Zitsanzo za mafunso okhudza lamulo losunga mphamvu zamakanika

Zitsanzo 16 za Mafunso Okhudza Lamulo Losunga Mphamvu Zamakina

Lamulo losunga mphamvu zamakanika mu kayendedwe ka kugwa kwaulere

1. Kokonati yolemera makilogalamu awiri imagwa momasuka kuchokera kutalika kwa mamita 6. Mphamvu ya kayendedwe ka kokonati ikafika pansi ndi… g = 10 m/s²
Zokambirana
Ndizodziwika kuti :
Unyinji wa kokonati (m) = 2 kg
Kutalika (h) = mamita 6
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa mphamvu ya kinetic (EK)
Yankhani :

Mphamvu yoyambirira yamakina
Ngati chinthu chili mu free fall, sichikhala ndi liwiro loyambirira. Chifukwa palibe liwiro loyambirira, palibe mphamvu yoyambira ya kinetic. Poyamba, chinthucho chili pamtunda wa mamita 6, kotero ndithudi, chinthucho chili ndi mphamvu yoyambira yokoka. Chifukwa chake, mphamvu yoyambira yamakina (EM) ndi_o) ndi mphamvu yokoka (EP).
EM_o = EP = mgh = (2)(10)(6) = 120 Joules

Mphamvu yomaliza yamakina
Popita pansi, kutalika kwa chinthu kumachepa, kotero mphamvu yake yokoka imachepa. Mphamvu yokoka simatayika koma imasinthidwa kukhala mphamvu ya kinetic. Ikafika pansi, kutalika kwa chinthucho kumakhala kofanana ndi kutalika kwa nthaka (h = 0), kotero mphamvu yake yokoka ndi zero (h = 0, kotero EP = mgh = 0). Mphamvu zonse zokoka zimasinthidwa kukhala mphamvu ya kinetic. Chifukwa chake, mphamvu yomaliza yamakina (EM) ndi_t) ndi mphamvu ya kinetic (EK).
EM_t = EK = ½ mv²

Lamulo losunga mphamvu zamakanika :
Mphamvu yoyambirira yamakina = mphamvu yomaliza yamakina
EM_o = EM_t
EP = EK
120 = EK
Mphamvu ya kayendedwe ka kokonati ikafika pansi ndi 100 Joules.

2. Mpira wolemera makilogalamu awiri kugwa kwaulere kuchokera pamalo A monga momwe chithunzichi chikusonyezera. (g = 10 ms^-2). Mukafika pa mfundo B, mphamvu ya kinetic imakhala yofanana ndi mphamvu yomwe ingatheke kawiri, kotero kutalika kwa mfundo B kuchokera pansi ndi…

A. 80 m
B. 70 m
C. 60 m
D. 40 m
E. 30 m

Zokambirana
Ndizodziwika kuti :
Kulemera kwa mpira (m) = 2 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms^-2
Kutalika A (h)_A) = mamita 90
Anafunsa Kutalika B (h)_B)
Yankhani :

Ketika bola tiba di titik B, energi kinetik bola di titik B sama dengan 2 kali energi potensial gravitasi bola di titik B.
EK = 2 EP
½ mv² = 2 mgh_B
½ v² = 2 gh_B
v² = 2(2)(10) h_B
v² = maola 40_B
Hitung liwiro (v) mpira ukafika pa point B utagwa kuchokera pa point A.
v² = 2 gh = 2(10)(90–h_B) = 20 (maola 90–maola_B)
Sinthani v² mu equation pamwambapa ndi v² mu equation iyi.
v² = maola 40_B
20 (maola 90–maola_B) = maola 40_B
1800-20 h_B = maola 40_B
1800 = maola 40_B + 20h_B
1800 = maola 60_B
h_B = 1800/60
h_B = 30 mita
Yankho lolondola ndi E.

