Nā pilikia i hoʻoponopono ʻia ma ke ʻano kumu

ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā

1. Hoʻopili ʻia kahi ikaika P i kekahi wēlau o kahi kaola me ka lōʻihi o 2 m. He aha ka nui o ka ikehuʻO ke axis o ka wili ma ke kiko A.

ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā 1 ʻIke ʻia:

Ikaika (F) = 10 N

Ka lōʻihi o AB (r_AB) = 2 mika

Ua kū pololei ka ikaika F i ke kukuna.

ʻO ka lima lever (l) =r_ABhewa 90^o= (2 mika)(1) = 2 mika

Makemake: ʻO ka torque e pili ana i ke axis o ka rotation

Lōlā:

ʻO ka torque:

τ = F l = (10 N)(2 m) = 20 N m

ʻO ka hōʻailona hoʻohui ma muli o ke kukuna hoʻohuli i ka ʻaoʻao ʻē aʻe o ka uaki.

2. Ka lōʻihi o kahi kaola He 2 m ʻo AB a ʻo ka nui o ka ikaika F he 10 N. He aha ka nui o ka torque? ʻO ke axis o ka wili ma ke kiko A.

ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā 2 ʻIke ʻia:

Ikaika (F) = 10 N

Ka lōʻihi o AB (r_AB) = 2 mika

ʻO ka lima lever (l) =r_ABhewa 60^o= (2 m)(0.5√3) = √3 m

Makemake: ʻO ka torque e pili ana i ke axis o ka rotation

Lōlā:

ʻO ka torque:

τ = F l = (10 N)(√3 m) = 10√3 N m

ʻO ka hōʻailona hoʻohui no ka mea ʻo ka ikaika F ke kumu o ke kukuna hoʻohuli i ka ʻaoʻao ʻē aʻe o ka uaki.

3. ʻO ka lōʻihi o kahi kaola he 2 m. ʻO ka nui o F₁ he 10 N a ʻo ka nui o F₂ he 15 N. E hoʻoholo i ka torque upena e pili ana i ke kikowaena o ke kaola.

ʻO ke koʻi o ka wili ma ke kikowaena o ke kukuna.

ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā 3 ʻIke ʻia:

Ikaika 1 (F₁) = 10 N

ka mamao ma waena o F₁ a me ke kikowaena o ke kukuna (r₁) = 1 mika

ʻO ka lima lever 1 (l₁) =r₁hewa 90^o= (1 mika)(1) = 1 mika

ʻO Force F₁ ua kū pololei i ke kaola.

Ikaika 2 (F₂) = 15 N

Ka mamao ma waena o F₂ a me ke kikowaena o ke kukuna (r₂) = 1 mika

ʻO Force F₂ ua kū pololei i ke kaola.

ʻO ka lima lever 2 (l₂) =r₁hewa 90^o= (1 mika)(1) = 1 mika

Makemake ʻia: Tka torque upena e pili ana i ke axis o ka wili

Lōlā:

ʻO ka torque 1:

τ₁ =F₁ l₁ = (10 N)(1 m) = 10 N m

ʻO ka hōʻailona hoʻohui ma muli o ka ikaika o F₁ke kumu o ke kukuna hoʻohuli i ka ʻaoʻao ʻē aʻe o ka uaki.

ʻO ka torque 2:

τ₂ =F₂ l₂= (15 N)(1 m) = -15 N

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika F₂ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque upena:

Στ = τ₁– τ₂= 10 – 15 = – 5 N m

ʻO ka hōʻailona minus no ka mea ʻo ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

4. ʻO ka lōʻihi o ke kaola AB 2 m, Ka nui o F₁ he 10 N a ʻo ka nui o F₂is 10 N. E hoʻoholo i ka torque upena e pili ana i ke kikowaena o ke kaola.

ʻO ke koʻi o ka wili ma ke kikowaena o ke kukuna.

ʻIke ʻia:

Ikaika 1 (F₁) = 10 Nn

Ka mamao ma waena o F₁ a me ke kikowaena o ke kukuna (r₁) = 1 mika

ʻO ka lima lever 1 (l₁) =r₁hewa 60^o= (1 m)(0.5√3) = 0.5√3 m

Ikaika 2 (F₂) = 10 N

Ka mamao ma waena o F₂ a me ke kikowaena o ke kukuna (r₂) = 1 mika

ʻO Force F₂ ua kū pololei i ke kaola.

ʻO ka lima lever 2 (l₂) = r₂hewa 90^o= (1 mika)(1) = 1 mika

Makemake ʻia: ʻO ka torque upena e pili ana i ke axis o ka wili

Lōlā:

ʻO ka torque 1:

τ₁ =F₁ l₁ = (10 N)(0.5√3 m) = 5√3 = 8.7 Nm

ʻO ka hōʻailona hoʻohui no ka mea ʻo ka ikaika F₁ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque 2:

τ₂ =F₂ l₂= (10 N)(1 m) = -10 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika F₂ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque upena:

Στ = τ₁– τ₂= 8.7 – 10 = – 1.3 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika upena ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

5. ʻO ka lōʻihi o ke kaola he 10 m, ʻo ka nui o F₁he 10 N, ka nui o F₂ he 10 N a ʻo ka nui o F₃ he 15 N. ʻO ka mamao ma waena o ke kiko A a me ke kiko C he 7.5 m. ʻO ka ikaika F₂ aia ma ke kikowaena o ke kukuna. E hoʻoholo i ka torque net e pili ana i ke kiko C aia ma 2.5 m mai ke kiko B.

Aia ke axis o ka wili ma ke kiko C

ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā 5 ʻIke ʻia:

Ikaika 1 (F₁) = 10 N

Ka mamao ma waena o F₁ a me ke kiko C (r₁) = 2.5 m

ʻO Force F₁ ua kū pololei i ke kaola.

