Chitsanzo cha funso loti mudziwe liwiro lomaliza la kayendedwe ka parabolic

3 Zitsanzo za mafunso okhudza kudziwa liwiro lomaliza la kayendedwe ka parabolic

1. Mpira umakankhidwa mmwamba pa ngodya 30^o motsutsana ndi pamwamba pa munda ndi liwiro loyamba la 14 m/s. Kodi ndi zingati liwiro mapeto a mpira ukafika pamwamba pa bwalo? Kuthamanga kwa mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 30^o
Liwiro loyambirira (v)_o) = 14 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Liwiro lomaliza la mpira likafika pamwamba pa bwalo
Yankho:
Njira ya mpira ili monga momwe chithunzichi chikusonyezera.
Gawo lolunjika la liwiro loyambirira la mpira:
v_ox =v_o cos θ = (14 m/s)(cos 30^o) = (14 m/s)(0,5√3) = 7√3 m/s
Gawo loyima la liwiro loyambirira la mpira:
v_oy =v_o uchimo θ = (14 m/s)(uchimo 30^o) = (14 m/s)(0,5) = 7 m/s

Kuyenda molunjika molunjika kumasanthulidwa ngati mayendedwe ofanana a mzere, pomwe mayendedwe olunjika akuwunikidwa ngati kuyenda koyima mmwamba.

Liwiro lomaliza la mpira mbali yowongoka
Mpirawo ukakwera mmwamba, umabwerera pansi. Liwiro lomaliza la mpirawo ukafika pansi limawerengedwa pogwiritsa ntchito njira yoyendera mmwamba moyimirira.
Pothetsa vuto la kuyenda molunjika mmwamba, kuchuluka kwa vekitala Vekitala yomwe imayang'ana mmwamba imapatsidwa chizindikiro chabwino, vekitala yomwe imayang'ana pansi imapatsidwa chizindikiro choipa.
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 7 m/s (zabwino chifukwa chiwongolero cha liwiro chili mmwamba)
Kuthamanga chifukwa cha mphamvu yokoka (g) = -10 m/s² (zoipa chifukwa njira yokoka imayendera pansi)
Kutalika (h) = 0 (mpira umabwerera pamalo ake oyambirira kotero kusintha kwa kutalika ndi zero)
Anafunsa kuti: Liwiro lomaliza la mpira (v)_t)
Yankho:
Zikudziwika kuti v_o, g, h ndipo anafunsa v_t kotero njira yoyendetsera moyimirira mmwamba yomwe imagwiritsidwa ntchito ndi v_t² =v_o² + 2 gh

v_t² =v_o² + 2 gh = 72 + 2(-10)(0) = 49 – 0 = 49
v_t = √49 = 7 m/s
Tinganene kuti liwiro loyamba la mpira ukakwera mmwamba ndi lofanana ndi liwiro lomaliza la mpira ukafika pamwamba pa bwalo.

Liwiro lomaliza la mpira mbali yopingasa
Liwiro loyamba lolunjika ndi 7√3 m/s. Mu kuyenda kofanana kwa mzere, liwiro limakhala losasintha, kotero liwiro loyamba limakhala lofanana ndi liwiro lomaliza. Chifukwa chake, liwiro lomaliza lolunjika la mpira ndi 7√3 m/s.

Liwiro lomaliza la mpira likafika pamwamba pa bwalo
Liwiro lomaliza la mpira ndi kuphatikiza kwa liwiro lomaliza mbali yopingasa ndi liwiro lomaliza mbali yoyimirira.

Ngati njira yoyendera ndi yophiphiritsira monga momwe zilili pachithunzi pamwambapa, ndiye kuti liwiro loyambirira ndi lofanana ndi liwiro lomaliza.