3. Chinthu cholemera makilogalamu 1 chimagwa momasuka kuchokera pamwamba pa nyumba yokhala ndi zipinda zambiri zomwe zili ndi kutalika kwa mamita 80. Ngati kukangana ndi mpweya sikunyalanyazidwa ndipo kuthamanga chifukwa cha mphamvu yokoka (g) kuli 10 m/s² Kotero mphamvu ya kinetic ya chinthucho ikafika pansi ndi...
Zokambirana
Ndizodziwika kuti :
Kulemera (m) = 1 kg
Kutalika (h) = mamita 80
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic (EK) ya chinthu pamene chinthucho chifika pamwamba pa nthaka
Yankhani :
Zinthu zimagwa momasuka motero chinthucho sichikhala ndi liwiro loyambirira. Chifukwa chake, chikakhala pamtunda wa mamita 80, chinthucho chimakhala ndi mphamvu yokoka koma chinthucho chilibe mphamvu ya kinetic (v = 0 kotero EK = ½ mv² = 0). Chifukwa chake mphamvu yoyambirira yamakina (EM)_o) = mphamvu yokoka (EP).

EM _o = EP = mgh = (1)(10)(80) = 800 Joules

Pa nthawi yogwa mwaulere, mphamvu yokoka imasinthidwa kukhala mphamvu ya kinetic. Chinthu chikagunda pansi, mphamvu zake zonse yokoka imasinthidwa kukhala mphamvu ya kinetic. Chifukwa chake, chikafika pansi, chinthucho chimakhala ndi mphamvu ya kinetic koma palibe mphamvu yokoka (h = 0, kotero EP = mgh = 0). Chifukwa chake, mphamvu yomaliza yamakina (EM _t ) = mphamvu ya kinetic (EK)

Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya kinetic.
EM_o = EM_t
EP = EK
800 = EK
Mphamvu ya kinetic (EK) ya chinthucho ikafika pansi ndi 800 Joules.

4. Chinthu chimagwa momasuka kuchokera kutalika kwa mamita 10 pamwamba pa nthaka. Ngati kulemera kwa chinthucho ndi 4 kg ndipo kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^–2 , ndiye kuti mphamvu ya kinetic ndi liwiro la chinthucho pamtunda wa mamita 5 pamwamba pa nthaka ndi…

Zokambirana
Ndizodziwika kuti :
Kusintha kwa kutalika (h) = 10 – 5 = mamita 5
Kulemera (m) = 4 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic ya chinthu pamtunda wa mamita 5
Yankhani :
(a) Mphamvu ya kinetic ya chinthu pamtunda wa mamita awiri
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yokoka (EP)
EM_o = EP = mgh = (4)(10)(5) = 200 Joules
Mphamvu yomaliza yamakina (EM)_t) = mphamvu ya kinetic (EK)
EM_t = EK
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina.
EM_o = EM_t
200 = EK
Mphamvu ya kinetic ya chinthu chomwe chili pamtunda wa mamita 5 pamwamba pa nthaka ndi ma Joules 200.

(b) Liwiro la chinthucho pamtunda wa mamita 5
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
EP = EK
200 = ½ mv²
2(200) / 4 = v²
100 = v²
v = √100
v = mamita 10/sekondi
Liwiro la chinthucho ndi mamita 10 pa sekondi

5. Chipatso cha mango chimagwa momasuka kuchokera kutalika kwa mamita awiri. Ngati g = 10 ms^-2, werengerani liwiro la mango isanagwe pansi pogwiritsa ntchito lamulo la mphamvu yamakina.
Zokambirana
Ndizodziwika kuti :
Kutalika (h) = mamita 2
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : liwiro la mango lisanagwe pansi (v)
Yankhani :
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yokoka (EP)
EM_o = EP = mgh = m (10)(2) = 20 m
Mphamvu yomaliza yamakina (EM)_t) = mphamvu ya kinetic (EK)
EM_t = EK = ½ mv²
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina.
EM_o = EM_t
20 m = ½ mv²
20 = ½ v²
2(20) = v²
40 = v²
v = √40 = √(4)(10) = 2√10 mamita/sekondi
Liwiro la mango lisanafike pansi ndi mamita 2√10 pa sekondi.
Ndikofunikira kudziwa kuti powerengera, timanyalanyaza kukangana kwa mpweya. Zoona zake n'zakuti, ngati chinthu chilichonse chagwa momasuka pamwamba pa Dziko Lapansi, kukangana kwa mpweya kumakhudzanso kayendedwe kake, zomwe zimapangitsa kuti liwiro lake likhale lotsika kuposa momwe tawerengera pamwambapa.