ʻO ka lima lever 1 (l₁) =r₁hewa 90^o= (2.5 m)(1) = 2.5 m

Ikaika 2 (F₂) = 10 N

Ka mamao ma waena o F₂ a me ke kiko C (r₂) = 2.5 m

ʻO ka ikaika F₂ ua kū pololei i ke kaola.

ʻO ka lima lever 2 (l₂) = r₂hewa 90^o= (2.5 m)(1) = 2.5 m

Ikaika 3 (F₃) = 15 N

Ka mamao ma waena o F₃ a kuhikuhi C (r₃) = 7.5 mika

ʻO ka ikaika F₃ ua kū pololei i ke kaola.

ʻO ka lima lever 3 (l₃) = r₃ hewa 90^o= (7.5 mika)(1) = 7.5 mika

Makemake ʻia: ʻO ka torque upena e pili ana i ke axis o ka wili

Lōlā:

ʻO ka torque 1:

τ₁ =F₁ l₁ = (10 N)(2.5 m) = 25 N m

ʻO ka hōʻailona hoʻohui no ka mea ʻo ka ikaika F₁ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque 2:

τ₂ =F₂ l₂= (10 N)(2.5 m) = 25 N m

Tka hōʻailona hoʻohui no ka mea ʻo ka ikaika F₂ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque 3:

τ₃ =F₃ l₃ = (15 N)(7.5 m) = -112..5 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika F₃ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque upena:

Στ = τ₁+ τ₂– τ₃= 25 + 25 - 112.5 = – 62.5 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika upena ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

6. ʻO ka lōʻihi o ke kaola he 10 m, ʻo ka nui o F₁ he 10 N, ka nui o F₂ he 10 N a ʻo ka nui o F₃ he 10 N. E hoʻoholo i ka torque net e pili ana i ke kiko A, aia ma 5 m mai ke kikowaena ʻO ka nui o ka torque net - nā pilikia a me nā hoʻonā 6 nt o ka hoʻopili ʻana o ka ikaika F₁.

ʻO ke axis o ka wili ma ke kiko A.

ʻIke ʻia:

Ikaika 1 (F₁) = 10 N

Ka mamao ma waena o F₁ a me ke kiko A (r₁) = 5 mika

ʻO ka lima lever 1 (l₁) =r₁hewa 60^o= (5 m)(0.5√3) = 2.5√3 m

Kaha 2 (F₂) = 10 N

Ka mamao ma waena o F₂ a me ke kiko A (r₂) = 0

ʻO ka ikaika F₂ ua kū pololei i ke kaola.

ʻO ka lima lever 2 (l₂) = r₂hewa 90^o= (0)(1) = 0

ʻO ka ikaika 3 (F₃) = 10 N

Ka mamao ma waena o F₃ a me ke kiko A (r₃) = 10 mika

ʻO ka lima lever 3 (l₃) = r₃hewa 30^o= (10 mika)(0.5) = 5 mika

Makemake ʻia: ka torque upena e pili ana i ke axis o ka wili

Lōlā:

ʻO ka torque 1:

τ₁ =F₁ l₁ = (10 N)(2.5√3 mika) = 25√3 = 43.3 N m

ʻO ka hōʻailona hoʻohui no ka mea ʻo ka ikaika F₁ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque 2:

τ₂ =F₂ l₂= (10 N)(0) = 0

ʻO ka torque 3:

τ₃ =F₃ l₃ = (10 N)(5 m) = -50 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika F₃ ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

ʻO ka torque upena:

Στ = τ₁+ τ₂– τ₃= 43.3 + 0 - 50 = – 6.7 N m

ʻO ka hōʻailona minus no ka mea ʻo ka ikaika upena ke kumu o ke kukuna i hoʻohuli i ka ʻaoʻao ʻākau.

heluhelu hou

Nā kuʻi ʻana inelastic hapa ma ke ana hoʻokahi - nā pilikia a me nā hoʻonā

1. A 500-grhe mea, ʻo A, e neʻe ana ma 10 m / s a me ka mea 200-gram, B, e neʻe ana ma 12 m/s. Hoʻokokoke nā mea kekahi i kekahi a kuʻi. Inā ʻo ka wikiwiki o ka mea A ma hope o ka hookui ʻO 6 m/s ka wikiwiki, he aha ka wikiwiki o ka mea B ma hope o ke kuʻi ʻana?

ʻIke ʻia:

Ka Mass o ka mea 1 (m₁) = 500 grams = 0.5 kg

Ka Mass o ka mea 2 (m₂) = 200 grams = 0.2 kg

Hoʻomaka ka wikiwiki o ka mea 1 (v₁) = -10 m/s

Ka wikiwiki mua o ka mea 2 (v₂) = 12 m/s

ʻO ka wikiwiki hope loa o ka mea 1 (v₁') = 6 m/s

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

makemake : ka wikiwiki hope loa o ka mea 2 (v₂')

Lōlā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(0.5)(-10) + (0.2)(12) = (0.5)(6) + (0.2)(v₂')

-5 + 2.4 = 3 + 0.2 v₂'

-2.6 = 3 + 0.2 v₂'

-2.6 – 3 = 0.2 v₂'

-5.6 = 0.2 v₂'

v₂' = -5.6 / 0.2

v₂' = -28 m/s

ʻO ka wikiwiki o ka mea 2 ma hope o ke kuʻi ʻana he 28 m/s.

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

2. Hoʻokokoke nā mea ʻelua me ke kaumaha like kekahi i kekahi a kuʻi. ʻO ka wikiwiki o ka mea 1 he 6 m/s a ʻo ka wikiwiki o ka mea 2 he 8 m/s. Ma hope o ke kuʻi ʻana, neʻe ka mea 2 i ka hema me ka wikiwiki o 5 m/s. He aha ka nui a me ke kuhikuhi o ka wikiwiki o ka mea 1 ma hope o ka hookui?

