COLLEGE PHYSICS,VOLUME 1
COLLEGE PHYSICS,VOLUME 1
2nd Edition
ISBN: 9781319115104
Author: Freedman
Publisher: MAC HIGHER
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Chapter 10, Problem 28QAP
To determine

(a)

The gravitational force on the passenger at cruising altitude.

Expert Solution
Check Mark

Answer to Problem 28QAP

Gravitational force on the passenger at cruising altitude is 683.97 N

Explanation of Solution

Given:

Mass of earth, mEarth=5.98×1024kg

The average mass of the person, mPerson=70kg

Cruising height of flight, h = 10000 m

Radius of earth, REarth=6.38×106m

Formula used:

The gravitational force on the passenger

  F=GmPersonm Earth ( R earth +h) 2

Where,

h = height of flight from sea level.

Calculation:

The gravitational force on the passenger at cruising height ( h = 104m)

  F=GmPersonm Earth ( R earth +h) 2=(6.67× 10 11 N m 2 kg 2 )(70kg)(5.98× 10 24kg)( 6.38× 10 6 m+1 0 4 m)2=683.79N

Conclusion:

Gravitational force on the passenger at cruising altitude is 683.97 N

To determine

(b)

How much "lighter" would a person be in flight as compared to at sea level?

Expert Solution
Check Mark

Answer to Problem 28QAP

Person become 2.14 N lighter in flight as compared to at sea level.

Explanation of Solution

Given:

Mass of earth, mEarth=5.98×1024kg

The average mass of the person, mPerson=70kg

Cruising height of flight, h = 10000 m

Radius of earth, REarth=6.38×106m

Formula used:

The gravitational force on the passenger

  F=GmPersonm Earth ( R earth +h) 2

Where,

h = height of flight from sea level.

Calculation:

Weight of the person above the earth surface is equal to the magnitude of gravitational force acting on that person.

  W=|F|=|GmPersonm Earth ( R earth +h) 2|

The weight of person at sea level (h = 0)

  Wsealevel=|GmPersonm Earth ( R earth +h) 2|=|(6.67× 10 11 N m 2 kg 2 )(70kg)(5.98× 10 24kg)( 6.38× 10 6 m+0m)2|=685.93N

The weight of person at cruising height ( h = 104m)

  Wcruisingheight=|GmPersonm Earth ( R earth +h) 2|=|(6.67× 10 11 N m 2 kg 2 )(70kg)(5.98× 10 24kg)( 6.38× 10 6 m+1 0 4 m)2|=683.79N

Change in weight,

  WsealevelWcruisingheight=(685.93N)(683.79N)=2.14N

Conclusion:

Person become 2.14 N lighter in flight as compared to at sea level.

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