Lamulo losunga mphamvu zamakanika poyenda moyimirira mmwamba ndi pansi

6. Chinthu cholemera makilogalamu 1 chimaponyedwa molunjika pansi ndi liwiro loyamba la 2 m/s kuchokera m'mphepete mwa nyumba ya mamita 40. Mphamvu ya kayendedwe ka chinthucho chikakhala pamtunda wa mamita 10 kuchokera pansi ndi… g = 10 m/s ²

Zokambirana
Ndizodziwika kuti :
Kulemera kwa chinthu (m) = 1 kg
Liwiro loyambirira (v)_o) = 2 m/s
Kusintha kwa kutalika = 40 - 10 = mamita 30
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic ya chinthu chomwe chili pamtunda wa mamita 10 kuchokera pansi
Yankhani :

Mphamvu yoyambirira yamakina
Poyamba, chinthucho chili ndi mphamvu yokoka komanso mphamvu ya kinetic.
Mphamvu yoyambira yokoka (EP) = mgh = (1)(10)(30) = 300 Joules
Mphamvu yoyambirira ya kinetic (EK) = ½ mv_o² = ½ (1)(2)² = ½ (4) = 2 Joule
Kotero mphamvu yoyamba yamakina = mphamvu yoyamba yokoka + mphamvu yoyamba ya kinetic = 300 + 2 = 302 Joules.

Mphamvu yomaliza yamakina
Pamene chinthu chikuyenda pansi, kutalika kwake kumachepa, motero kumachepetsa mphamvu yake yokoka. Mphamvu yokoka iyi imasinthidwa kukhala mphamvu ya kinetic. Pambuyo poyenda mamita 30, kapena pamene chinthucho chili pamtunda wa mamita 10 kuchokera pansi, mphamvu yake yonse yokoka imasinthidwa kukhala mphamvu ya kinetic.
Kotero mphamvu yomaliza yamakina = mphamvu yomaliza ya kinetic = mphamvu yoyamba yokoka + mphamvu yoyambirira ya kinetic = 300 + 2 = 302 Joules.

7. Chinthu cholemera makilogalamu 1 chimaponyedwa molunjika mmwamba ndi liwiro loyambirira la 10 m/s. Dziwani (a) mphamvu yokoka pamalo okwera kwambiri (b) malo okwera kwambiri kapena kutalika kwakukulu komwe chinthucho chingafikire… g = 10 m/s²
Zokambirana
Ndizodziwika kuti :
Kulemera kwa chinthu (m) = 1 kg
Liwiro loyambirira (v)_o) = 10 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu yokoka pamalo apamwamba kwambiri komanso otsika kwambiri
Yankhani :
(a) Mphamvu yokoka pamalo okwera kwambiri
Mphamvu yoyambirira yamakina
Poyamba chinthucho chimakhala ndi mphamvu ya kinetic koma chinthucho sichikhala ndi mphamvu yokoka. Mphamvu yoyamba yamakina = mphamvu yoyamba ya kinetic (EK) = ½ mv_o² = ½ (1)(10)² = ½ (100) = 50 Joules.
 
Mphamvu yomaliza yamakina
Pambuyo poyenda molunjika mmwamba, kutalika kwa chinthucho kumawonjezeka, motero kumawonjezera mphamvu yake yokoka. Mphamvu yokoka iyi siimabwera yokha koma imachokera ku mphamvu ya kinetic. Pa kutalika kwake kwakukulu kapena pamalo apamwamba kwambiri, chinthucho chimakhala chilili kwa kanthawi chisanabwerere m'mbuyo. Chifukwa chimakhala chilili kwa kanthawi, liwiro lake ndi zero, ndipo mphamvu yake ya kinetic nayonso ndi zero. Mphamvu zonse za kinetic zimasinthidwa kukhala mphamvu yokoka.
Mphamvu yomaliza yamakina = mphamvu yokoka (EP)

Lamulo losunga mphamvu zamakanika:
Mphamvu yoyambirira yamakina = mphamvu yomaliza yamakina
EK = EP
50 = EP
Mphamvu yokoka ndi 50 Joules.

