Textbook Chap 4 Gravitational force and fields answers

.docx

School

The University of Queensland *

*We aren’t endorsed by this school

Course

QCE

Subject

Physics

Date

Apr 3, 2024

Type

docx

Pages

Uploaded by UltraTank13365 on coursehero.com

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.

Apply, analyse and interpret 6 Black holes are supermassive collapsed stars. The closest anything can get to one and still escape its gravitational force is called the ‘event horizon’. Determine the force acting on a 15 tonne spacecraft at the event horizon of 30 km from a black hole that has a mass equal to 10 times that of the Sun. Mass of Sun = 2.0 × 10 30 kg; 1 tonne = 1000 kg 7 When a star collapses to form a black hole, the size of the star is greatly reduced although the mass remains the same. Deduce what would happen to the gravitational force of the Sun on our Earth if the Sun unexpectedly collapsed to form a black hole? Gravity acts between bodies as if they were point masses, so a smaller Sun with the same mass would have no effect on the gravitational force between the Sun and Earth. In reality, if the Sun shrank there would be enormous heating effects from friction and an outpouring of radiation that would affect Earth. Investigate, evaluate and communicate 8 Jupiter is about 300 times more massive than Earth so it would be easy to deduce that an object on the surface of Jupiter would weigh 300 times more than on the surface of Earth. For example, a rover (spacecraft) with a weight of 9000 N on Earth might be expected to weigh 2 700 000 N on the surface of Jupiter. But this is not the case. A 9000 N rover on Earth weighs only about 27000 N on the surface of Jupiter. Evaluate this scenario and identify any misunderstandings. Diameter of Earth = 12742 km, therefore radius of Earth r E = 6371 km Diameter of Jupiter = 139822 km, therefore radius of Jupiter r J = 69911 The 9000 N rover weighs 22 422 N on the surface of Jupiter. 9 A 1 tonne communications satellite is orbiting a planet. A student said that ‘if you double the mass of the satellite or the planet the force will double’. Another student said that doubling the mass of the planet had to have a bigger effect than just going from a 1 tonne satellite to a 2 tonne satellite. Evaluate both claims and decide who is correct. The formula for the gravitational force between two objects is . It doesn’t matter whether the value of M is doubled to 2 M , or m is doubled to 2 m , it still has the same effect on the force (doubling it). 3 © 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.

10 Construct a graph of gravitational field strength versus distance from Earth’s centre, using the data from Table 1 on page 129. Determine the relationship. Construct a second graph to confirm your prediction. The graph appears to be inverse or inverse square. The formula is an inverse square relationship, so to linearise we plot F vs 1/ d 2 . This has linearised it. 11 The gravitational field strength 100 km from the Earth’s centre is 3.99 × 10 4 m s –2 . That’s 40 000 m s –2 . Deduce why this nonsensical. The formula doesn’t hold for inside the Earth. Besides, there would be a cancelling out of field strength from mass above this point. Investigate, evaluate and communicate 12 Jupiter is about 300 times more massive than Earth so it would be easy to deduce that an object on the surface of Jupiter would weigh 300 times more than on the surface of Earth. But this is not the case. It is just three times as heavy. Evaluate this scenario and identify any misunderstandings. Radius of Earth r E = 6371 km Radius of Jupiter r J = 69911 Ratio: The force acting on an object on the surface of Jupiter is about 2.5 times the weight on the surface of Earth. The misunderstanding is that Jupiter has a bigger radius so the force acting on the surface is less because of distance even though it is more due to extra mass of Jupiter. 6 © 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.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version