COLLEGE PHYSICS-CONNECT ACCESS
COLLEGE PHYSICS-CONNECT ACCESS
5th Edition
ISBN: 9781260486834
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 6, Problem 55P
To determine

The comet’s speed at its perihelion.

Expert Solution & Answer
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Answer to Problem 55P

The comet’s speed at its perihelion is 55 km/s.

Explanation of Solution

The total mechanical energy of the comet will be constant.

Write the equation for the conservation of energy of the comet.

  Kp+Up=Ka+Ua        (I)

Here, Kp is the kinetic energy of the comet at the perihelion, Up is the potential energy of the comet at the perihelion, Ka is the kinetic energy of the comet at the aphelion and Ua is the potential energy of the comet at the aphelion.

Write the equation for Kp.

  Kp=12mvp2        (II)

Here, m is the mass of the comet and vp is the speed of the comet at the perihelion.

Write the equation for Up.

  Up=GMSmrp        (III)

Here, G is the universal gravitation constant, MS is the mass of the sun and rp is the distance from the perihelion to the sun.

Write the equation for Ka.

  Ka=12mva2        (IV)

Here, va is the speed of the comet at the aphelion.

Write the equation for Ua.

  Ua=GMSmra        (V)

Here, ra is the distance from the aphelion to the sun.

Put equations (II) to (V) in equation (I).

  12mvp2+(GMSmrp)=12mva2+(GMSmra)12vp2GMSrp=12va2GMSra12vp2=12va2+GMS(1rp1ra)vp=va2+2GMS(1rp1ra)        (VI)

Conclusion:

The value of G is 6.67×1011 m3/kgs2 and the mass of the sun is 1.989×1030 kg.

Substitute 10.0 km/s for va , 6.67×1011 m3/kgs2 for G , 1.989×1030 kg for MS , 5.3×1012 m for ra and 8.9×1010 m for rp in equation (VI) to find vp.

  vp=(10.0 km/s1000 m1 km)2+2(6.67×1011 m3/kgs2)(1.989×1030 kg)(18.9×1010 m15.3×1012 m)=55.0×103 m/s=55.0×103 m/s1 km1000 m=55 km/s

Therefore, the comet’s speed at its perihelion is 55 km/s.

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Chapter 6 Solutions

COLLEGE PHYSICS-CONNECT ACCESS

Ch. 6.5 - Prob. 6.5CPCh. 6.5 - Prob. 6.7PPCh. 6.6 - Prob. 6.9PPCh. 6.6 - Prob. 6.10PPCh. 6.7 - Prob. 6.7CPCh. 6.7 - Prob. 6.11PPCh. 6.8 - Prob. 6.13PPCh. 6.8 - Prob. 6.14PPCh. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - Prob. 3CQCh. 6 - A mango falls to the ground. During the fall, does...Ch. 6 - Can static friction do work? If so, give an...Ch. 6 - In the design of a roller coaster, is it possible...Ch. 6 - Prob. 7CQCh. 6 - A gymnast is swinging in a vertical circle about a...Ch. 6 - Prob. 9CQCh. 6 - The main energy expenditure involved in running...Ch. 6 - Prob. 12CQCh. 6 - Prob. 13CQCh. 6 - Prob. 1MCQCh. 6 - Prob. 2MCQCh. 6 - Prob. 3MCQCh. 6 - Questions 3–6. The orbit of Mercury is much more...Ch. 6 - Prob. 5MCQCh. 6 - Prob. 6MCQCh. 6 - Prob. 7MCQCh. 6 - Prob. 8MCQCh. 6 - What speed does the catapult give a pebble of mass...Ch. 6 - Prob. 10MCQCh. 6 - Prob. 11MCQCh. 6 - Prob. 1PCh. 6 - A sled is dragged along a horizontal path at a...Ch. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Starting from rest, a horse pulls a 250 kg cart...Ch. 6 - Prob. 9PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - A crate of mass m1 = 12.4 kg is pulled by a...Ch. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - In Problem 6, what is the pile driver’s speed just...Ch. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - Prob. 34PCh. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 40PCh. 6 - Prob. 41PCh. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - Prob. 48PCh. 6 - Prob. 49PCh. 6 - Prob. 50PCh. 6 - Prob. 51PCh. 6 - Prob. 53PCh. 6 - Prob. 54PCh. 6 - Prob. 55PCh. 6 - Prob. 56PCh. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Prob. 62PCh. 6 - Prob. 63PCh. 6 - Prob. 64PCh. 6 - Prob. 65PCh. 6 - Prob. 66PCh. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Prob. 69PCh. 6 - Prob. 70PCh. 6 - Prob. 71PCh. 6 - Prob. 72PCh. 6 - Prob. 73PCh. 6 - Prob. 74PCh. 6 - Prob. 75PCh. 6 - Prob. 76PCh. 6 - Prob. 77PCh. 6 - Prob. 78PCh. 6 - Prob. 79PCh. 6 - Prob. 80PCh. 6 - Prob. 81PCh. 6 - Prob. 82PCh. 6 - Prob. 83PCh. 6 - Prob. 84PCh. 6 - Prob. 85PCh. 6 - Prob. 86PCh. 6 - Prob. 87PCh. 6 - Prob. 88PCh. 6 - Prob. 89PCh. 6 - Prob. 90PCh. 6 - Prob. 91PCh. 6 - Prob. 92PCh. 6 - Prob. 93PCh. 6 - Prob. 94PCh. 6 - Prob. 95PCh. 6 - Prob. 96PCh. 6 - Prob. 97PCh. 6 - A spring scale in a French market is calibrated to...Ch. 6 - Prob. 99PCh. 6 - Prob. 100PCh. 6 - Prob. 101PCh. 6 - Prob. 102PCh. 6 - Prob. 103PCh. 6 - Prob. 104PCh. 6 - Prob. 105PCh. 6 - Prob. 106PCh. 6 - Prob. 107PCh. 6 - Prob. 108PCh. 6 - Prob. 109PCh. 6 - Prob. 110PCh. 6 - A spring with k = 40.0 N/m is at the base of a...Ch. 6 - Prob. 112PCh. 6 - Prob. 113PCh. 6 - Prob. 114PCh. 6 - Prob. 115PCh. 6 - Prob. 117PCh. 6 - A 0.50 kg block, starting at rest, slides down a...Ch. 6 - Prob. 119PCh. 6 - Prob. 121PCh. 6 - Prob. 123PCh. 6 - Prob. 124PCh. 6 - Prob. 125PCh. 6 - Prob. 126PCh. 6 - Prob. 127PCh. 6 - Prob. 128PCh. 6 - Prob. 129PCh. 6 - Prob. 130PCh. 6 - Prob. 131PCh. 6 - Prob. 132PCh. 6 - Prob. 133PCh. 6 - Prob. 135PCh. 6 - Prob. 136PCh. 6 - Prob. 137PCh. 6 - Prob. 138PCh. 6 - Prob. 139PCh. 6 - Prob. 140PCh. 6 - Prob. 141PCh. 6 - Prob. 142P
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Mechanical work done (GCSE Physics); Author: Dr de Bruin's Classroom;https://www.youtube.com/watch?v=OapgRhYDMvw;License: Standard YouTube License, CC-BY