Kev sib npaug ntawm lub ntiajteb txawj nqus

3 cov lus nug txog Gravity equation

1. Peb lub khoom me me uas hnyav 1 kg nyob ntawm cov ces kaum ntawm daim duab peb sab uas ntev 1 m. Lub zog gravitational loj npaum li cas uas txhua lub ntsiab lus me me (hauv G) raug?

tshuaj

Qhov loj ntawm lub zog gravitational uas ib qho ntawm cov khoom me me tau ntsib.

F ₁₂ = G (m ₁ )(m ₂ ) / r ² = G (1)(1) / 1 ² = G/1 = G

F ₁₃ = G (m ₁ )(m ₃ ) / r ² = G (1)(1) / 1 ² = G/1 = G

Lub zog gravitational tshwm sim ntawm qhov chaw 1:

F ₁ = √1 ² +1 ² = √1+1 = √2 Newtons

2. Daim duab hauv qab no qhia txog peb yam khoom m ₁ = 6 kg; m ₂ = 3 kg thiab m ₃ = 4 kg pw ntawm ib txoj kab ncaj. Txheeb xyuas qhov loj thiab kev coj ntawm lub zog gravitational uas m2 ntsib! (hais ua G)

Paub:

m₁ = 6 kg

m2 = ₃ kg

m3 = ₄ kg

lub zog gravitational tas mus li = G

r ₂₁ = 4 m

r ₂₃ = 2 m

Xav tau: F qhov hnyav uas m _{2 tau ntsib}

tshuaj:

Lub zog gravitational ntawm _m2 thiab _m3 :

F = G (3)(4) / 2 ² = G 12 / 4 = 3G

Lub zog gravitational ntawm _m2 thiab _m1 :

F = G (3)(6) / 4 ² = G 18 / 16 = 1,125G

3. Khoom A uas hnyav 1 kg thiab khoom B uas hnyav 2 kg raug sib cais los ntawm qhov deb 2 m ntawm ib leeg. Qhov chaw P yog 2 m ntawm khoom A thiab 2 m ntawm khoom B. Lub zog gravitational ntawm qhov chaw P muaj zog npaum li cas?

Paub:

mA = ₁ kg

mB = ₂ kg

r _PA = 2 m

r _PB = 2 m

Lub ntiajteb txawj nqus tas li = G

Xav tau: Lub ntiajteb txawj nqus E ntawm qhov chaw P

tshuaj:

E _PA = G (m _A ) / r ² = G (1) / 2 ² = G / 4 = 0,25G

E _PB = G (mB ₎ / ^r2 = G (2) / 2 ² = 2G/4 = 0,5G

Lub zog ntawm lub zog gravitational ntawm qhov chaw P:

E = √0,25G ² +0,5G ² = √0,0625G ² +0,25G ² = √0,3125G ² = 0,56G N/kg