(b) Malo okwera kwambiri kapena kutalika kwakukulu
EP = mgh
50 = (1)(10) h
50 = maola 10
h = 50 / 10 = mamita 5
Malo okwera kwambiri kapena kutalika kwakukulu komwe chinthu chingafikire ndi mamita 5 kuchokera pamwamba pa nthaka.

 

Lamulo losunga mphamvu zamakanika zomwe zikuyenda pa ndege yopendekeka

8. Kuchokera pamalo opumula, chipika chimatsetsereka popanda kukangana motsatira mtunda wopendekeka. Liwiro la chipikacho likafika pansi pa mtunda wopendekeka ndi… g = 10 m/s²
Zokambirana
Ndizodziwika kuti :
Kutalika (h) = mamita 8
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : liwiro (v) la chipikacho likafika pansi pa ndege yopendekeka
Yankhani :
Ikakhala pamtunda wa mamita 8, chipikacho chimakhala ndi mphamvu yokoka koma palibe mphamvu ya kayendedwe kake chifukwa sichinasunthebe. Chifukwa chake, mphamvu yoyamba yamakina ya chipikacho ndi mphamvu yokoka.
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yokoka (EP)
EM_o = EP = mgh = m (10)(8) = 80 m
Pamene chipikacho chikuyamba kutsika pansi, mphamvu yake yokoka imayamba kusintha kukhala mphamvu ya kinetic. Ikafika pansi pa kutsika, mphamvu yake yonse yokoka imasintha kukhala mphamvu ya kinetic. Motero, mphamvu yomaliza ya makina a chipikacho ndi mphamvu ya kinetic.
Mphamvu yomaliza yamakina (EM)_t) = mphamvu ya kinetic (EK)
EM_t = EK = ½ mv²
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina.
EM_o = EM_t
80 m = ½ mv²
80 = ½ v²
160 = v²
v = √160 = √(16)(10) = 4√10 m/s
Liwiro la chipika chomwe chili pansi pa plane yopendekeka ndi 4√10 mamita/sekondi.

9. Chinthu cholemera makilogalamu 1, poyamba chili pamalo opumulira, chimatulutsidwa kuchokera pamwamba pa malo osalala opendekeka omwe ali ndi kutalika kwa mamita 8. Dziwani mphamvu ya kinetic chinthucho chikayenda pamalo opendekeka kwa mamita 5…. (g = 10 m/s²)
Zokambirana
Ndizodziwika kuti :
Kulemera kwa chinthu (m) = 0,2 kg
Kutalika kwa hypotenuse komwe chinthucho chimadutsa = mamita 5
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic (EK) ya chinthu chitatha kutsetsereka mamita 5
Yankhani :
Gawo loyamba pothetsa vutoli ndikuwerengera kusintha kwa kutalika kwa chinthucho pambuyo poti chinthucho chayenda pa mtunda wopendekeka kwa mamita 5.
tchimo 30^o = kutalika kwa mbali yoyimirira / kutalika kwa hypotenuse
0,5 = kutalika kwa mbali yoyimirira / 5
Kutalika kwa mbali yoyimirira = (0,5)(5) = mamita 2,5
Kusintha kwa kutalika kwa chinthucho ndi mamita 2,5.

Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yokoka (EP)
EM_o = EP = mgh = (1)(10)(2,5) = 25 Joules
Mphamvu yomaliza yamakina (EM)_t) = mphamvu ya kinetic (EK)
EM_t = EK
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina.
EM_o = EM_t
25 = EK
Mphamvu ya kinetic ya chinthucho ikatha kuyenda mamita 5 ndi ma Joules 25.

