The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may...

10
1 (a) The Earth may be considered to be a uniform sphere of radius 6.38 × 10 6 m. Its mass is assumed to be concentrated at its centre. Given that the gravitational field strength at the Earth’s surface is 9.81 N kg –1 , show that the mass of the Earth is 5.99 × 10 24 kg. [2] (b) A satellite is placed in geostationary orbit around the Earth. (i) Calculate the angular speed of the satellite in its orbit. angular speed = ........................................ rad s –1 [3] (ii) Using the data in (a), determine the radius of the orbit. radius = ........................................ m [3] For Examiner’s Use 1 Compiled and rearranged by Sajit Chandra Shakya

Transcript of The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may...

Page 1: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

1 (a) The Earth may be considered to be a uniform sphere of radius 6.38 × 106 m. Its mass isassumed to be concentrated at its centre.

Given that the gravitational field strength at the Earth’s surface is 9.81 N kg–1, show thatthe mass of the Earth is 5.99 × 1024 kg.

[2]

(b) A satellite is placed in geostationary orbit around the Earth.

(i) Calculate the angular speed of the satellite in its orbit.

angular speed = ........................................ rad s–1 [3]

(ii) Using the data in (a), determine the radius of the orbit.

radius = ........................................ m [3]

ForExaminer’s

Use1

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 2: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

2 The orbit of the Earth, mass 6.0 × 1024 kg, may be assumed to be a circle of radius1.5 × 1011 m with the Sun at its centre, as illustrated in Fig. 1.1.

Fig. 1.1

The time taken for one orbit is 3.2 × 107 s.

(a) Calculate

(i) the magnitude of the angular velocity of the Earth about the Sun,

angular velocity = ............................... rad s–1 [2]

(ii) the magnitude of the centripetal force acting on the Earth.

force = ....................................... N [2]

Earth,mass 6.0 x 1024 kg

Sun

1.5 x 1011 m

ForExaminer’s

Use2

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 3: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

(b) (i) State the origin of the centripetal force calculated in (a)(ii).

...................................................................................................................................

...............................................................................................................................[1]

(ii) Determine the mass of the Sun.

mass = ..................................... kg [3]

ForExaminer’s

Use3

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 4: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use

3 (a) (i) Define the radian.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

(ii) A small mass is attached to a string. The mass is rotating about a fixed point P at constant speed, as shown in Fig. 1.1.

mass rotatingat constant speed

P

Fig. 1.1

Explain what is meant by the angular speed about point P of the mass.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

4

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 5: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use

(b) A horizontal flat plate is free to rotate about a vertical axis through its centre, as shown

in Fig. 1.2.

M

d

plate

Fig. 1.2

A small mass M is placed on the plate, a distance d from the axis of rotation. The speed of rotation of the plate is gradually increased from zero until the mass is

seen to slide off the plate.

The maximum frictional force F between the plate and the mass is given by the expression

F = 0.72W,

where W is the weight of the mass M. The distance d is 35 cm.

Determine the maximum number of revolutions of the plate per minute for the mass M to remain on the plate. Explain your working.

number = ........................................... [5]

(c) The plate in (b) is covered, when stationary, with mud. Suggest and explain whether mud near the edge of the plate or near the centre will first

leave the plate as the angular speed of the plate is slowly increased.

..........................................................................................................................................

..........................................................................................................................................

...................................................................................................................................... [2]

5

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 6: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

4 A particle is following a circular path and is observed to have an angular displacementof 10.3°.

(a) Express this angle in radians (rad). Show your working and give your answer to threesignificant figures.

angle = ...............................................rad [2]

(b) (i) Determine tan10.3° to three significant figures.

tan10.3° = ..........................................................

(ii) Hence calculate the percentage error that is made when the angle 10.3°, asmeasured in radians, is assumed to be equal to tan10.3°.

percentage error = ..........................................................[3]

ForExaminer’s

Use6

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 7: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use

5 (a) Explain

(i) what is meant by a radian,

..................................................................................................................................

..................................................................................................................................