2. Chipolopolocho chimawomberedwa mmwamba pa ngodya ya 30°^o Kuthamanga mopingasa kuchokera pamalo okwana mamita 5 kuchokera pansi. Liwiro loyamba la chipolopolo ndi 10 m/s. Kodi liwiro lomaliza la chipolopolocho likafika pansi ndi lotani? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 30^o
Kutalika koyambirira (h)_o) = mamita 5
Liwiro loyambirira (v)_o) = 10 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Liwiro lomaliza la chipolopolo chikafika pansi
Yankho:
Gawo lolunjika la liwiro loyambirira la mpira:
v_ox =v_o cos θ = (10 m/s)(cos 30^o) = (10 m/s)(0,5√3) = 5√3 m/s
Gawo loyima la liwiro loyambirira la mpira:
v_oy =v_o uchimo θ = (10 m/s)(uchimo 30^o) = (10 m/s)(0,5) = 5 m/s

Kuyenda molunjika molunjika kumasanthulidwa ngati mayendedwe ofanana a mzere, pomwe mayendedwe olunjika akuwunikidwa ngati kuyenda koyima mmwamba.

Liwiro lomaliza la chipolopolo mbali yoyimirira
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 5 m/s (zabwino chifukwa chiwongolero cha liwiro chili mmwamba)
Kuthamanga chifukwa cha mphamvu yokoka (g) = -10 m/s² (zoipa chifukwa njira yokoka imayendera pansi)
Kutalika (h) = -5 m (koipa chifukwa pamwamba pa nthaka pali pansi pa kutalika koyambirira)
Anafunsa kuti: Liwiro lomaliza la mpira (v)_t)
Yankho:
Zikudziwika kuti v_o, g, h ndipo anafunsa v_t kotero njira yoyendetsera moyimirira mmwamba yomwe imagwiritsidwa ntchito ndi v_t² =v_o² + 2 gh

v_t² =v_o² + 2 gh = 5² + 2(-10)(-5) = 25 + 100 = 125
v_t = √125 m/s

Liwiro lomaliza la chipolopolo mbali yopingasa
Liwiro loyamba lolunjika ndi 5√3 m/s. Mu kuyenda kofanana kwa mzere, liwiro limakhala losasintha, kotero liwiro loyamba limakhala lofanana ndi liwiro lomaliza. Chifukwa chake, liwiro lomaliza lolunjika la chipolopolo ndi 5√3 m/s.

Liwiro lomaliza la chipolopolo chikafika pansi
Liwiro lomaliza la chipolopolo ndi kuphatikiza kwa liwiro lomaliza mbali yopingasa ndi liwiro lomaliza mbali yoyimirira.

3. Marble imaponyedwa mopingasa kumanja kuchokera kutalika kwa mamita 12 ndi liwiro loyambirira la 8 m/s. Kodi liwiro lomaliza la marble likafika pansi ndi lotani? Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Kutalika (h) = mamita 12
Liwiro loyambirira (v)_o) = 8 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Liwiro lomaliza (v)_t) mabulo akagunda pansi
Yankho:
Njira ya miyala ya marble ili monga momwe yasonyezedwera pachithunzichi.
Liwiro loyamba la mpira mbali yopingasa:
v_ox =v_o = 8 m/s
Liwiro loyamba la mpira mbali yowongoka:
v_oy = 0 m/s

Kuyenda molunjika molunjika kumasanthulidwa ngati mayendedwe ofanana a mzere, pomwe mayendedwe olunjika akuwunikidwa ngati kuyenda kwaulere kwa kugwa.

Liwiro lomaliza la marble kumbali yowongoka
Liwiro lomaliza limawerengedwa pogwiritsa ntchito njira yolowera yaulere.
Amadziwika kuti:
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kutalika (h) = 12 m
Anafunsa kuti: Liwiro lomaliza (v)_t)
Yankho:
Popeza g, h ndi asked vt, njira yoyendetsera kayendedwe ka free fall yomwe yagwiritsidwa ntchito ndi v_t² = 2 gh
v_t² = 2 gh = 2(10)(12) = 240
v_t = √240 m/s

Liwiro lomaliza la marble mbali yopingasa
Liwiro loyamba lolunjika ndi 8 m/s. Mu kuyenda kofanana kwa mzere, liwiro limakhala losasintha, kotero liwiro loyamba limakhala lofanana ndi liwiro lomaliza. Chifukwa chake, liwiro lomaliza lolunjika la marble ndi 8 m/s.

Liwiro lomaliza la marble likafika pansi
Liwiro lomaliza la miyala yamtengo wapatali ndi kuphatikiza kwa liwiro lomaliza mbali yopingasa ndi liwiro lomaliza mbali yoyimirira.

[Chingerezi: Kuthetsa mavuto oyenda ndi projectile - kudziwa liwiro lomaliza]