Zitsanzo za Mafunso Okhudza Lamulo Losunga Mphamvu
Lamulo la Kusunga Mphamvu ndi mfundo yofunikira mu fizikisi, yonena kuti mphamvu mu dongosolo lotsekedwa silingathe kulengedwa kapena kuwonongedwa, koma lingasinthidwe kuchokera ku mawonekedwe ena kupita ku ena. Lingaliro ili ndi lofunika kwambiri ndipo limagwiritsidwa ntchito nthawi zambiri m'magawo osiyanasiyana a sayansi ndi ukadaulo, kuphatikizapo makina, thermodynamics, ndi electromagnetism. M'nkhaniyi, tikambirana zitsanzo zingapo za mavuto okhudzana ndi Lamulo la Kusunga Mphamvu, pamodzi ndi kufotokozera mwatsatanetsatane.
Chitsanzo Funso 1: Mphamvu ya Makina mu Chinthu Chogwa Momasuka
Funso: Mpira wolemera makilogalamu 0,5 umagwetsedwa kuchokera kutalika kwa mamita 20. Musanyalanyaze kukana kwa mpweya. Kodi liwiro la mpirawo likafika pansi ndi lotani?
Kukambirana:
Gawo 1: Dziwani mphamvu yoyambira ndi yomaliza.
Mphamvu yoyamba pamene mpira uli pamtunda wa mamita 20 ndi mphamvu yokoka (EP), yomwe ingawerengedwe pogwiritsa ntchito njira iyi:
\[ EP = mgh \]
Kumene:
– \( m \) ndi kulemera kwa mpira (0,5 kg)
– \( g \) ndi kufulumira chifukwa cha mphamvu yokoka (9,8 m/s²)
– \( h \) ndi kutalika (20 m)
\[ EP_{initial} = 0,5 \nthawi 9,8 \nthawi 20 = 98 \, \malemba{J} \]
Mphamvu yomaliza pamene mpira wafika pansi ndi kinetic energy (EK), yomwe ingawerengedwe pogwiritsa ntchito fomula iyi:
\[ EK = \frac{1}{2} mv^2 \]
Kumene:
– \( v \) ndi liwiro la mpira ukafika pansi
Gawo 2: Gwiritsani ntchito Lamulo la Kusunga Mphamvu kuti munene kuti mphamvu yoyambira yomwe ingatheke ndi yofanana ndi mphamvu yomaliza ya kinetic.
\[ EP_{initial} = EK_{final} \]
\[ 98 = \frac{1}{2} \nthawi 0,5 \nthawi v^2 \]
Gawo 3: Konzani equation kuti mupeze \( v \).
\[ 98 = 0,25v^2 \]
\[ v^2 = \frac{98}{0,25} = 392 \]
\[ v = \sqrt{392} \pafupifupi 19,8 \, \text{m/s} \]
Kotero, liwiro la mpirawo likafika pansi ndi pafupifupi 19,8 m/s.
Chitsanzo Funso 2: Mphamvu mu Kasupe
Funso: Kasupe wokhala ndi kasupe wosasintha \( k \) = 200 N/m amakanikizidwa mamita 0,1 kuchokera pamalo ake ofanana. Kodi mphamvu yochuluka bwanji yokhazikika imasungidwa mu kasupe?
Kukambirana:
Gawo 1: Gwiritsani ntchito njira yolumikizira mphamvu ya elastic potential.
\[ EP_{elastic} = \frac{1}{2} kx^2 \]
Kumene:
– \( k \) ndi nthawi yokhazikika ya masika (200 N/m)
– \( x \) ndi mtunda wopanikizika (0,1 m)
Gawo 2: Ikani mfundo zodziwika bwino mu fomula.
\[ EP_{elastic} = \frac{1}{2} \times 200 \times (0,1)^2 \]
\[ EP_{elastic} = \frac{1}{2} \times 200 \times 0,01 \]
\[ EP_{elastic} = 1 \, \text{J} \]
Kotero, mphamvu yotha kusungunuka yomwe imasungidwa m'nyengo ya masika ndi 1 Joule.
Chitsanzo Funso 3: Mphamvu Yokoka ndi Mphamvu ya Kinetic mu Kuyenda Kwa Parabolic
Funso: Chowombera cholemera makilogalamu awiri chimayambitsidwa ndi liwiro loyambirira la 30 m/s pa ngodya ya 45° kupita ku yopingasa. Kodi mphamvu za kinetic ndi potential za chowomberacho ndi ziti pamalo apamwamba kwambiri a trajectory yake?
Kukambirana:
Gawo 1: Gawani liwiro loyamba kukhala magawo opingasa ndi olunjika.
\[ v_{x} = v_0 \cos \theta \]
\[ v_{y} = v_0 \sin \theta \]
Kumene:
– \( v_0 \) ndi liwiro loyambirira (30 m/s)
– \( \theta \) ndi ngodya yoyambira (45°)
\[ v_{x} = 30 \cos 45° = 30 \times \frac{\sqrt{2}}{2} = 21,21 \, \text{m/s} \]
\[ v_{y} = 30 \sin 45° = 30 \times \frac{\sqrt{2}}{2} = 21,21 \, \text{m/s} \]
Gawo 2: Pamalo okwera kwambiri, liwiro loyima (v_y) ndi 0, koma liwiro lopingasa (v_x) limakhalabe lokhazikika.
\[ v_{x \, mfundo \, yapamwamba kwambiri} = 21,21 \, \malemba{m/s} \]
Gawo 3: Werengani mphamvu ya kinetic ya projectile pamalo ake apamwamba kwambiri.
\[ EK = \frac{1}{2} mv^2 \]
\[ EK_{point \, highest} = \frac{1}{2} \times 2 \times (21,21)^2 \]
\[ EK_{point \, highest} = 1 \times 449,21 = 449,21 \, \text{J} \]
Gawo 4: Werengani kutalika kwakukulu komwe chida chowombera chidafikira.
\[ h = \frac{v_{y}^2}{2g} \]
\[ h = \frac{(21,21)^2}{2 \times 9,8} \]
\[ h \pafupifupi 22,9 \, \text{m} \]
Gawo 5: Werengani mphamvu yokoka pamalo okwera kwambiri.
\[ EP_{point \, highest} = mgh \]
\[ EP_{point \, highest} = 2 \times 9,8 \times 22,9 \]
\[ EP_{point \, highest} \pafupifupi 449,72 \, \text{J} \]
Kotero, mphamvu ya kinetic ya projectile pamalo okwera kwambiri ndi 449,21 Joules, ndipo mphamvu yokoka pamalo okwera kwambiri ndi 449,72 Joules.
Chitsanzo Funso 4: Mphamvu ya Kutentha mu Kukangana
Funso: Bokosi lolemera makilogalamu 10 limakankhidwira pansi lopanda mphamvu kwa mamita 5 ndi mphamvu yosalekeza ya 30 N. Coefficient ya kinetic friction pakati pa bokosi ndi pansi ndi 0,2. Kodi mphamvu zingati zomwe zimasinthidwa kukhala mphamvu ya kutentha chifukwa cha friction?
Kukambirana:
Gawo 1: Werengani mphamvu ya kukangana.
\[ f_{friction} = \mu N \]
Kumene:
– \( \mu \) ndi coefficient of friction (0,2)
– \( N \) ndi mphamvu yachibadwa. Pa malo osalala, \( N = mg \)
\[ f_{friction} = 0,2 \nthawi 10 \nthawi 9,8 = 19,6 \, \malemba{N} \]
Gawo 2: Werengani ntchito yochitidwa ndi mphamvu yokangana.
\[ W = f_{friction} \times d \]
Kumene:
– \( d \) ndi mtunda (5 m)
\[ W = 19,6 \nthawi 5 = 98 \, \lemba{J} \]
Mphamvu yomwe imasinthidwa kukhala mphamvu yotentha chifukwa cha kukangana ndi 98 Joules.
Mapeto
Lamulo la Kusunga Mphamvu ndi lingaliro lamphamvu lomwe limagwira ntchito pazochitika zambiri za sayansi. Kulimvetsa kumatithandiza kusanthula zochitika zosiyanasiyana zakuthupi, kuyambira zinthu zomwe zimagwa momasuka ndi kuyenda kwa zipolopolo mpaka mphamvu zomwe zimapangidwa ndi kukangana. Zitsanzo zomwe zili pamwambapa zimatithandiza kumvetsetsa momwe mphamvu ingasinthire mawonekedwe ake pamene ikupitirirabe kuchuluka kwake. Kumvetsetsa bwino lingaliro ili ndikofunikira kwambiri pa maphunziro ndi ntchito zothandiza mu uinjiniya ndi sayansi.
