Laʻana o nā nīnau Plane Inclined

9 mau laʻana o nā nīnau mokulele inclined

E aʻo i ka mea Nā kānāwai o Newton , ka ikaika maʻamau a hiki ka ikaika friction i mea e hoʻomaopopo maikaʻi ai i ke kūkākūkā ʻana ma kēia mea.

1. Ua hoʻokuʻu ʻia kahi poloka o 5 kg ma luna o kahi mokulele hilig laumania e like me ka mea i hōʻike ʻia ma ke kiʻi! (g = 10 ms ^-2 a me tg 37 ^o = 3/4). ʻO ka wikiwiki o ka poloka…

A. 4,5 ms^-2

B. 6,0 ms^-2

C. 7,5 ms^-2

D. 8,0 ms^-2

E. 10,0 ms^-2

Pahana

Ua ʻike ʻia:

m = 5 kg, g = 10 m/s²

w = mg = (5)(10) = 50 N

ka lōʻihi o ka ʻaoʻao lalo = 4

ka lōʻihi o ka ʻaoʻao kū pololei = 3

ʻOiai ʻo ka ʻaoʻao lalo = 4 a ʻo ka ʻaoʻao kū pololei = 3 a laila ʻo ka hypotenuse = 5. Hiki iā ʻoe ke hōʻoia iā ia me ka hoʻohana ʻana i ke ʻano Pythagorean.

Nīnau: ka wikiwiki o ka poloka (a)?

Pane:

ʻO ka ikaika e hoʻoneʻe ai i ka poloka he w_xHe laumania ka mokulele hilig no laila ʻaʻohe friction.

w_x = w hewa θ = (w)(ʻaoʻao kū / hypotenuse)

w_x = (50)(3/5)

w_x = 30 Newton

He aha ka wikiwiki (a) o ka poloka?

ΣF = ma

w_x = ma

30 = (5) a

a = 30 / 5

a = 6 m/s²

ʻO ka pane pololei ʻo B.

2. E nānā i ke kiʻi! Hoʻomaha mua kahi poloka, a laila huki ʻia i luna me ka ikaika F e kūlike ana me ka mokulele inclined. ʻO ke kaumaha o ka poloka he 8 kg, ʻo ke coefficient of friction he µ._s = 0,5 a me θ = 45^oI mea e neʻe ai ka poloka i luna, pono ka ikaika F….

A. 40 N

B. 60 N

C. 60√2 N

D. 80 N

E. 80√2 N

Pahana

Ua ʻike ʻia :

Ka helu kuʻi paʻa (µ)_s) = 0,5

Kihi (θ) = 45^o

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

Ka nuipa o ka poloka (m) = 8 kilokani

Kaumaha o ka poloka (w) = mg = (8 kg)(10 m/s)²) = 80 kg m/s² = 80 Newton

Ua nīnau ʻia : Ka nui o ka ikaika F i hiki ai i ka poloka ke neʻe i luna

Pane :

E neʻe i luna ka poloka ʻākau inā F ≥ w_x + f_s. 

ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :

w_x = w hewa θ = (80)(hala 45) = (80)(0,5√2) = 40√2

ʻO ka ʻāpana o ke koʻikoʻi kū pololei i ka mokulele i hoʻohuli ʻia :

w_y = w cos θ = (80)(cos 45) = (80)(0,5√2) = 40√2

Ka ikaika maʻamau :

N = w_y = 40√2

Ka ikaika kuʻi paʻa :

f_s = µ_s N = (0,5)(40√2) = 20√2

ʻO ka nui o ka ikaika F i hiki ai i ka poloka ke neʻe i luna :

F ≥ w_x + f_s

F ≥ 40√2 + 20√2

F ≥ 60√2 Newton

ʻO C ka pane pololei.

