## Takaitaccen bayani game da gravitational field

• A physics, gravitational field model ne da ake amfani da shi wajan bayanin tasirin da massive body ya ke da shi wajan zuwa sararin samaniya around itself producing a force on another body. Gravitational force of attraction da ke tsakanin body guda biyu ana governing din shine da  Newton�s law of universal gravitation. Wannan law din ana bayaninta ne a Turance kamar haka: Newton�s law of universal gravitation states that, any two particles of matters attracts one another with a force F, which is proportional to the product of their masses m1 & m2 and inversely proportional to the square of their distance r,apart.

Yanzu zamu duba wani diagram sannan mu fitar da formula da ake amfani da ita wajan lissafi. Fig 1.1

Gravitational force between two masses is given by

F = Gm1m2 / r2

Wannan shine equation na universal gravitation

Where

m1 and m2 are the two masses of the two particles ;

r is the distance between masses m1 and m2;

G is the gravitational constant = 6.67 � 10-11Nm2kg-2

Yanzu, kamar kullum, zamu dauki misalai wanda tambayoyi ne da ke fitowa a jarabawar karshen aji shidda na sakandire wato, WAEC, da NECO da kuma JAMB muyi lissafinsu.

Misali na daya:

Two spheres of masses 100kg and 90kg respectively have their centers separated by a distance of 1.0m. Calculate the magnitude of the force of attraction between them.

[ G = 6.70 � 10-11Nm2kg-2 ]  WAEC 2002

Amsar tambaya:

Duba fig 1.2 force of attraction F = Gm1m2 / r2

= 6.70 � 10-11 � 100 � 90 / 12   = 6.03 � 10-7 N

Misali na biyu:

A force of 200N acts between two objects at a certain distance apart.The value of the force when the distance is halved is:

A.100N  B.200N  C.800N  D.400N           JAMB 2005

Dubi: Darasi game da general gas law

Amsar tambaya:

Zamu fara fitar da data

Intial force ,F1 = 200N

Final force (when distance is halved) F2 = ?

Initial distance , r1 = r

Final distance ,r2 = r/2 (---the distance is halved---)

Gravitational force is inversely proportional to the square of the distance;

F ? 1/ r2

F1  = F2

200 � r2 = F2 � ( r / 2)

200 � r2 = F2 � r2 /4

Rearrange F2 = 4�200 r2 /r2

therefore F2 = 800N

Misali na uku:

The gravitational force between two objects of masses 1024 and 1027 is 6.67N. calculate the distance between the ( G = 6.67 � 10-11Nm2kg-2)   NECO 2008.

Amsar tambaya:

F = Gm1m2 / r2

Yanzu zamu maida  r2  ta zama subject of the formular don haka formula dinmu zata koma

r2 = Gm1m2 / F, tunda mun nemo fomula daya kamata mu yi amfani da ita yanzu zamu sa abubuwanda aka bamu a ciki muyi lissafi,

r2 = 6.67 � 10-11  � 1024 � 1027   / 6.67 = 10-11 � 1024 � 1027 = 10-11+24+27 = 1040

r  = square root of 1040 = 1.0 � 1020 m

Gravitational potential

Gravitational potential, V , is the potential due to the gravitational field of the earth. Ana bayanin sa ne a matsayin work done in taking a unit mass from infinity to the point ( a particular distance form the center of the earth. Ana amfani da wata fomula wajan lissafin gravitational potential ga ta kamar haka.

Gravitational potential ,V =  -GM / r

Inda kowanne baki yana da ma'anarsa

M = mass of the earth

G = gravitational constant

r = distance of the point from center of earth

Shi kuma alama na negative yana nuna potential yana raguwa a yayin da object ya matsa daga infinity zuwa earth.

Zamu dauki misali mu gwada amsa tambaya tare da wannan fomula ta gravitational potential.

Misali na hudu:

What is the gravitational potential at a point on the surface of the earth  if G = 6.6�10-11Nm2kg-2 and the radius and mass of the earth are respectively 6.4�106m and 5.98�1024kg?

Amsar tambaya:

Zamu fara da fitar da data akan abubuwan da aka bamu.

M = 5.98�1024kg

r = 6.4�106m

G = 6.6�10-11Nm2kg-2

Yanzu zamu yi amfani da fomula mu ta gravitational potential

Gravitational potential, V = - GM / r =6.6�10-11 � 5.98�1024 / 6.4�106

= 3.95 � 1014 / 6.4 � 106 = 6.2 � 107Jkg-1

Wannan misalin da muka dauka shine misalin yadda ake lissafin gravitational potential, yanzu zamu duba wasu abubuwa guda biyu wanda a karkashin gravitational field suna da matukar mahimmanci wadannan abubuwan sune kamar haka.

Za a iya duba: Bayani kan conservation of linear momentum

Acceleration due to gravity / gravitational field intensity

Acceleration due to gravity (g) ana  kiransa da wani suna a matsayin force per unit mass (m) of an object and is responsible for the weight or force an object experiences on the earth. Yanzu zamu fitar da formula ta acceleration due to gravity kuma mu ga yadda take zama dai dai da force per unit mass.

From F = Gmem /  ( me and re are mass and radius of the earth respectively)

Force per unit mass F /m = Gme /

Acceleration due to gravity is equal to force per unit mass

There fore , g = F / m or g = Gme /

Hence , F = mg

Yanzu zamu dauki misali  daga cikin tambayoyin WAEC.

Misali na biyar:

The magnitude of the gravitational attraction between the earth and a particle is 40N. If the mass of the particle is 4kg, calculate the magnitude of the gravitational field intensity of the earth on the particle.  WAEC 2002

Amsar tambaya:

Force of attraction on particle, F = 40N;

Mass of particle m = 4kg

Gravitational field intensity, g = F / m = 40 / 4 = 10Nkg-1

Misali na shida:

The mass and weight of a body on earth are 8kg and 80N respectively. Determine the mass and weight of the body respectively on a planet where the pull of gravity is 1/8 that on earth.  WAEC 2005

Amsar tambaya:

Mass m = 8kg

Weight w = 80N

Weight = mass � acceleration due to gravity

W = mg

Therefore , g = w/m = 80/8 = 10ms-2

1/8 0f g = 1/8 � 10 = 1.25ms-2

m = 8kg mass of object do not change whatever their location.

From w = mg; w = 8�1.25 = 10N

Amsoshin wannan tambaya sune , 8kg, 10N

A wannan makala mun koyi lissafi tare da fomulas kala uku, don haka  yana da kyau dalibi ya je ya kara kokarin amsa wasu tambayoyi ta hanyar yin amfani da wadannan fomuloli domin kara karfafa fahimta.