 

Lamulo losunga mphamvu ya makina yoyenda mu ndege yokhota

10. Chinthu cholemera makilogalamu 1 chimatsetsereka popanda kukangana kuchokera kutalika kwa mamita 5 popanda liwiro loyambirira. Mphamvu ya kayendedwe ka chinthucho pamalo otsika kwambiri ndi… g = 10 m/s²
Zokambirana
Ndizodziwika kuti :
Kulemera kwa chinthu (m) = 1 kg
Kusintha kwa kutalika (h) = mamita 5
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic (EK) ndi liwiro (v) la chinthucho pamalo otsika kwambiri
Yankhani :

(a) Mphamvu ya kinetic ya chinthucho pamalo otsika kwambiri
Chikakhala pamtunda wa mamita 5 ndipo sichinayambe kuyenda, chinthucho chimakhala ndi mphamvu yokoka koma palibe mphamvu yokoka chifukwa chimakhala chili pamalo opumulira. Chifukwa chake, mphamvu yoyamba yamakina chinthucho chisanayambe kuyenda ndi mphamvu yokoka. Chinthucho chikayamba kuyenda pansi, mphamvu yokoka imayamba kusintha kukhala mphamvu yokoka. Chikafika pamalo otsika kwambiri, mphamvu yonse yokoka imasanduka mphamvu yokoka. Chifukwa chake, mphamvu yomaliza yamakina ndi mphamvu yokoka.
Mphamvu yoyambirira yamakina = mphamvu yokoka
EM_o = EP = mgh = (1)(10)(5) = 50 Joules
Mphamvu yomaliza yamakina = mphamvu ya kinetic
EM_t = EK = ½ mv_t²
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina..
EM_o = EM_t
EP = EK
50 = EK
Mphamvu ya kinetic (EK) yomwe ili pansi kwambiri ndi 50 Joules.

(b) Liwiro la chinthucho pamalo otsika kwambiri
Njira yoyamba:
Lamulo losunga mphamvu zamakanika:
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka (EP) = mphamvu ya kinetic (EK)
50 = ½ mv²
2(50) / m = v²
100 / 1 = v²
100 = v²
v = √100
v = mamita 10/sekondi
 
Njira yachiwiri:
Lamulo losunga mphamvu zamakanika :
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka (EP) = mphamvu ya kinetic (EK)
mgh = ½ mv²
gh = ½ v²
2 gh = v²
2(10)(5) = v²
100 = v²
v = √100
v = mamita 10/sekondi
Liwiro la chinthucho pamalo otsika kwambiri ndi 10 m/s.

11. Chinthu cholemera makilogalamu awiri chomwe poyamba chimakhala pamalo opumulira, chimatsetsereka popanda kukangana kuchokera kutalika kwa mamita 10 kuchokera pansi. Mphamvu ya kayendedwe ka chinthucho pamtunda wa mamita awiri kuchokera pansi ndi… g = 10 m/s²
Zokambirana
Ndizodziwika kuti :
Kulemera kwa chinthu (m) = 2 kg
Kusintha kwa kutalika (h) = 10 – 2 = mamita 8
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic (EK) ndi liwiro (v) la chinthucho pamtunda wa mamita awiri pamwamba pa nthaka.
Yankhani :
Yankho la vutoli likufanana ndi yankho la vuto lakale.

(a) Mphamvu ya kinetic ya chinthu pamtunda wa mamita awiri
Mphamvu yoyambirira yamakina = mphamvu yokoka
EM_o = EP = mgh = (2)(10)(8) = 160 Joules
Mphamvu yomaliza yamakina = mphamvu ya kinetic
EM_t = EK = ½ mv_t²
Lamulo losunga mphamvu ya makina limati mphamvu yoyamba ya makina ndi yofanana ndi mphamvu yomaliza ya makina..
EM_o = EM_t
EP = EK
160 = EK
Mphamvu ya kinetic (EK) pamtunda wa mamita awiri ndi 160 Joules.

