Textbook Chap 4 Gravitational force and fields answers
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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.
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6. Data & Tables
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Part A
Select the correct equations that show that a freely falling rock drops a distance of 45 m when it falls from rest for 3 s.
O s=g² t/2= (10 m/s²)² - (3 s)/2 = 45 m
%3D
O s=t/(2-g) = (3 s)²/(2 - (10 m/s²)) = 45 m
II
O s=g t/2=D (10 m/s²) - (3 s)/2 = 45 m
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%3D
O s=g.e/2=D (10 m/s²) - (3 s)²/2 = 45 m
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Fill in the blanks with the correct term/s. Write your answers on a sen.
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is the tendency of an object to resist any change in its in
On
1.
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other hand, if it is initially moving at constant velocity, it tends
continue moving unless acted upon by a
2. Inertia depends on the object's
3. Newton's
object at rest remains at rest and an object in motion will continue t
move in a straight path with constant velocity unless acted upon by an
also known as the
states that
force.
4. Newton's
also known as the
states th
acceleration of an object is directly proportional to the net force causing
and inversely proportional to its mass. In symbol,
Σ
= mã
5. Newton's
every action, there is an equal and opposite reaction.
also known as the
states that 0
6. When air resistance is neglected, all objects fall toward the ground wi
the same acceleration called
It is approximately equal
The force that causes object to…
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Answer questions on vectors and scalars
Exam words
1.
What is meant by the terms physical quantity, equal vector and
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define: give a full meaning
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in a dictionary
draw: show in a visual way
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Write definitions for vector quantity, scalar quantity and
resultant vector.
3
explain: give the details of
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Classify the following quantities as vectors or scalars: mass,
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Force F = 5 N acts to the right.
4.
Draw a fully labelled scale drawing of the 5 N force using a scale of
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4.2.2 0,5F
4.1
calculate: work out
4.2
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e p
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Learning Goal:
To understand Newton's law of universal gravitation and be able to
apply it in two-object situations and (collinear) three-object
situations; to distinguish between the use of G and g.
In the late 1600s, Isaac Newton proposed a rule to quantify the
attractive force known as gravity between objects that have mass,
such as those shown in the figure. (Figure 1) Newton's law of
universal gravitation describes the magnitude of the attractive
gravitational force Fg between two objects with masses m₁ and
m₂ as
F₁ = G ( m₂
where r is the distance between the centers of the two objects and
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Figure
m1m2
The gravitational force is attractive, so in the figure it pulls to the
right on m₁ (toward m₂) and toward the left on m2 (toward m₁).
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PowerPoint Slide Show - [newton 2nd law-syr] - PowerPoint
horizontal plane
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A car of mass 2000kg moves horizontally starting from rest. The car attains a velocity V after moving 100m in
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1. Represent all forces on the figure.
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- Student Resources ScienceFlix Schola.. answer the following questions ScienceFlix | Schola.. mat Tools Add-ons Help Accessibility Last edit was 10 minutes agg lormal text Arial 11 BIUA 4. C.slow down due to friction 5. D.speed up due to momentum 4.In the example of a soccer ball rolling to a stop, friction acts as ball's motion. A. An outside force that changes the B. Momentum C. Kinetic energy D. A theory 5.Newton's 2nd Law of Motion describes the relationship between all of the following, except A.Mass B.Force C.Velocity D. Acceleration 6.If someone with a mass of 40 kg accelerated down a water slide at 4 m/s/s, they would hit the water with a force of: A.10 Newtons B.16 Newtons C.160 Newtons D 16.000 Newtons states that for every action, there is an equal andarrow_forwardThe class I'm taking is physics for scientists and engineers! *** I need help with parts D and E only*** I have attached the problem below! Please view attachment before answering. If you can please explain your answer so I can fully understand. Thank you so so much!arrow_forwardMatch the items about gravity. There are extra answers in your options, so take care in selecting the correct one. We will give partial credit if you miss some. Newton's universal law of gravity Approximate force of gravity on 1 kg near Earth's surface Approximate force of gravity on the Earth from 1 kg near its surface Change in potential energy of a mass m when it is moved a distance h in a direction away from Earth near its surface A. GmM/R2 B. C. mgh D. 10 N downward E. 0 F. 10 N upwardarrow_forward
- 4. A student feels a gravity force of 800 N from the Earth when they're sitting in this classroom. a. How big is the gravity force that the Earth feels because of the student? Explain. b. Two students discuss part a) Student 1: "The Earth is much heavier than the student, so its gravity must pull harder on the student than the student's gravity pulls on the Earth. The gravity force the Earth feels must be less than 800 N." Student 2: "That might be true, but I think that same 800 N would have less of an effect on the Earth than it would on a person. Using a = F/m, the acceleration the Earth feels might be very small from an 800 N force, because Earth is so heavy." Which of these students, if any, do you agree with? Justify your response with words and/or equations.arrow_forwardStuck need help! The class I'm taking is physics for scientists and engineers! Problem is attached. please view attachment before answering. ***I need help with parts A,B,C, and D*** Really struggling with this concept. Any help will be greatly appreciated! Please detail explain so I can fully understand how to solve. Thank you so much.arrow_forward1. Which statement about Issac Newton is not true? A. Made huge advances in math, science, and other area B. His discoveries came naturally in "flashes of brilliance" due to his genius C. He came from very humble beginnings D. He thought long and hard to solve problems 2. An object falling at a steady rate as the force of gravity is equal to air resistance, is not in a state of a. Dynamic equilibrium b. Mechanical equilibrium c. non-free fall d. Free-fall 3. An object falling under only the influence of gravity is in a. Free fall b. Non-free fall c. Mechanical equilibrium d. Dynamic equilibriumarrow_forward
- Complete the following paragraph by Identifying the terms. Drag and drop your answer/s into the provided box. By the end of the sixteenth century, the observation of the astronomical bodies had progressed to a remarkable degree. Tycho Brahe built the large observatory on an island near Copenhagen. Tycho painstakingly recorded precise observations of the motions of the planets using and After Tycho's death, Johannes Kepler studied his data and devise the three laws of planetary motion. The first law states that each planet moves along a/an with the sun at one focus. The second law says that the from the sun to a planet sweeps out equal areas in On the other, the third law says that the of a planet's orbital motion is proportional to the cube of its from the sun. :: mechanical gadgetry :: unaided eye :: telescope : elliptical path :: radius vector :: equal intervals of time square of the period :: mean distance :: areaarrow_forwardQ Search View Help Tell me what you want to do Editing v rences Review IU A m、而、 国 三 Edito .. A AT 6. Data & Tables 1. Relate gravitational force to masses of objects and distance between objects. 2. Explain Newton's third law for gravitational forces. 3. Design experiments that allow you to derive an equation that relates mass, distance, and gravitational force. 4. Use measurements to determine the universal gravitational constant. Table I: Force Distance Constantarrow_forwardThe class I'm taking is physics for scientists and engineers! **I just need help with part G** I have attached the problem below! Please view both attachments before answering. If you can please explain your answer so I can fully understand. Thank you so so much!arrow_forward
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