ʻike:

Ka Mass o ka mea 1 (m₁) = m

Ka Mass o ka mea 2 (m₂) = m

Ka wikiwiki mua o ka mea 1 (v₁) = -6 m/s

ka wikiwiki mua o ka mea 2 (v₂) = 8 m/s

ʻO ka wikiwiki hope loa o ka mea 2 (v₂') = -5 m/s

makemake : ka nui a me ke kuhikuhi o ka mea 1 ma hope o ke kuʻi ʻana

Lōlā:

Haʻilula o ka mālama ʻana i ka momentum linear :

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

mv₁ +m v₂ = m v₁' + m v₂'

m (ʻiwi)₁ + i loko₂) = m (v₁' + v₂')

v₁ + i loko₂ = v₁' + v₂'

-6 + 8 = v₁' – 5

2 = v₁' – 5

2 + 5 = v₁'

v₁' = 7 m/s

Ka wikiwiki o ka mea 1 ma hope o ke kuʻi ʻana (v₁') is 3m/s.

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

3. He like ke kuhikuhi o ka pōpō 1-kg a me ka pōpō 2-kg a ua kuʻi like lāua me ke ʻano inelastic. Ma mua o ke kuʻi ʻana, neʻe ka pōpō 1 me ka wikiwiki o 10 m/s a neʻe ka pōpō 2 me ka wikiwiki o 5 m/s. ʻO ka wikiwiki o ka pōpō 2 ma hope o ke kuʻi ʻana he 4 m/s. E hoʻoholo i ka wikiwiki o ka pōpō 1 ma hope o ke kuʻi ʻana.

ʻIke ʻia:

Ka Mass poepoe 1 (m₁) = 1 kg

Ka Mass poepoe 2 (m₂) = 2 kg

Ka wikiwiki o ka pōpō 1 (i loko₁) = 10 m/s

Ka wikiwiki o ka pōpō 2 (v₂) = 5 m/s

ʻO ka wikiwiki hope loa o ka pōpō 2 (v₂') = 4 m/s

Hōʻike ka hōʻailona hoʻohui o ka wikiwiki he like ke kuhikuhi o nā pōpō.

makemake : ka wikiwiki hope loa o ka pōpō 1 (v₁')

Lōlā:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(1)(10) + (2)(5) = (1)(v)₁') + (2)(4)

10 + 10 = v₁' + 8

20 – 8 = v₁'

v₁' = 12 m/s

ʻO ka wikiwiki o ka pōpō 1 ma hope o ke kuʻi ʻana 12m/s.

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heluhelu hou

Nā kuʻi ʻole inelastic ma hoʻokahi ana - nā pilikia a me nā hoʻonā

1. Ua kuʻi kahi pōkā 30-gram e neʻe ana ma 30 m/s me kahi poloka 1-kg i ka wā hoʻomaha. E hoʻoholo i ka wikiwiki o ka poloka inā paʻa ka pōkā a me ka poloka ma muli o ka hookui.

ʻIke ʻia:

Ka Mass o ka pōkā (m₁) = 30 grams = 0.03 kg

Ka Mass o ka poloka (m₂) = 1 kg

Ka wikiwiki mua o ka pōkā (v₁) = 30 m/s

ka wikiwiki mua o ka poloka (v₂) = 0 (poloka i ka hoʻomaha)

makemake : ka wikiwiki o ka pōkā a me ka poloka ma hope o ke kuʻi ʻana (ʻoiaʻiʻo)

Lōlā:

m₁v₁ +m₂ v₂ = (m₁ +m₂) v'

(0.03)(30) + (1)(0) = (0.03 + 1) v'

0.9 + 0 = 1.03 v'

0.9 = 1,03 v'

v' = 0.9 / 1,03

v' = 0.87 m/s

2. Pōpō biliard A me ke kaumaha he 2 kg e neʻe ana me ka wikiwiki v_A = 6 ms^-1kuʻi maka me ka pōpō B o ke kaumaha like. Inā he inelastic kūpono ke kuʻi ʻana, he aha ka wikiwiki o nā pōpō ʻelua ma hope o ke kuʻi ʻana.

ʻIke ʻia:

Nuipaʻa A (m_A) = 2 kg

Nuipaʻa B (m_B) = 2 kg

Ka wikiwiki mua o ka pōpō A (v_A) = -6 m/s

Ka wikiwiki mua o ka pōpō B (v_B) = 4 m/s

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

makemake: ka wikiwiki o nā pōpō ʻelua ma hope o ke kuʻi ʻana. (v')

Lōlā:

m_A v_A +m_B v_B = (m_A' + m_B) v'

(2)(-6) + (2)(4) = (2 + 2) v'

-12 + 8 = 4 v'

-4 = 4 v'

v' = -4 / 4

v' = -1 m/s

3. m₁ = 3 kg a m₂ = 4 kg e hoʻokokoke aku kekahi i kekahi ma ke ʻaoʻao ʻē aʻe me ka wikiwiki o v₁ = 10m/s a v₂ = 12 m/s. Inā he inelastic loa ke kuʻi ʻana, he aha ka wikiwiki o nā pōpō ʻelua ma hope o ke kuʻi ʻana.

ʻIke ʻia:

Ka Mass mea 1 (m₁) = 3 kg

Ka Mass mea 2 (m₂) = 4 kg

Ka wikiwiki o ka mea 1 (v₁) = -10 m/s

Ka wikiwiki o ka mea 2 (v₂) = 12 m/s

makemake : ka wikiwiki ma hope o ke kuʻi ʻana (ʻoiaʻiʻo)

Lōlā:

m₁ v₁ +m₂ v₂ = (m₁' + m₂) v'

(3)(-10) + (4)(12) = (3 + 4) v'

-30 + 48 = 7 v'

18 = 7 v'

v' = 18 / 7

v' = 2.6 m/s

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heluhelu hou

Nā kuʻi elastic kūpono i hoʻokahi ana - nā pilikia a me nā hoʻonā

1. He pōpō A he 200-kalama ka nui, e neʻe ana ma ka wikiwiki o 10 m/s e kuʻi ana i kahi pōpō B he 200-kalama ka nui, i ka wā hoʻomaha. He aha ka wikiwiki o ka pōpō A a me ka pōpō B ma hope o ka hookui?