3.BUa kau ʻia kahi poloka me ke kaumaha o 8 kg ma luna o kahi mokulele hilig ʻino e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ka ikaika kūwaho liʻiliʻi e pono ai e pale i ka poloka mai ka paheʻe ʻana i lalo he… (sin 37^o = 0,6, cos 37^o = 0,8, g = 10 ms^-2, µ_k = 0,1)

A. 6,4 N

B. 4,6 N

C. 48,5 N

D. 54,4 N

E. 68,8 N

Pahana

Ua ʻike ʻia :

Ka nuipa o ka poloka (m) = 8 kg

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

Kaumaha o ka poloka (w) = mg = (8)(10) = 80 Newton

Hewa 37^o = 0,6

ʻO Cos 37^o = 0,8

Ka helu o ka haʻalulu kinetic (µ)_k) = 0,1

N = w_y = w cos 37^o = (80)(0,8) = 64 Newton

Ua nīnau ʻia : ʻO ka ikaika kūwaho liʻiliʻi loa (F) e paʻa ana i ke kaola i ʻole e paheʻe i lalo ke kaola

Pane :

ʻAʻole e paheʻe ka poloka i lalo inā F = w_x

ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :

w_x = w hewa θ = (80)(hala 37) = (80)(0,6) = 48

f_k = µ_k N = (0,1)(64) = 6,4

ʻO ka ikaika haʻahaʻa loa F i ʻole e paheʻe i lalo ka poloka :

F + f_k - w_x = 0

F = w_x - f_k = 48 – 6,4 = 41,6 Newton

4. Ua huki ʻia kahi mea me ke kaumaha he 5,0 kg e ke kaula i luna o kahi mokulele hilig ʻino e ka ikaika o 71 N (g = 10 m s ).^-2, hewa 37^o = 0,6, cos 37^o = 0,8). Inā ʻo ke koina o ka friction ma waena o ka mea a me ka mokulele he 0,4, ʻo ka wikiwiki i ʻike ʻia e ka mea…

A. 0,5 ms^-2

B. 2 ms^-2

C. 2,5 ms^-2

D. 3 ms^-2

E. 5 ms^-2

Pahana

Ua ʻike ʻia :

Ka nuipa o ka mea (m) = 5 kg

4. Nā Nīnau Hoʻokolohua Lahui no ke Kino SMA 2012/2013 SA 67 Helu 5

Ua huki ʻia kahi mea me ke kaumaha he 5,0 kg e ke kaula i luna o kahi mokulele hilig ʻino e ka ikaika o 71 N (g = 10 m s ).^-2, hewa 37^o = 0,6, cos 37^o = 0,8). Inā ʻo ke koina o ka friction ma waena o ka mea a me ka mokulele he 0,4, ʻo ka wikiwiki i ʻike ʻia e ka mea…

A. 0,5 ms^-2

B. 2 ms^-2

C. 2,5 ms^-2

D. 3 ms^-2

E. 5 ms^-2

Pahana

Ua ʻike ʻia :

Ka nuipa o ka mea (m) = 5 kg

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

Kaumaha o ka mea (w) = mg = (5)(10) = 50 Newtons

Ikaika F = 71 Newton

Hewa 37^o = 0,6

ʻO Cos 37^o = 0,8

Ka helu o ka haʻalulu = 0,4

Ua nīnau ʻia : Ka wikiwiki o ka mea (a)

Pane :

Ka Mana Hopena

E helu mua i ka hopena o ka ikaika e hana ana ma luna o ka mea.

ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :

w_x = w hewa θ = (50)(hala 37) = (50)(0,6) = 30

ʻO ka ʻāpana o ke koʻikoʻi kū pololei i ka mokulele i hoʻohuli ʻia :

w_y = w cos θ = (50)(cos 37) = (50)(0,8) = 40

Ka ikaika maʻamau :

N = w_y = 40

Ka ikaika kuʻi kinetic :

f_k = µ_k N = (0,4)(40) = 16

Ka hopena o ka ikaika e hana ana ma kahi mokulele i hoʻohaʻahaʻa ʻia:

ΣF = F – w_x - f_k = 71 – 30 – 16 = 25 Newtons

Ka wikiwiki ʻana o kahi mea

Ua helu ʻia ka wikiwiki o kahi mea me ka hoʻohana ʻana i ke ʻano kānāwai lua o Newton:

a = ∑F / m = 25 / 5 = 5 m/s²

ʻO ka pane pololei ʻo E.

5.
E nānā i ke kiʻi! Hoʻomaha mua kahi poloka, a laila huki ʻia me ka ikaika i luna F e kūlike ana me ka mokulele i hoʻohuli ʻiaʻO ke kaumaha o ka poloka he 8 kg, ʻo ke koina o ka friction he µ_s = 0,5 a me θ = 45^oI mea e neʻe ai ka poloka i luna, pono ka ikaika F….

A. 40 N
B. 60 N
C. 60√2 N
D. 80 N
E. 80√2 N

Pahana
Ua ʻike ʻia :
Ka helu hana ka haʻalulu paʻa (µ_s) = 0,5
Kihi (θ) = 45^o
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Ka nuipa o ka poloka (m) = 8 kilokani
Kaumaha o ka poloka (w) = mg = (8 kg)(10 m/s)²) = 80 kg m/s² = 80 Newton
Ua nīnau ʻia : Ka nui o ka ikaika F i hiki ai i ka poloka ke neʻe i luna
Pane :

E neʻe i luna ka poloka ʻākau inā F ≥ w_x + f_s.
ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :
w_x = w hewa θ = (80)(hala 45) = (80)(0,5√2) = 40√2
ʻO ka ʻāpana o ke koʻikoʻi kū pololei i ka mokulele i hoʻohuli ʻia :
w_y = w cos θ = (80)(cos 45) = (80)(0,5√2) = 40√2
Ka ikaika maʻamau :
N = w_y = 40√2
Ka ikaika kuʻi paʻa :
f_s = µ_s N = (0,5)(40√2) = 20√2
ʻO ka nui o ka ikaika F i hiki ai i ka poloka ke neʻe i luna :
F ≥ w_x + f_s
F ≥ 40√2 + 20√2
F ≥ 60√2 Newton
ʻO C ka pane pololei.

6.
Ua kau ʻia kahi poloka me ke kaumaha o 8 kg ma luna o kahi mokulele hilig ʻino e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ka ikaika kūwaho liʻiliʻi loa e pono ai e pale i ka poloka mai ka paheʻe ʻana i lalo he… (sin 37^o = 0,6, cos 37^o = 0,8, g = 10 ms^-2, µ_k = 0,1)

A. 6,4 N
B. 4,6 N
C. 48,5 N
D. 54,4 N
E. 68,8 N

Pahana
Ua ʻike ʻia :
Ka nuipa o ka poloka (m) = 8 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Kaumaha o ka poloka (w) = mg = (8)(10) = 80 Newton
Hewa 37^o = 0,6
ʻO Cos 37^o = 0,8
Ka helu o ka haʻalulu kinetic (µ)_k) = 0,1
Ua nīnau ʻia : ʻO ka ikaika kūwaho liʻiliʻi loa (F) e paʻa ana i ke kaola i ʻole e paheʻe i lalo ke kaola
Pane :
ʻAʻole e paheʻe ka poloka i lalo inā F = w_x
ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :
w_x = w hewa θ = (80)(hala 37) = (80)(0,6) = 48
f_k = µ_k N = (0,1)(64) = 6,4
ʻO ka ikaika haʻahaʻa loa F i ʻole e paheʻe i lalo ka poloka :
F + f_k - w_x = 0
F = w_x - f_k = 48 – 6,4 = 41,6 Newton