..............................................................................................................................[2]

(ii) why one complete revolution is equivalent to an angular displacement of 2π rad.

..................................................................................................................................

..............................................................................................................................[1]

(b) An elastic cord has an unextended length of 13.0 cm. One end of the cord is attached to a fixed point C. A small mass of weight 5.0 N is hung from the free end of the cord. The cord extends to a length of 14.8 cm, as shown in Fig. 1.1.

14.8

cm

C

smallmass

Fig. 1.1

The cord and mass are now made to rotate at constant angular speed ω in a vertical plane about point C. When the cord is vertical and above C, its length is the unextended length of 13.0 cm, as shown in Fig. 1.2.

7

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 8: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use

13.0

cm

C

L

C

Fig. 1.2 Fig. 1.3

(i) Show that the angular speed ω of the cord and mass is 8.7 rad s–1.

[2]

(ii) The cord and mass rotate so that the cord is vertically below C, as shown in Fig. 1.3.

Calculate the length L of the cord, assuming it obeys Hooke’s law.

L = ............................................ cm [4]

8

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 9: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use

6 A spherical planet has mass M and radius R.

The planet may be assumed to be isolated in space and to have its mass concentrated at its centre.

The planet spins on its axis with angular speed ω, as illustrated in Fig. 1.1.

R

mass

m

pole ofplanet

equator ofplanet

Fig. 1.1

A small object of mass m rests on the equator of the planet. The surface of the planet exerts a normal reaction force on the mass.

(a) State formulae, in terms of M, m, R and ω, for

(i) the gravitational force between the planet and the object,

.............................................................................................................................. [1]

(ii) the centripetal force required for circular motion of the small mass,

.............................................................................................................................. [1]

(iii) the normal reaction exerted by the planet on the mass.

.............................................................................................................................. [1]

(b) (i) Explain why the normal reaction on the mass will have different values at the equator and at the

poles.

..................................................................................................................................

..................................................................................................................................

.............................................................................................................................. [2]

9

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a

Page 10: The Earth may be considered to be a uniform …...2 The orbit of the Earth, mass 6.0× 1024 kg, may be assumed to be a circle of radius 1.5 × 1011m with the Sun at its centre, as

ForExaminer’s

Use (ii) The radius of the planet is 6.4 × 106 m. It completes one revolution in 8.6 × 104 s. Calculate the magnitude of the centripetal acceleration at

1. the equator,

acceleration = .........................................m s–2 [2]

2. one of the poles.

acceleration = .........................................m s–2 [1]

(c) Suggest two factors that could, in the case of a real planet, cause variations in the acceleration of free fall at its surface.

1. ......................................................................................................................................

..........................................................................................................................................

2. ......................................................................................................................................

..........................................................................................................................................[2]

10

Com

pile

d an

d re

arra

nged

by

Saj

it C

hand

ra S

haky

a


PHYSICAL SETTING EARTH SCIENCE - JMAP HOME Setting/Earth Science must be available for you to ... examination will be invalidated and no score will be ... deflection of the wind that

PHYSICAL SETTING EARTH SCIENCE - JMAP HOME Setting/Earth Science must be available for you to ... examination will be invalidated and no score will be ... deflection of the wind that

Active Earth Fault Compensation and Railway Application · PDF fileActive Earth Fault Compensation and Railway Application of Medium ... _00EN.PPT / Dr.J.JANNING / Be 6 Active Earth

Active Earth Fault Compensation and Railway Application · PDF fileActive Earth Fault Compensation and Railway Application of Medium ... _00EN.PPT / Dr.J.JANNING / Be 6 Active Earth

Fairall lecture merged - CIRES · Sun and by the distance between Earth (r s-e = 1.5 x 1011m) and the Sun’s radius, r sun =2.3 x 10 9m. 2 4 2 0 * s e sun sun r T r S − = σ Solar

Fairall lecture merged - CIRES · Sun and by the distance between Earth (r s-e = 1.5 x 1011m) and the Sun’s radius, r sun =2.3 x 10 9m. 2 4 2 0 * s e sun sun r T r S − = σ Solar

Water on the Earth Notes Earth Science Grade 8. The Earth is the only planet in the solar system to be covered in water. The Earth is the only planet.