ʻIke ʻia:

Ka Mass o ka pōpō A (m_A) = 200 grams = 0.2 kg

Ka nuipa o ka pōpō B (m_B) = 200 grams = 0.2 kg

Ka wikiwiki o ka pōpō A ma mua o ke kuʻi ʻana (v_A) = 10 m/s

Ka wikiwiki o ka pōpō B ma mua o ke kuʻi ʻana (v_B) = 0

Makemake: ka wikiwiki o ka pōpō A (v_A') a me ka wikiwiki o ka pōpō B (v_B') ma hope o kahi ulia

Lōlā:

v_A' = v_B= 0

v_B' = v_A= 10m/s

2. Hoʻokokoke nā mea ʻelua like ke kaumaha kekahi i kekahi, kuʻi a laila lele. ʻO ka wikiwiki o ke kaumaha A ma mua o ke kuʻi ʻana he 8 m/s a ʻo ka wikiwiki o ke kaumaha B ma mua o ke kuʻi ʻana he 12 m/s. He aha ka nui a me ke kuhikuhi o ka wikiwiki o ke kaumaha A a me ke kaumaha B ma hope o ke kuʻi ʻana!

ʻIke ʻia:

Nuipaʻa A (m_A) = m

Nuipaʻa B (m_B) = m

Ka wikiwiki o ke kaumaha A ma mua o ke kuʻi ʻana (v_A) = -8 m/s

Ka wikiwiki o ke kaumaha B ma mua o ke kuʻi ʻana (v_B) = 12 m/s

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

Makemake: ka nui a me ke kuhikuhi o ka wikiwiki o ka nuipa A (v_A') a me ka nuipa B (v_B') ma hope o kahi ulia

Lōlā:

I loko o kahi kuʻi elastic kūpono, inā like ka nui o nā mea a laila ʻo ka wikiwiki o A ma hope o ke kuʻi ʻana (v_A') = ka wikiwiki o B ma mua o ke kuʻi ʻana (v_B) a me ka wikiwiki o B ma hope o ke kuʻi ʻana (v_B') = ka wikiwiki o A ma mua o ke kuʻi ʻana (v_A).

Inā ma mua o ke kuʻi ʻana, neʻe ʻo A i ka ʻākau a neʻe ʻo B i ka hema, a laila, ma hope o ke kuʻi ʻana, neʻe ʻo A i ka hema a neʻe ʻo B i ka ʻākau.

Ua like ka nuipa o nā mea a me he elastic kūpono ke kuʻi ʻana no laila ua hoʻololi nā mea ʻelua i ka wikiwiki.

v_A' = -v_B= -12 m/s

v_B' = v_A= 8m/s

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

3. ʻO kahi mea 2-kg, ʻo A, e neʻe ana ma ka wikiwiki o 10 m/s e kuʻi ana i kahi pōpō 4-kg, ʻo B, e neʻe ana ma ka wikiwiki o 20 m/s. Inā he elastic kūpono ke kuʻi ʻana, he aha ka wikiwiki o ka mea A a me ka mea B ma hope o ke kuʻi ʻana?

ʻIke ʻia:

Nuipaʻa A (m_A) = 2 kg

Nuipaʻa B (m_B) = 4 kg

Ka wikiwiki o ka mea A ma mua o ke kuʻi ʻana (v_A) = 10 m/s

Ka wikiwiki o ka mea B ma mua o ke kuʻi ʻana (v_B) = 20 m/s

makemake : ka wikiwiki o ka mea A (v_A') a me ka wikiwiki o ka mea B (v_B') ma hope o ke kuʻi ʻana

pāʻoihana :

In kuʻi elastic kūpono, inā like ka nuipa o nā mea a hoʻokokoke kekahi i kekahi, ua helu ʻia ka wikiwiki o ka mea ma hope o ke kuʻi ʻana me ka hoʻohana ʻana i kēia haʻilula:

Nā kuʻi elastic kūpono i hoʻokahi ana - nā pilikia a me nā hoʻonā 1

Ka wikiwiki o ka mea A ma hope o ke kuʻi ʻana:

Nā kuʻi elastic kūpono i hoʻokahi ana - nā pilikia a me nā hoʻonā 2

4. Hoʻokuʻi kahi 100-gram e neʻe ana ma 20 m/s i kahi kuʻi elastic kūpono o ka paia. He aha ka nui a me ke kuhikuhi o ka wikiwiki o ka mea ma hope o ke kuʻi ʻana.

ʻIke ʻia:

Nuipaʻa (m_A) = 100 grams = 0.1 kg

Ka nui o ka pā (m_B) = palena ʻole

ʻO ka wikiwiki o ka nuipa ma mua o ke kuʻi ʻana (v_A) = 20 m/s

ʻO ka wikiwiki o ke kaumaha ma hope o ke kuʻi ʻana (v_B) = 0

makemake : ka nui a me ke kuhikuhi o ka wikiwiki ma hope o ke kuʻi ʻana

Lōlā:

Inā v_B = 0, m_A liʻiliʻi loa a me m₂ nui loa ia ma mua o v_A' = -v_A a me v₂' = 0.

