Mibvunzo yeMienzaniso neKukurukurirana kweNewton's Relative Motion
Pendauluan
Kufamba kwehukama ipfungwa huru mufizikisi inotsanangura kuti kumhanya nenzvimbo yechinhu zvinogona kuchinja sei zvichienderana nemuoni. Sir Isaac Newton, nemitemo yake yekufamba uye simba rinokwevera pasi, vakaisa hwaro hwekunzwisisa mashandiro ekufamba kwehukama. Chinyorwa chino chichataura nezvemienzaniso yakati wandei nehurukuro dzekufamba kwehukama kwaNewton. Tichatsanangura matambudziko aya nematanho ekugadzirisa akadzama kuti zvive nyore kunzwisisa.
Pfungwa huru yaNewton yekufamba kwehukama
MuNewtonian physics, kufamba kwechinhu kunoyerwa nguva dzose zvichienderana nefuremu yekutarisa. Kana tine mafuremu maviri ekutarisa achifamba achienzaniswa nevelocity v, saka nzvimbo uye velocity yechinhu zvinogona kuonekwa zvakasiyana mumafuremu maviri. Mamwe mazano ekunzwisisa ndeaya:
1. Inertial Frame of Reference: Frame of reference umo chinhu chinofamba nekumhanya kusingagumi kana pasina simba rinoita chinhu chacho.
2. Kumhanya kwechinhu: Kumhanya kwechinhu kunoyerwa zvichienderana nechimwe chimiro chekutarisa.
3. Kuchinjana Kwezvinhu: Musiyano uripo pakati pezvinhu zviviri kana chimwe chinhu chine maframe maviri akasiyana ekutarisa.
Newton akatsanangura mafambiro epfungwa zvakanaka kuburikidza nemutemo wake wemafambiro, uye tinogona kushandisa shanduko dzeGalilean kuti tishandure pakati pemafuremu maviri ekutarisa.
Mibvunzo Yekukurukurirana Yemuenzaniso
Mubvunzo 1: Kutama Kwekufamba Kwemhuri
Mubvunzo:
Ngarava mbiri, Ngarava A neNgarava B, dziri mugungwa guru. Ngarava A iri kufamba ichienda kumabvazuva ichimhanya 20 m/s, ukuwo Ngarava B iri kufamba ichienda kuchamhembe ichimhanya 30 m/s. Verenga kumhanya kweNgarava B uchienzaniswa neNgarava A.
Kukurukurirana:
Kuti tigadzirise dambudziko iri, tinoshandisa pfungwa ye relative velocity. Relative velocity yeShip B kana tichienzanisa neShip A inogona kuverengwa tichishandisa nzira yevector.
1. Inomiririra kumhanya kweShip A (\(\vec{v_A}\)) uye Ship B (\(\vec{v_B}\)) semavector.
\[
\vec{v_A} = 20 \, \text{m/s kumabvazuva} \zvinoreva \vec{v_A} = 20 \hat{i} \, \text{m/s}
\]
\[
\vec{v_B} = 30 \, \text{m/s kuchamhembe} \zvinoreva \vec{v_B} = 30 \hat{j} \, \text{m/s}
\]
2. Kumhanya kweShip B kuenda kuShip A (\(\vec{v_{BA}}\)) kunoverengerwa ne:
\[
\vec{v_{BA}} = \vec{v_B} – \vec{v_A}
\]
Tsiva kukosha kwe \(\vec{v_A}\) uye \(\vec{v_B}\):
\[
\vec{v_{BA}} = 30 \hat{j} \, \text{m/s} – 20 \hat{i} \, \text{m/s}
\]
\[
\vec{v_{BA}} = -20 \hat{i} + 30 \hat{j} \, \text{m/s}
\]
3. Kuti uwane hukuru hwe relative velocity, shandisa dzidziso yePythagorean:
\[
|\vec{v_{BA}}| = \sqrt{(-20)^2 + (30)^2}
\]
\[
|\vec{v_{BA}}| = \sqrt{400 + 900}
\]
\[
|\vec{v_{BA}}| = \sqrt{1300} = 10 \sqrt{13} \, \text{m/s}
\]
Saka, kumhanya kweShip B zvichienzaniswa neShip A i \(10 \sqrt{13}\) m/s.
Mubvunzo 2: Kufamba kwehukama muhurongwa hwekubatana
Mubvunzo:
Munhu anofamba netsoka ari kufamba kuchamhembe ne5 m/s pamusoro pechitima chiri kufamba kumabvazuva ne20 m/s. Sarudza kumhanya kwemufambi uchienzaniswa nepasi.
Kukurukurirana:
Kuti tizive kumhanya kwemufambi kana tichienzanisa nepasi, tinoshandisa pfungwa yekuwedzera mafambiro emhepo zvakare.
1. Inomiririra kumhanya kwemufambi (\(\vec{v_P}\)) uye kumhanya kwechitima (\(\vec{v_K}\)) semavector.
\[
\vec{v_P} \text{ relative to the train} = 5 \hat{j} \, \text{m/s}
\]
\[
\vec{v_K} \text{ related to the ground} = 20 \hat{i} \, \text{m/s}
\]
2. Kumhanya kwemufambi kana tichienzanisa nepasi (\(\vec{v_{PT}}\)) ndiko kuwanda kwevector:
\[
\vec{v_{PT}} = \vec{v_P} + \vec{v_K}
\]
Tsiva kukosha kwe \(\vec{v_P}\) uye \(\vec{v_K}\):
\[
\vec{v_{PT}} = 5 \hat{j} \, \text{m/s} + 20 \hat{i} \, \text{m/s}
\]
3. Kuti uwane hukuru hwe relative velocity:
\[
|\vec{v_{PT}}| = \sqrt{(20)^2 + (5)^2}
\]
\[
|\vec{v_{PT}}| = \sqrt{400 + 25}
\]
\[
|\vec{v_{PT}}| = \sqrt{425} = 5 \sqrt{17} \, \text{m/s}
\]
Saka, kumhanya kwemufambi kana tichienzanisa nepasi i \(5 \sqrt{17}\) m/s.
Mubvunzo 3: Kufamba Kwepakati Pandege Yakarerekera
Mubvunzo:
Bhora rinokandwa nekumhanya kwe \( \vec{u} = 10 \hat{i} + 10 \hat{j} \) m/s zvichienzaniswa nengoro iri kufamba nekumhanya kwakafanana kwe15 m/s. Sarudza kumhanya kwebhora zvichienzaniswa nepasi.
Kukurukurirana:
Shandisa pfungwa imwecheteyo mukuwedzera vector.
1. Ratidza kumhanya kwebhora (\(\vec{u}\)) zvichienzaniswa nengoro uye kumhanya kwengoro (\(\vec{v_K}\)) semavector.
\[
\vec{u} = 10 \hat{i} + 10 \hat{j} \, \text{m/s}
\]
\[
\vec{v_K} = 15 \hat{i} \, \text{m/s}
\]
2. Kumhanya kwebhora kana tichienzanisa nepasi (\(\vec{v_{BT}}\)) ndekwekuti:
\[
\vec{v_{BT}} = \vec{v_K} + \vec{u}
\]
\[
\vec{v_{BT}} = 15 \hat{i} + (10 \hat{i} + 10 \hat{j})
\]
\[
\vec{v_{BT}} = (15 + 10) \hat{i} + 10 \hat{j}
\]
\[
\vec{v_{BT}} = 25 \hat{i} + 10 \hat{j}
\]
3. Kuti uwane hukuru hwe relative velocity:
\[
|\vec{v_{BT}}| = \sqrt{(25)^2 + (10)^2}
\]
\[
|\vec{v_{BT}}| = \sqrt{625 + 100}
\]
\[
|\vec{v_{BT}}| = \sqrt{725} = 5 \sqrt{29} \, \text{m/s}
\]
Saka, kumhanya kwebhora kana tichienzanisa nepasi i \(5 \sqrt{29}\) m/s.
Mhedziso
Pfungwa yaNewton yekufamba kwehukama ndiyo hwaro hwakakosha hwefizikisi yekare. Tichishandisa misimboti mikuru yakadai sekuwedzera kwevector, tinogona kuona kumhanya kwehukama uye kutama kwechinhu chimwe kana ma frame akasiyana ereferensi. Mienzaniso iri pamusoro inoratidza mashandisirwo epfungwa iyi mumamiriro akasiyana-siyana, zvichipa kunzwisisa kwakadzama kwekufamba kwehukama.
Nekunzwisisa nekushandisa pfungwa idzi, tinogona kunzwisisa zviri nani mitemo yaNewton yekufamba uye kuti inoshanda sei munyika chaiyo. Ruzivo urwu harungobatsiri chete kugadzirisa matambudziko efizikisi asiwo runopa ruzivo rwakadzama pamusoro pekuti zvinhu zvose zvinoshanda sei.