(b) Liwiro la chinthucho pamalo otsika kwambiri
Njira yoyamba:
Lamulo losunga mphamvu zamakanika:
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka (EP) = mphamvu ya kinetic (EK)
160 = ½ mv²
160 = ½ (2) v²
160 = v²
v = √160 = √(16)(10) = 4√10 mamita/sekondi

Njira yachiwiri:
Lamulo losunga mphamvu zamakanika :
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka (EP) = mphamvu ya kinetic (EK)
mgh = ½ mv²
gh = ½ v²
2 gh = v²
2(10)(8) = v²
160 = v²
v = √160 = √(16)(10) = 4√10 mamita/sekondi
Liwiro la chinthu pamtunda wa mamita awiri ndi 4√10 mamita/sekondi.

12. M'nyengo yozizira, ku Sweden, mpikisano wa kutsetsereka pa ayezi umachitika m'mapiri. Otsetsereka pa ayezi amatsetsereka kuchokera kutalika A monga momwe zasonyezedwera pachithunzi 2.

Ngati liwiro loyamba la wokwera skier = zero, ndipo liwiro chifukwa cha mphamvu yokoka = 10 ms ^-2 , ndiye kuti liwiro la wokwera skier pa kutalika B ndi…

A. √2 ms ^-1

B. 5 √2 ms ^-1

C. 10 √2 ms ^-1

D. 20 √2 ms ^-1

E. 25 √2 ms ^-1

Zokambirana

Amadziwika kuti:

Liwiro loyambirira (v _o ) = 0

Kutalika koyambirira (h _o ) = 50 m – 10 m = 40 m

Kutalika komaliza (h _t ) = 0

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

Funso: Liwiro lomaliza (v _t )

Yankho:

Kusintha kwa mphamvu ya kinetic:

ΔEK = 1/2 m (v_t² -v_o²) = 1/2 m (v_t² - 0) = 1/2 mv_t²

Kusintha kwa mphamvu zomwe zingatheke:

Δ EP = mg (h _t – ho ₎ = m (10)(0-40) = m (10)(-40) = – 400 m

Werengerani liwiro lomaliza (v _t ) pogwiritsa ntchito njira ya lamulo losunga mphamvu zamakanika:

0 = Δ EK + Δ EP

0 = 1/2 mv _t ² - 400 m

1/2 mv _t ² = 400 m

1/2 v _t ² = 400

v _t ² = 2 (400)

v _t = √(400)(2)

v _t = 20√2 m/s

Yankho lolondola ndi D.

13. Mpira wolemera makilogalamu 1 umatulutsidwa ndipo umatsetsereka kuchokera pamalo A kupita pamalo C m'njira yosalala yokhota monga momwe chithunzi chili pansipa chikusonyezera. kuthamanga chifukwa cha mphamvu yokoka = 10 ms^-2, ndiye mphamvu ya kinetic (Ek) ya mpira ikafika pa mfundo C ndi….

A. majoule 25,0
B. 22,5 majoule
C. 20,0 majoule
D. 12,5 majoule
E. 7,5 majoule

Zokambirana
Amadziwika kuti:
Kulemera kwa mpira (m) = 1 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kusintha kwa kutalika (h) = 0,75 m

Mphamvu yokoka yoyambirira (EP)_o) = mgh = (1)(10)(0,75) = 7,5 Joules
Mphamvu yoyambirira ya kinetic (EK)_o) = ½ mv_o² = ½ m (0)²= = 0
Mphamvu yokoka yomaliza (EP)_t) = mgh = mg (0) = 0
Funso: Mphamvu ya kinetic (EK) ya mpira ikafika pa mfundo C
Yankho:

Lamulo losunga mphamvu ya makina limati mphamvu ya makina ya mpira pamalo ake oyamba ndi yofanana ndi mphamvu yake yomaliza ya makina pamalo ake omaliza. Mu vutoli, malo oyamba ndi malo a mpirawo usanatulutsidwe, ndipo malo omaliza ndi mfundo C.

Mphamvu yoyambirira yamakina (EM)_o) = Mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka yoyambirira (EP)_o) + Mphamvu yoyambira ya kinetic (EK)_o) = Mphamvu yokoka yomaliza (EP)_t) + Mphamvu yomaliza ya kinetic (EK)_t)
7,5 Joules + 0 = 0 + EK_t
7,5 Joules = EK_t
Mphamvu ya kinetic (EK) ya mpira pa mfundo C ndi 7,5 Joules.
Yankho lolondola ndi E.