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

5. ʻElua mau pōpō, A me ka nui o 2 kg a me ka pōpō B me ka nui o 5-kg, Ua hōʻike ʻia ma ke kiʻi ma lalo nei nā ʻano ma mua a ma hope o ke kuʻi ʻana. Inā he elastic kūpono ke kuʻi ʻana, he aha ka wikiwiki o ka pōpō A ma mua o ke kuʻi ʻana?

ʻIke ʻia:

Ka nui o ka pōpō A (m_A) = 2 kg Kuʻi elastic kūpono - nā pilikia a me nā hoʻonā 1

Ka nui o ka pōpō B (m_B) = 5 kg

Ka wikiwiki o ka pōpō B ma mua o ke kuʻi ʻana (v_B) = 2 m/s

Ka wikiwiki o ka pōpō A ma hope o ke kuʻi ʻana (v_A') = 5 m/s

Ka wikiwiki o ka pōpō B ma hope o ke kuʻi ʻana (v_B') = 4 m/s

Ke neʻe nei nā pōpō ʻelua i ka ʻākau no laila ua hōʻailona ʻia ko lāua wikiwiki he maikaʻi.

Makemake ʻia: Ka wikiwiki o ka pōpō A ma mua o ke kuʻi ʻana (v_A)

Lōlā:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

2(ʻaoʻao)_A) + (5)(2) = (2)(5) + (5)(4)

2(ʻaoʻao)_A) + 10 = 10 + 20

2(ʻaoʻao)_A) + 10 = 30

2(ʻaoʻao)_A) = 30 – 10

2(ʻaoʻao)_A) = 20

v_A= 20 / 2

v_A = 10m/s

6. Hele nā mea A a me B ma ka ʻaoʻao o ka mokulele ʻākea, e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Inā he elastic kūpono ke kuʻi ʻana a ʻo ka wikiwiki o ka mea B ma hope o ke kuʻi ʻana he 15 m / s¹, he aha ka wikiwiki o ka mea A ma hope o ke kuʻi ʻana.

ʻIke ʻia:

Ka nui o ka mea A (m_A) = 5 kg Kuʻi elastic kūpono - nā pilikia a me nā hoʻonā 2

Ka nui o ka mea B (m_B) = 2 kg

Ka wikiwiki o ka mea A ma mua o ke kuʻi ʻana (v_A) = 12 m/s

Ka wikiwiki o ka mea B ma mua o ke kuʻi ʻana (v_B) = 10 m/s

Ka wikiwiki o ka mea B ma hope o ke kuʻi ʻana (v_B') = 15 m/s

Neʻe nā mea ʻelua, ma mua a ma hope o ke kuʻi ʻana, i ka ʻākau no laila ua hōʻailona ko lākou wikiwiki i ka maikaʻi.

Makemake ʻia: Ka wikiwiki o ka mea A ma hope o ke kuʻi ʻana (v_A')

Lōlā:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

(5)(12) + (2)(10) = (5)v_A' + (2)(15)

60 + 20 = (5)v_A' + 30

80 = (5)v_A' + 30

80 – 30 = (5)v_A'

50 = (5)v_A'

v_A' = 50/5

v_A' = 10 m/s

[wpdm_package id='1156′]

heluhelu hou

Ka ikaika a me ka impulse - nā pilikia a me nā hoʻonā

1. Ua kiola ʻia kahi pōpō liʻiliʻi me ka wikiwiki mau o 10 m/s. Paʻi ka pōpō i ka paia a hōʻike me ka wikiwiki like. He aha ka loli o ka ikaika laina o ka pōpō?

ʻIke ʻia:

Ka Mass (m) = 0.2 kg

Ka wikiwiki mua (v_o) = -10 m/s

Ka wikiwiki hope loa (v_t) = 10 m/s

Hōʻike nā hōʻailona hoʻohui a me ka hoʻēmi e neʻe ana nā mea i ka ʻaoʻao ʻē aʻe.

makemake : ka loli o ka momentum linear (Δp)

Lōlā:

ʻO ke ʻano o ka loli o ka momentum linear :

Δp = mv_t – mv_o= m (v_t - v_o)

Ka loli o ka momentum linear:

Δp = 0.2 (10 – (-10)) = 0.2 (10 + 10)

Δp = 0.2 (20)

Δp = 4 kg m/s

2. He pōpō 10-kalama hāʻule manuahi mai kahi kiʻekiʻe, paʻi i ka papahele ma 15 m/s, a laila huli i luna ma 10 m/s. E hoʻoholo i ka impulse!

ʻIke ʻia:

Nuipaʻa (m) = 10 grams = 0.01 kg

Ka wikiwiki mua (v_o) = -15 m/s

Ka wikiwiki hope loa (v_t) = 10 m/s

Makemake ʻia: Pākuʻi (I)

Lōlā:

Ua like ka impulse (I) me ka loli o ka momentum (Δp)

ʻO wau = mv_t– mv_o = m (v_t - v_o)

Manaʻo wikiwiki:

ʻO I = 0.01 (10 – (-15)) = 0.01 (10 + 15)

ʻO wau = 0.01 (25)

ʻO I = 0.25 kg m/s

3. Ua kiola ʻia kahi pōpō 200-gram me ka wikiwiki o 4 m/s, a laila ua kuʻi ʻia ka pōpō ma ke kuhikuhi like. ʻO ka lōʻihi o ka hoʻopā ʻana o ka pōpō me ka ʻōpeʻapeʻa he 2 milellisekona a ʻo ka wikiwiki o ka pōpō ma hope o ka haʻalele ʻana i ka pā he 12 m/s. ʻO ka ka nui o ikaika hooikaika e ka mea hahau ma luna o ka pōpō he ...

