Makalu

Physics: Bayani kan conservation of linear momentum

  • A darasinmu na kimiyya da fasaha a bangaren kimiyyar lissafi (physics) a yau, za mu yi dubi ne zuwa ga maudu'i mai suna conservation of linear momentum. In mai karatu na biye da mu zai ga cewa a durrusanmu da suka gabata mun yi bayani tare da kawo misalai akan linear momentum, za a iya dubawa kafin mu ci gaba. 

    Conservation of linear momentum shima wani law ne wanda aka same shi daga laws guda biyu, wato Newton’s law na biyu da kuma na uku wanda aka fitar da law of conservation a karkashinsu. Ga abinda aka ce game da shi wannan law din:

    Law of conservation state that, when two or more bodies  act upon one another, their total momentum which remains constant, provided no external forces are acting. Dubi wannan don karin bayani.

    Akwai misalai da zamu dauka yanzu wadanda za su taimaka wajen bayanin wannan law din sosai, wadanan misalan daga cikin jarabawar karshe ta gama sakandire zamu dauko su. Kuma misalan zasu nuna mana yadda momentum, velocity da kuma kinetic energy na colliding body  ake lissafinsu.

    Misali na farko                 

    1. An object of mass 5.0kg moving with a velocity of 12ms-1 due North hits a stationary body of mass 7.0. if they stick together after collision and move with velocity v due North, calculate the magnitude of v. NECO 2005

    Akwai abinda ya kamata musani wanda yana da mahimmanci wajen amsa tambaya a karkashin law of conservation,

    Momentum before collision = momentum after collision

    Fig 6.2

    Idan muka duba fig 6.2 ya fitar mana da data da muke bukata sai mu yi amfani da fomula wajan lissafin kai tsaye

     m1 v1 + m2v2 = (m1 + m2 )v

    5×12 + 7× 0 = (5 + 7 )v

    60 + 0 = 12v

    V = 60/12 = 5ms-1

    Misali na biyu

    A tractor of mass 5.0 × 103 kg is used to tow a car of mass 2.5×103 The tractor moved with speed of 3.0ms-1 just before the towing rope becomes taut. Calculate the:

    1. Speed of the tractor immediately the rope becomes taut.
    2. Loss in K.E of the system just after the car has started moving.
    3. Impulse in the rope when it jerks the car into motion. WAEC 2003

    Wannan tambayar ta hada abubuwa uku, velocity, kinetic energy da kuma impulse don haka zamu bi su daya bayan daya mu amsasu kamar yadda aka jera tambayoyin, amma da farko zamu fitar da data tukuna.

    Amsar tambaya       

    Kafin mu fara amsa tambayoyi zamu fara fitar da bayanan da aka bamu daga cikin tambayar, abu na farko shine mass na tractor , m1 = 5.0 × 10kg:  velocity tractor na ainihi , u1 = 3.0ms-1

    Mass na mota , m2 = 2.5 × 10kg;  velocity mota na ainihi , u2 = 0ms-1

    Zamu dauki 'v' a matsayin velocity na mota da tractor

    Gudun tractor a yayinda igiyar ta zama taut shine velocity na tractor da mota a lokacin da dukansu suka fara tafiya.

    Momentum kafin su fara tafiya = momentum bayan sunfara tafiya

    m1u1 + m2u2 = ( m1 + m2 )v

    yanzu zamu dauko a cikin bayanan da muka fitar kowanne mu sa shi a cikin matsayinsa a wannan fomula sannan mu yi lissafinsu.

    5.0 × 10× 2.5 × 103 × 103 × 0 = (5.0 × 103 + 2.5 × 103 × 10)

    1.5 × 104 = 7.5 × 103 v

    v = 1.5 × 10/ 7500 = 2ms-1 

    Loss K.E = final K.E – initial K.E

    A wannan tambayar zamu yi amfani da fomula ta kinetic energy da ta momentum

    initial K.E = K.E na tractor da ke tafiya = ½ m1 ( from KE = ½ mv)

    = ½ 5.0 × 103 × 32  = 2.25 × 104J

    Yanzu mun samo amsar kinetic energy na ainihi saura mu nemo kinetic energy na karshe

    Final energy = K.E na tractor da mota da ke tafiya shine zai zama = ½ (m1 + m2)v2

    = ½ (5.0 × 103 + 2.5× 103 )× 22

    = ½ (7500) × 4 = 15000 = 1.5 × 104J

    Yanzu tunda mun nemo initial K.E da final K.E sai musa su a cikin fomulamu, wato:

    Loss K.E = final K.E – initial K.E

    Loss in K.E = 1.5 × 104 - 2.25 × 104 = - 7500J

    = 7500J

    Negative sign din yayi signifaying loss in K.E

     

    • Impulse = change in momentum

    = final momentum – intial momentum

    = (m1+ m2 )v – (m1u1 + m2u2)

    =7500 × 2 – 1.5 × 104 + 0

    = 1.5 × 104 -1.5 × 104

    = 0Ns ko kuma 0 kgms-1

    Wadannan kadan ne daga cikin misalan lissafi na conservation of linear momentum. Insha Allah a makala ta gaba zan kawo wasu misalan wanda za su gamsar sosai susa a fahimci yadda ake yin kowannensu. Na gode, sai mun hadu a makala ta gaba.

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