface. 9 Derive a location between the Sun and Earth where the gravitational field between them due to their mass is equal to zero. Let x be the distance from the point to the Sun. 5 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

7 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

Student book answers Chapter 4 Review Pages 132–135 Revision questions The relative difficulty of these questions is indicated by the number of stars beside each question number: * = low; ** = medium; *** = high. For questions that follow, use the following data: Constant Value G (on surface of Earth) = 9.8 ms –2 r Mo (radius of Moon’s orbit around Earth) = 3.8  10 11 m G = 6.67  10 –11 Nm 2 kg –2 r Eo (radius of Earth’s orbit around Sun) = 1.5  10 11 m Body Mass Radius Earth m E = 5.97  10 24 kg r E = 6.37  10 6 m Moon m M = 7.34  10 22 kg r M = 1.74  10 6 m Sun m S = 2.0  10 30 kg r S = 6.96  10 8 m Multiple choice 1 Select the diagram in Figure 1 that cannot be used as a diagram for a gravitational field. FIGURE 1 Answer: A. Reason: The field should point towards mass. 2 There are many planets in the universe orbiting a star other than our own Sun. Most of these planets are quite huge – as big as Jupiter. The planet Kepler-7b has a mass 0.433 times that of Jupiter and a radius 1.614 times that of Jupiter. If the gravitational field strength at the surface of Kepler-7b is g K , and the gravitational field strength at the surface of Jupiter to be g J , the ratio is: *A 0.17 B 0.27 C 0.69 8 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

FIGURE 2 Answer B. There is a gravitational force pulling on the Moon that acts towards Earth. This provides the centripetal force that keeps the Moon in orbit. There is only one force ( F g ) but it is equal in magnitude and direction to F c . We can eliminate A as F c points the wrong way. We can eliminate D as F c points the wrong way and is a different magnitude. Option C has both forces pointing the right way and equal in size but because there is only one force (not two) it is wrong. 5 Select the statement that best defines gravitational field strength. A It is the force acting on a small object in the field. *B It is the force acting on a 1 kg object in the field. C It is the work done on a 1 kg object to shift it 1.0 m in the field. D It is the work done by a field on shifting a 1 kg object 1.0 m in the field. Reason: The gravitational field strength ( g ) is the net force ( F ) per unit mass ( m ) at a particular point in the gravitational field. 6 On the surface of a planet with a radius r P , a mass experiences a gravitational force of attraction of g . At a height of 4 r P above the planet, the mass experiences a force of: A B C *D Reason: 10 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

11 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

13 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

9 Two planets have the same gravitational potential at their surfaces. Select one of the following ratios that must also be the same for the two planets. A *B C D radius 10 Planet X has mass M and radius R . Planet Y has mass 10 M and radius 4 R . Determine the ratio: A 0.5 *B 1.6 C 2.0 D 2.5 Reason: 14 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

b two protons ( m p = 1.7 × 10 –27 kg) at a distance of 5 × 10 –15 m apart. . Apply, analyse and interpret *16 Clarify the difference between heliocentric and geocentric models of the solar system. The heliocentric model has the sun (‘helios’) at the centre and all planets revolve around it. The geocentric model has the Earth (‘geo’) at the centre and the sun and planets revolve around it. The heliocentric model is the accepted model. *17 A satellite is orbiting Earth at a distance of 35 kilometres. The satellite has a mass of 500 kg. Determine the force between the planet and the satellite. *18 An astronaut is on the Moon. a Calculate the acceleration due to gravity on its surface. 16 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

b Determine the time it would it take a spanner to fall from rest from a height of 1.5 m to the surface of the Moon. *19 A 15 kg object has a weight of 8000 N. Calculate is the gravitational field strength at this point. *20 Determine the gravitational field strength of the Sun (mass 2 × 10 30 kg) at a distance of 15 × 10 10 m from its centre. 17 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

d 1000 m above the surface of the Moon e on the surface of the Sun. **23 A hydrogen atom consists of an electron of mass 9 × 10 –31 kg and a proton of mass1.9 × 10 –27 kg separated by an average distance of 6 × 10 –11 m. Determine the gravitational force between them. 19 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.

**24 A satellite is orbiting Earth in a circular orbit at a distance of two Earth radii from Earth’s surface. a Calculate the acceleration due to gravity aboard the satellite. b Calculate the weight of a 70 kg astronaut aboard the satellite. **25 Determine the distance between two objects of mass 6 × 10 5 kg and 3 × 10 5 kg, if the gravitational force between them is 1.5 × 10 8 N. 20 © Oxford University Press 2019 New Century Physics for Queensland Units 3 & 4 Teacher o book a ssess ISBN 9780190313685 Permission has been granted for this page to be photocopied within the purchasing institution only.