ʻIke ʻia:

Nuipaʻa (m) = 200 grams = 0.2 kg

Ka wikiwiki mua (v_o) = 4 m/s

Ka wikiwiki hope loa (v_t) = 12 m/s

Ka manawa manawa (t) = 2 milisekona = (2/1000) kekona = 0.002 kekona

makemake : Ka nui o ka ikaika (F)

Lōlā:

Ke ʻano o ka impulse:

ʻO wau = Ft

Ke ʻano o ka loli o ka momentum:

mv_t – mv_o = m (v_t - v_o)

Ua like ka impulse (I) me ka loli o ka momentum (Δp)

ʻO I = Δp

Ft = m (v_t - v_o)

F (0.002) = (0.2)(12 – 4)

F (0.002) = (0.2)(8)

F (0.002) = 1.6

F = 1.6 / 0.002

F = 800 Newton

[wpdm_package id='1155′]

heluhelu hou

Ka momentum linear - nā pilikia a me nā hoʻonā

1. Hele kekahi mea ma kahi wikiwiki mau o 10 m/s. E helu i ka ka ikaika laina o ka mea.

Kaulana :

Ka Mass (m) = 1 kg

māmā holo (v) = 10 m/s

Makemake ʻia: ka momentum linear (p)

Lōlā:

ʻO ke ʻano o ka momentum linear:

p = mv

p = ka momentum linear, m = ka nuipa, v = ka wikiwiki

ʻO ka momentum linear:

p = mv = (1)(10) = 10 kg m/s²

2. Neʻe kahi poloka 2-kg a me kahi poloka 4-kg ma kahi wikiwiki mau 20 m/s. He aha ka momentum linear o nā poloka.

ʻIke ʻia:

Ka Mass o ka poloka A (m_A) = 2 kg

Ka Mass o ka poloka B (m_B) = 4 kg

Ka wikiwiki o ka poloka A (v_A) = 20 m/s

Ka wikiwiki o ka poloka B (v_B) = 20 m/s

Makemake ʻia: Ka momentum linear o ka poloka A (p_A) a me ka momentum linear o ka poloka B (p_B)

Lōlā:

Ka momentum linear o ka poloka A :

p_A = m_A v_A = (2)(20) = 40 kg m/s

Ka momentum linear o ka poloka B :

p_B = m_B v_B = (4)(20) = 80 kg m/s

3. Neʻe kahi poloka 2-kg ma kahi mau 2 m/s a neʻe kahi poloka 2-kg ma kahi mau 4 m/s. E hoʻoholo i ka momentum linear o nā poloka.

ʻIke ʻia:

Ka Mass o ka poloka A (m_A) = 2 kg

Ka nui o ka poloka B (m_B) = 2 kg

Ka wikiwiki o ka poloka A (v_A) = 2 m/s

Ka wikiwiki o ka poloka B (v_B) = 4 m/s

Makemake ʻia: ka momentum linear o nā poloka

Lōlā:

Linear mʻōmuku o ka poloka A :

p_A = m_A v_A = (2)(2) = 4 kg m/s

Ka momentum linear o ka poloka B:

p_B = m_B v_B = (2)(4) = 8 kg m/s

4. He mea 5-kg i ka wā hoʻomaha. He aha ka momentum linear o ka momentum.

ʻIke ʻia:

Nuipaʻa (m) = 5 kg

Ka wikiwiki o ka mea (v) = 0

makemake : ka momentum linear (p)

Lōlā:

p = mv = (5)(0) = 0

[wpdm_package id='1155′]

heluhelu hou

Mana - nā pilikia a me nā hoʻonā

ʻO ka mana ka wikiwiki o ka hana ʻana i ka hana i loko o kahi manawa i hāʻawi ʻia. Ma ke ʻano makemakika, ʻo ka mana ka lakio hana/manawa.

P = W/t

Wehewehe: P = mana (Joule/kekona = Watt), W = hana (Joule), t = manawa (kekona)

Ma muli o kēia kaulike, hiki ke hoʻoholo ʻia ʻo ka nui o ka hana, ʻo ka nui o ka mana. Ma ka ʻaoʻao ʻē aʻe, ʻo ka liʻiliʻi o ka hana, ʻo ka liʻiliʻi o ka mana. ʻO ka hana e pili ana i ka hana.

He scalar ka mana. ʻO ke anakahi SI o ka mana ʻo Joule/kekona. ʻO ka Joule/kekona = Watt (i hoʻopōkole ʻia ʻo W), i kapa ʻia pēlā e hoʻohanohano iā James Watt. ʻO ke anakahi imperial Pelekane no ka mana he kapuaʻi-paona i kekona.

He liʻiliʻi loa kēia ʻāpana no nā hana pono, no laila ua hoʻohana ʻia ka ʻāpana horsepower nui aʻe (i hoʻopōkole ʻia e like me hp). Hoʻokahi horsepower = 550 kapuaʻi-paona i kekona = 764 Watts = ¾ kilowatt.

Hiki ke hōʻike ʻia ka nui o ka hana ma nā anakahi mana x manawa, no ka laʻana, kilowatt-hola a i ʻole kWh. ʻO hoʻokahi kWh e pili ana i ka hana i hana ʻia ma ka wikiwiki mau o 1 kiloWatt no hoʻokahi hola.

1. He 50-kg holo ke kanaka i luna o ke alapiʻi he 10 mika ke kiʻekiʻe in 2 minuke. Ahoʻolalelale ma muli o ʻo ke kaumaha (g) he 10 m/s². E hoʻoholo i ka mana.

ʻIke ʻia:

Ka Mass (m) = 50 kg

kiʻekiʻe (h) = 10 mikalehua

ʻO ka wikiwiki ma muli o ka umekaumaha (g) = 10 m/s²

manawa wā mawaena (t) = 2 minuke = 2 (60) = 120 ka luas

makemake : mana (P)

Lōlā:

Haʻilula o ka mana:

P = W / t

P= mana, W = hana, t = manawa

Ke ʻano o ka hana:

W = Fs = wh = mgh

W= hana, F = ikaika, w = kaumaha, d = ka haʻalele, h = kiʻekiʻe, m = ka nuipaʻa, g = ka wikiwiki ma muli o ka umekaumaha

W = mgh = (50)(10)(10) = 5000 Joules.