Water on the Earth Notes Earth Science Grade 8. The Earth is the only planet in the solar system to be covered in water. The Earth is the only planet.

Let ’ s be Friends of the Earth !

Let ’ s be Friends of the Earth !

Christ's Reign on Earth: What It Will Be Like

Christ's Reign on Earth: What It Will Be Like

Earth, Wind and Fire: Be Prepared if Disaster Strikes

Earth, Wind and Fire: Be Prepared if Disaster Strikes

Who Wants To Be A Millionaire Earth Science Review.

Who Wants To Be A Millionaire Earth Science Review.

Be Receptive to the Good Earth

Be Receptive to the Good Earth

Reliable, accurate and quick for comprehensive earth testing · 2018. 7. 6. · earth connection to be tested, thus avoiding the influence of the parallel earth connections. EARTH

Reliable, accurate and quick for comprehensive earth testing · 2018. 7. 6. · earth connection to be tested, thus avoiding the influence of the parallel earth connections. EARTH

Astronautics - Virginia Techcdhall/courses/aoe2104/Astronautics.pdfAmount of Earth that can be seen by a satellite is much greater than can be seen by an Earth-bound observer. Low-Earth

Astronautics - Virginia Techcdhall/courses/aoe2104/Astronautics.pdfAmount of Earth that can be seen by a satellite is much greater than can be seen by an Earth-bound observer. Low-Earth

Earth Materials - cairo7thgrademath.weebly.com€¦ · Earth Materials Weathering: Rocks can be broken down by forces on Earth in a process called weathering. Once rocks are broken

Earth Materials - cairo7thgrademath.weebly.com€¦ · Earth Materials Weathering: Rocks can be broken down by forces on Earth in a process called weathering. Once rocks are broken

Be down to earth: protect the soil...Be down to earth: protect the soil ... Ü ~

Be down to earth: protect the soil...Be down to earth: protect the soil ... Ü ~

Let There Be Peace On Earth - NYSSB New York State ...nyssb.com/All PDF Music/Let There Be Peace On Earth SATB...20f3 oth-er , Let There Be Peace On Earth me, mo take, Let - men t

Let There Be Peace On Earth - NYSSB New York State ...nyssb.com/All PDF Music/Let There Be Peace On Earth SATB...20f3 oth-er , Let There Be Peace On Earth me, mo take, Let - men t

to the earth, nothing will ever be the same. the earth, nothing will ever be the same. Worldwide tidal waves. Earthquakes. Volcanic Eruptions. ... on their marriage, they'd still be

to the earth, nothing will ever be the same. the earth, nothing will ever be the same. Worldwide tidal waves. Earthquakes. Volcanic Eruptions. ... on their marriage, they'd still be

Around Virginia….. To BE or not to BE……an Earth Science teacher. Most earth science teachers have a degree in one type of earth science….geology, oceanography,

Around Virginia….. To BE or not to BE……an Earth Science teacher. Most earth science teachers have a degree in one type of earth science….geology, oceanography,

Rare Earth - Stony Brook UniversityThe Goldilocks Effect Earth is “Just Right” Yes, life on Earth has adapted to Earth, but … Earth has just the right mass to be • Tectonically-active

Rare Earth - Stony Brook UniversityThe Goldilocks Effect Earth is “Just Right” Yes, life on Earth has adapted to Earth, but … Earth has just the right mass to be • Tectonically-active

19 Unique worm nutrients Unique worm nutrients from the earth to the earth ! from the earth to the earth ! Don’t be supprised to find live worms! Don’t.

19 Unique worm nutrients Unique worm nutrients from the earth to the earth ! from the earth to the earth ! Don’t be supprised to find live worms! Don’t.

How Can Objects on Earth be Located?

How Can Objects on Earth be Located?

Structure and Composition of the Earth. The solid earth can be divided into:

Structure and Composition of the Earth. The solid earth can be divided into: