Problem

Determine the mass of the earth knowing that the …

Question

Answered step-by-step

Problem 77 Easy Difficulty

For the particle of Prob. $12.76,$ determine the tangential component $F_{t}$ of the central force $\mathbf{F}$ along the tangent to the path of the particle for $(a) \mathbf{u}=0,(b) \mathbf{u}=45^{\circ}$

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Keshav Singh

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Physics 101 Mechanics

Vector Mechanics for Engineers: Statics and Dynamics

Chapter 12

Kinetics of Particles: Newton’s Second Law

Discussion

You must be signed in to discuss.

Top Physics 101 Mechanics Educators

Watch More Solved Questions in Chapter 12

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Problem 94

Problem 95

Problem 96

Problem 97

Problem 98

Problem 99

Problem 100

Problem 101

Problem 102

Problem 103

Problem 104

Problem 105

Problem 106

Problem 107

Problem 108

Problem 109

Problem 110

Problem 111

Problem 112

Problem 113

Problem 114

Problem 115

Problem 116

Problem 117

Problem 118

Problem 119

Problem 120

Problem 121

Problem 122

Problem 123

Problem 124

Problem 125

Problem 126

Problem 127

Problem 128

Problem 129

Problem 130

Problem 131

Problem 132

Problem 133

Video Transcript

in this problem. We have a particle that is moving under a central force. And so the angular momentum per unit mass age is a constant. And if we use equation 12.27 we can see that age is also R squared. Deter dot And since this is a constant, we can call it h not, and h not is defined by are not the not the initial position times the initial velocity. So using that expression, we confined an expression for tita dot So, tita dot is simply are not the not over r squared. And so we can write this as are not the note and we can write out r squared as are not squared cost great theater and so one are not canceled from the top in the bottom, so that becomes the not over are not cost squared off data so that we have an expression for theater dot and will use this a bit later. So now we will calculate the radio component off the velocity. The radio component of velocity is VR and we are simply are dot So I'll not is the time derivative DDT off our, which is are not conspirator and from the change role this is minus are not signed pita peter dot So that's the radio component of the velocity In terms of pita. Now, the trans verse component of V, which is V pita is equal to are peter dot and using our expression for tita dot or using our expression for our rather we get this to be are not co sign of data simply times data dot So now we have both the radio and the transfers component of the velocity And so we confined the speed of the particle V So V, we know, is simply the square root off the squares the sum of squares off the radio and transfers components VR square plus the teeter squared on this simplifies to are not peter dot and now we can open up data dot So this becomes are not times we not all the are not course squared off data and now it becomes clear why we expand the data dot And so this is equal to see the Arnaud's cancel. So this is V note over costs cost squared pita. So we have an expression for the speed of the particle in terms off the angle, pita. Now that we have V, we can actually calculate the tangential component off the acceleration. Mhm. If we have a tendency to component acceleration, we can use that to calculate the tangential component of the force. So the conventional component of acceleration a T we know is D v D t. The rate of change of velocity. And so this is we not minus two, minus science. Tita data dot So we take our expression for V, and we differentiated with respect to time. So again, we'll have to use the chain rule. It's over cost great, Peter. So this is equal to to we not signed Pita over called squid Deaton multiplied by peter dot which is we not over are not costs grade data. So this simplifies to to the north squared scientific data over are not actually this is above. This is Cost Cube, Peter. So this becomes are not times cost data to the power five. So now we have the financial component off the acceleration. So since we have the financial computer deceleration, we confined the tangential component off the force. The financial component of the force, F T is equal to M 80 by Newton's second law. And so that's the mass off the particle, multiplied by the expression for the tangential force. So that's two m v, not squared science, Tita. All the are not cause enough data to the fourth power. So now we have an expression for the tangential force. So the tangential force we need to find into scenarios. So in part eight, data is equal to zero. If we let Tita equal to zero into the expression above, we get that obviously signed teachers equal to zero. And so this tangential force F T is equal to zero for part B. If we let Pita equal to 45 degrees and we substitute that into that expression, we get the tangential force. F T is to, um we not into sign 45 off are not into cost, Peter. The first power off details 45 45 degrees. And we get that the international force simplifies 28 mm. The not squared over are not

Get More Help with this Textbook

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

Determine the mass of the earth knowing that the …

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Vector Mechanics for Engineers: Statics and Dynamics

Related Topics

Discussion

Top Physics 101 Mechanics Educators

Andy Chen

Liev Birman

Aspen Fenzl

Jared Enns

Physics 101 Mechanics Courses

Recommended Videos

Watch More Solved Questions in Chapter 12

Video Transcript

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Aspen Fenzl

Jared Enns

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Aspen Fenzl

Jared Enns

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Andy Chen

Liev Birman

Aspen Fenzl

Jared Enns

Ferdinand Beer, Jr., E. Russell Johnston, David Mazurek

Vector Mechanics for Engineers: Statics and Dynamics