P = W / t = 5000 / 120 = 41.7 Joule/second.

2. E helu i ka mana e pono ai no ke kanaka 60-kg e piʻi ana i kahi lāʻau he 5 mika ke kiʻekiʻe i loko o 10 kekona. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s².

ʻIke ʻia:

Nuipaʻa (m) = 60 kg

kiʻekiʻe (h) = 5 mikas

ʻO ka wikiwiki ma muli o ka umekaumaha (g) = 10 m/s²

manawa wā mawaena (t) = 10 kekona

makemake : mana

Lōlā:

Hana:

W = mgh = (60)(10)(5) = 3000 Joules

Kaha:

P = W / t = 3000 / 10 = 300 Joule/sekūlana

3. He keaka hoʻokani wili me ka mana o 300 watts a me ka manawa o 5 mau minuke e hoʻohuli ana i 5 mau puni. ʻO ka ikehu e hoʻohana ai….

A. 15 kJ

B. 75 kJ

C. 90 kJ

D. 450 kJ

ʻIke ʻia:

Mana (P) = 300 Watts = 300 Joules/kekona

Ka Wā (T) = 5 mau minuke = 5 (60 kekona) = 300 kekona

Helu o nā hoʻohuli = 5

Makemake: Ikehu i hoʻohana ʻia e ka ʻakaʻaka rotary

Lōlā:

Mana - nā pilikia a me nā hoʻonā

ʻO D ka pane pololei.

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heluhelu hou

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma ka mokulele inclined - nā pilikia a me nā hoʻonā

1. Heʻe iho kahi poloka ma luna o ka laumania mokulele hilig ole kū'ēHe aha nā poloka ka wikiwiki ke kuʻi i ka honua. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s²

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma ka mokulele inclined 1 ʻIke ʻia:

Kiʻekiʻe (h) = 8 m

ʻO ka wikiwiki ma muli o ka umekaumaha (g) = 10 m/s²

makemake : ka wikiwiki (v)

pāʻoihana :

Ikehu mīkini mua (ME)_o) = ikehu hiki ke hoʻopaʻa ʻia (PE)

ME_o = PE = mgh = m (10)(8) = 80 m

Ikehu mīkini hope loa (ME_t) = ikehu kinetic (I)

ME_t = KE = ½ mv²

ʻŌlelo ke kumumanaʻo o ka mālama ʻana i ka ikehu mechanical ʻo ka mua ka ikaika mechanical = ka ikehu mechanical hope loa:

ME_o = ʻO wau_t

80 m = ½ mv²

80 = ½ v²

160 = v²

v = √160 = √(16)(10) = 4√10 m/s

2. Heʻe iho kahi mea 1-kg ma ke ʻano he 8 mika. E hoʻoholo i ka ikehu kinetic ma hope o ka neʻe ʻana o ka mea ma ke ʻano he 5 mika… Ka wikiwiki ma muli o ke koʻikoʻi g = 10 m/s²

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma ka mokulele inclined 2 ʻIke ʻia:

Nuipaʻa (m) = 0.2 kg

d = 5 mika

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

makemake : ikehu kinetic (KE)

Lōlā:

hewa 30^o = h / d

0.5 = h / 5

h = (0.5)(5) = 2.5 mika

ʻO ka loli o ke kiʻekiʻe o ka mea he 2.5 mika.

ʻO ka ikehu mechanical mua (ME_o) = ka ikehu hiki ke hoʻonui ʻia ke kaumaha (PE)

ME_o = PE = mgh = (1)(10)(2.5) = 25 Joules

ʻO ka ikehu mechanical hope loa (ME_t) = ikehu kinetic (KE)

ME_t = I

Ke kumu o ka mālama ʻana i ka ikehu mīkini ʻōlelo ʻia ʻo ka ikehu mechanical mua = ka ikehu mechanical hope loa:

ME_o = ʻO wau_t

25 = KE

ʻO ka ikehu kinetic = 25 Joule.

[wpdm_package id='1170′]

heluhelu hou

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma nā ʻili piʻo - nā pilikia a me nā hoʻonā

1. Heʻe iho kahi poloka 1-kg ma luna o ka ʻili laumania a piʻo. E hoʻoholo i ka ikehu kinetic a me ka wikiwiki o ka poloka ma ka ʻili haʻahaʻa loa. ʻO ka wikiwiki ma muli o ka umekaumaha he 10 m/s².

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma ka ʻili piʻo 1 ʻIke ʻia:

Ka Mass (m) = 1 kg

ʻO ka loli o ke kiʻekiʻe (h) = 5 m

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Makemake: Ikehu kinetic (KE) a me ka ka wikiwiki o ka poloka.

Lōlā:

(a) Ikehu kinetic

ka loiloi mua ka ikaika mechanical = ikehu hiki ke hoʻopaʻa ʻia

ME_o = PE = mgh = (1)(10)(5) = 50 Joules

ʻO ka ikehu mechanical hope loa = ikehu kinetic

ME_t = KE = ½ mv_t²

Kumuhana o ka mālama ʻana i ka ikehu mīkini ʻōlelo ʻia ʻo ka ikehu mechanical mua = ka ikehu mechanical hope loa:

ME_o = ʻO wau_t

PE = KE

50 = KE

ʻO ka ikehu kinetic (KE) = 50 Joules.

(b) Ka wikiwiki o ka poloka

ʻO ke kumumanaʻo o ka mālama ʻana i ka ikehu mechanical:

ʻO ka ikehu mechanical mua (ME_o) = ka ikehu mechanical hope loa (ME_t)

ʻO ka ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha (PE) = ikehu kinetic (KE)

50 = ½ mv²

2(50) / m = v²

100 / 1 = v²

100 = v²

v = √100

v = 10 m/s

2. Heheʻe iho kahi mea 2-kg me ka ʻole o ka friction. He aha ka ikehu kinetic a me ka wikiwiki o ka mea ma 2 mika ma luna o ka honua. ʻO ka wikiwiki ma muli o ke umekaumaha he 10 m/s²

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana ma ka ʻili piʻo 2 ʻIke ʻia:

Nuipaʻa (m) = 2 kg

ʻO ka loli o ke kiʻekiʻe (h) = 10 – 2 = 8 m

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

makemake : ikehu kinetic (KE) a me ka wikiwiki (v) ma 2 mika ma luna o ka honua.

Lōlā:

(a) Ikehu kinetic ma 2 mika ma luna o ka honua

ʻO ka ikehu mechanical mua = ka ikehu hiki ke hoʻopaʻa ʻia

ME_o = PE = mgh = (2)(10)(8) = 160 Joules

ʻO ka ikehu mechanical hope loa = ikehu kinetic

ME_t = KE = ½ mv_t²

ʻO ke kumumanaʻo o ka mālama ʻana i ka ikehu mechanical e ʻōlelo ana ʻo ka ikehu mechanical mua = ka ikehu mechanical hope loa:

ME_o = ʻO wau_t

PE = KE

160 = KE

ʻO ka ikehu kinetic (KE) ma 2 mika ma luna o ka honua he 160 Joules.

(b) Ka wikiwiki o ka mea ma ka ʻili haʻahaʻa loa

Kumumanaʻo o ka mālama ʻana i ka ikehu mechanical:

ʻO ka ikehu mechanical mua (ME_o) = ka ikehu mechanical hope loa (EM_t)

ʻO ka ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha (PE) = ikehu kinetic (KE)

160 = ½ mv²

160 = ½ (2) v²

160 = v²

v = √160 = √(16)(10) = 4√10 m/s

[wpdm_package id='1167′]

heluhelu hou

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana o ka projectile - nā pilikia a me nā hoʻonā

1. Ua haʻalele kahi pōpeku i kīkē ʻia i ka honua ma kahi kihi θ = 30^ome ka wikiwiki mua o 10 m/s. ʻO ka pōpō nuipa = 0.1 kg. ʻO ka wikiwiki ma muli o ka umekaumaha ʻo 1 kēia0 m / s². E hoʻoholo (a) i ka ikehu hiki ke hoʻopaʻa ʻia ma ke kiko kiʻekiʻe loa (b) Ke kiko kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa

ʻIke ʻia:

Nuipaʻa (m) = 0.1 kg

ʻO ka wikiwiki mua (v_o) = 10 m/s

Kihi = 30^o

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Lōlā:

(a) Ka ikehu hiki ke hoʻopaʻa ʻia

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana o ka projectile - nā pilikia a me nā hoʻonā 1

E helu i ka ʻāpana pae (v_ox) a me ka ʻāpana kū pololei (v_oy) o ka wikiwiki mua.

Ka hoʻohana ʻana i ka mālama ʻana i ka ikehu mechanical no ka neʻe ʻana o ka projectile - nā pilikia a me nā hoʻonā 2 v_ox= v_o hele θ = (10)(cos 30^o) = (10)(0.5√3) = 5√3 m/s

v_oy= v_o hewa θ = (10)(hewa 30^o) = (10)(0.5) = 5 m/s

ʻO ka ikehu mechanical mua

ka loiloi mua ka ikaika mechanical (ʻO wau_o) = ikehu kinetic (I)

ME_o= KE = ½ mv_o² = ½ (0.1)(10)² = ½ (0.1)(100) = ½ (10) = 5 Joules

ʻO ka ikehu mīkini hope loa

Ka ikehu kinetic ma ke kiko kiʻekiʻe loa:

KE = ½ mv_ox² = ½ (0.1)(5√3)²= ½ (0.1)((25)(3)) = ½ (0.1)(75) = 3.75 Joules

Kumumanaʻo o ka mālama ʻana i ka ikehu mechanical

ʻO ka ikehu mechanical mua (ME_o) = ka ikehu mechanical hope loa (ME_t)

KE = PE + KE

5 = EP + 3.75

PE = 5 – 3.75 = 1.25 Joule

ʻO ka ikehu hiki ke umekaumaha ma kahi kiʻekiʻe loa he 1.25 Joules.

(b) Ke kiko kiʻekiʻe loa a i ʻole ke kiʻekiʻe loa

PE = mgh

1.25 = (0.1)(10) hola

1.25 = h

ʻO ke kiʻekiʻe loa he 1.25 mika.

2. He pōpō 0.1-kg i hoʻolele ʻia ma ka ʻaoʻao me ka wikiwiki mua v_o = 10 m/s mai kahi hale he 10 mika ke kiʻekiʻe. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s²E hoʻoholo i ka ikehu kinetic o ka pōpō ke pā i ka honua.

ʻIke ʻia:

Nuipaʻa (m) = 0.1 kg

Ka wikiwiki mua (v_o) = 10 m/s

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

ʻO ka loli o ke kiʻekiʻe (h) = 10 – 2 = 8 m

Makemake: ikehu kinetic ma 2 mika ma luna o ka honua

Lōlā:

ʻO ka ikehu hiki ke hoʻopaʻa ʻia (PE) = mgh = (0.1)(10)(10) = 10 Joules

ʻO ka ikehu kinetic mua (KE) = ½ mv_o²= ½ (0.1)(10)² = ½ (0.1)(100) = ½ (10) = 5 Joules

ʻO ka ikehu kinetic hope loa = ka ikehu hiki ke hoʻokuʻu ʻia ke kaumaha mua + ka ikehu kinetic mua = 10 + 5 = 15 Joules

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