14. Mpira A wolemera makilogalamu awiri umatulutsidwa ndipo umayenda m'njira yosalala monga momwe chithunzichi chikusonyezera. Ngati kuthamanga chifukwa cha mphamvu yokoka kuli 10 m/s^-2, mphamvu ya kinetic ya mpira pamene mu B ndi….

A. majoule 4
B. 8 majoule
C. 10 majoule
D. 12 majoule
E. 24 majoule

Zokambirana
Amadziwika kuti:
Kulemera kwa mpira (m) = 2 kg
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kusintha kwa kutalika (h) = 120 cm = 1,2 mamita

Mphamvu yokoka yoyambirira (EP)_o) = mgh = (2)(10)(1,2) = 24 Joules
Mphamvu yoyambirira ya kinetic (EK)_o) = ½ mv_o² = ½ m (0)²= = 0
Mphamvu yokoka yomaliza (EP)_t) = mgh = mg (0) = 0
Funso: Mphamvu ya kinetic ya mpira pa B
Yankho:
Mphamvu ya makina ya mpira pa mfundo A (mphamvu yoyamba ya makina) ndi yofanana ndi mphamvu ya makina ya mpira pa mfundo B (mphamvu yomaliza ya makina).

Mphamvu yoyambirira yamakina (EM)_o) = Mphamvu yomaliza yamakina (EM)_t)
Mphamvu yokoka yoyambirira (EP)_o) + Mphamvu yoyambira ya kinetic (EK)_o) = Mphamvu yokoka yomaliza (EP)_t) + Mphamvu yomaliza ya kinetic (EK)_t)
24 Joules + 0 = 0 + EK_t
EK_t = 24 Joule
Mphamvu ya kinetic (EK) ya mpira pa mfundo C ndi 24 Joules.
Yankho lolondola ndi E.

 

Lamulo la kusunga mphamvu zamakanika mu kayendedwe ka parabolic

15. Mpira wolemera makilogalamu 0,1 umakankhidwa pa liwiro la 10 m/s. Ngati ngodya yokwezeka ndi 30^o ndipo kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s² , dziwani (a) mphamvu yokoka ya mpira pamalo okwera kwambiri (b) malo okwera kwambiri kapena kutalika kwakukulu.
Zokambirana
Ndizodziwika kuti :
Kulemera kwa mpira (m) = 0,1 kg
Liwiro loyambirira (v)_o) = 10 m/s
Ngodya yokwezeka = 30^o
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa : mphamvu ya kinetic (EK) ya mpira pamalo okwera kwambiri
Yankhani :

(a) Mphamvu yokoka ya mpira pamalo okwera kwambiri
Njira ya mpira ndi parabola monga momwe chithunzi chili pansipa chikusonyezera.
Choyamba werengani gawo loyambirira la liwiro m'njira yopingasa (v_ox) ndi woyimirira (v_oy).
Ngati njira yoyendera ya parabolic ili ngati chithunzi pamwambapa, ndiye kuti kayendetsedwe kake kolunjika kapena kopingasa kamasanthulidwa motere. mayendedwe ofanana a mzere ndipo kayendetsedwe ka njira yolunjika kakusanthulidwa ngati kuyenda koyima mmwamba. Mu kuyenda kofanana kwa mzere, liwiro limakhala losasintha nthawi yonse yoyenda. Mosiyana ndi zimenezi, mu kuyenda kolunjika mmwamba, chinthucho chikafika kutalika kwake kwakukulu kapena pamalo apamwamba kwambiri, chimayima kwakanthawi chisanabwerere mmbuyo. Chifukwa chake, pamalo apamwamba kwambiri, liwiro lolunjika la chinthucho ndi zero, koma pamalo apamwamba kwambiri, chinthucho chimakhalabe ndi liwiro la v._ox.

Mphamvu yoyambirira yamakina
Mpira ukayamba kuyenda, kutalika kwake kumakhala kofanana ndi pansi kapena pansi (h = 0), kotero mphamvu yake yokoka ndi zero (h = 0, kotero EP = mgh = 0). Mosiyana ndi zimenezi, mpira ukayamba kuyenda, umakhala ndi liwiro loyambirira, kotero mphamvu yake ya kinetic ndi yapamwamba kwambiri. Chifukwa chake, mphamvu yoyamba ya makina ya mpira ndi mphamvu ya kinetic.
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu ya kinetic (EK)
EM_o = EK = ½ mv_o² = ½ (0,1)(10)² = ½ (0,1)(100) = ½ (10) = 5 Joule

Mphamvu yomaliza yamakina
Pambuyo poyambira kuyenda, kutalika kwa mpira kumawonjezeka, kotero mphamvu yake yokoka imawonjezeka. Ukafika kutalika kwake kwakukulu, mphamvu yake yokoka imafika pamtengo wake wapamwamba kwambiri. Nanga bwanji mphamvu ya kinetic ya mpira? Pamalo ake apamwamba kwambiri, liwiro loyima la mpira (voy) ndi zero, koma umakhalabe ndi liwiro lopingasa (vox).
Mphamvu ya kinetic pa kutalika kwakukulu :
EK = ½ mv_ox² = ½ (0,1)(5√3)² = ½ (0,1)((25)(3)) = ½ (0,1)(75) = 3,75 Ma Joule

Lamulo losunga mphamvu zamakanika:
Mphamvu yoyambirira yamakina (EM)_o) = mphamvu yomaliza yamakina (EM)_t)
EK = EP + EK
5 = EP + 3,75
EP = 5 – 3,75 = 1,25 Joules
Mphamvu yokoka yomwe imatha kufika pamlingo wapamwamba kwambiri ndi 1,25 Joules.
 
(b) Malo okwera kwambiri kapena kutalika kwakukulu
EP = mgh
1,25 = (0,1)(10) h
1,25 = ola
Kutalika kwakukulu ndi mamita 1,25.

16. Mpira wolemera makilogalamu 0,1 umaponyedwa mopingasa pa liwiro la 10 m/s kuchokera m'mphepete mwa nyumba ya mamita 10 kutalika. Ngati kuthamanga chifukwa cha mphamvu yokoka pamalo amenewo kuli 10 m/s², ndiye mphamvu ya kinetic ya mpira ikafika pansi ndi….
Zokambirana
Ndizodziwika kuti :
Kulemera kwa mpira (m) = 0,1 kg
Liwiro loyambirira (v)_o) = 10 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kusintha kwa kutalika (h) = 10 – 2 = mamita 8
Anafunsa : mphamvu ya kinetic ya mpira pamtunda wa mamita awiri
Yankhani :
Mpirawo ukakhala wautali mamita 10, umakhala ndi mphamvu yokoka. Mpirawo umayamba kuyenda utaponyedwa ndi liwiro loyambirira la 10 m/s, kotero umakhalanso ndi mphamvu yokoka. Chifukwa chake, mphamvu yoyambirira ya makina a mpirawo ndi mphamvu yokoka + mphamvu yokoka.
Mphamvu yoyambira yokoka (EP) = mgh = (0,1)(10)(10) = 10 Joules
Mphamvu yoyambirira ya kinetic (EK) = ½ mv_o² = ½ (0,1)(10)² = ½ (0,1)(100) = ½ (10) = 5 Joule

Pamene mpira ukutsika pansi, kutalika kwake kumachepa, motero kumachepetsa mphamvu yake yokoka. Ukafika pansi, kutalika kwake kumakhala kofanana ndi kutalika kwa nthaka (h = 0), kotero mphamvu yake yokoka ndi zero (h = 0, kotero EP = mgh = 0). Mphamvu zonse zokoka zimasanduka mphamvu ya kinetic.
Mphamvu yomaliza ya kinetic = mphamvu yoyambira yokoka + mphamvu yoyambira ya kinetic = 10 + 5 = 15 Joules