7.
Ua huki ʻia kahi mea me ke kaumaha he 5,0 kg e ke kaula i luna o kahi mokulele hilig ʻino e ka ikaika o 71 N (g = 10 m s ).^-2, hewa 37^o = 0,6, cos 37^o = 0,8). Inā ʻo ke koina o ka friction ma waena o ka mea a me ka mokulele he 0,4, ʻo ka wikiwiki i ʻike ʻia e ka mea…
A. 0,5 ms^-2
B. 2 ms^-2
C. 2,5 ms^-2
D. 3 ms^-2
E. 5 ms^-2
Pahana
Ua ʻike ʻia :
Ka nuipa o ka mea (m) = 5 kg
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²
Kaumaha o ka mea (w) = mg = (5)(10) = 50 Newtons
Ikaika F = 71 Newton
Hewa 37^o = 0,6
ʻO Cos 37^o = 0,8
Ka helu o ka haʻalulu = 0,4
Ua nīnau ʻia : Ka wikiwiki o ka mea (a)
Pane :
Ka Mana Hopena
E helu mua i ka hopena o ka ikaika e hana ana ma luna o ka mea.
ʻO ka ʻāpana o ke koʻikoʻi e kūlike ana me ka mokulele inclined :
w_x = w hewa θ = (50)(hala 37) = (50)(0,6) = 30
ʻO ka ʻāpana o ke koʻikoʻi kū pololei i ka mokulele i hoʻohuli ʻia :
w_y = w cos θ = (50)(cos 37) = (50)(0,8) = 40
Ka ikaika maʻamau :
N = w_y = 40
Ka ikaika kuʻi kinetic :
f_k = µ_k N = (0,4)(40) = 16
Ka hopena o ka ikaika e hana ana ma kahi mokulele i hoʻohaʻahaʻa ʻia:
∑F = F – w_x - f_k = 71 – 30 – 16 = 25 Newtons
Ka wikiwiki ʻana o kahi mea
Ua helu ʻia ka wikiwiki o kahi mea me ka hoʻohana ʻana i ke ʻano kānāwai lua o Newton:
a = ∑F / m = 25 / 5 = 5 m/s²
ʻO ka pane pololei ʻo E.

8. E nānā i ke kiʻi! Hoʻomaha mua kahi poloka, a laila huki ʻia me ka ikaika F i luna e kūlike ana me ka mokulele inclined. ʻO ke kaumaha o ka poloka he 2 kg, ʻo ke coefficient o ka friction static = 0,3 a ʻo ke kihi = 45^oI mea e neʻe ai ka poloka i luna, pono ka ikaika F… g = 10 m/s²

Pahana
Ua ʻike ʻia:
m = 2 kg, g = 10 m/s², = 45^o, μ_s = 0,3
Nīnau: I mea e neʻe pololei ai ka poloka i luna, pehea ka nui o ka ikaika F?
Pane:

ʻIke: F = ka ikaika tensile, w = ka ikaika umekaumaha, w_x = ʻāpana o ke kaumaha o ka poloka e kūlike ana i ka ʻili o ka mokulele i hoʻohuli ʻia, w_y = ʻāpana o ke kaumaha o ka poloka e kū pono ana i ka ʻili o ka mokulele i hoʻohuli ʻia, N = ikaika maʻamau, f_s = ka ikaika kuʻi paʻa.

Ma ka nīnau, ua ʻike ʻia ke koina o ka friction static, ʻo ia hoʻi, he ʻinoʻino ka ʻili o ka mokulele inclined i loaʻa ai kahi ikaika friction e kāohi ana i ka neʻe ʻana o ka poloka.
I mea e neʻe ai ka poloka i luna, pono e like ka ikaika F me w._x +f_sNeʻe ka mea i luna ke ʻoi aku ʻo F ma mua o w_x +f_s.

w = mg = (2)(10) = 20 Newtons
w_x = w sin 45^o = (20)(½ √2) = 10√2 Newtons
w_y = w cos 45^o = (20)(½√2) = 10√2 Newtons
N = w_y = 10√2
f_s = μ_s N = (0,3)(10√2) = 3√2 Newtons

I mea e neʻe ai ka poloka i luna a laila:
F = w_x +f_s = 10√2 + 3√2= 13√2 Nā Newton
ʻO C ka pane pololei.

9. Ua kau ʻia kahi mea me ke kaumaha o 2 kg ma luna o kahi mokulele hilig e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Inā ʻo ke koina o ka friction static ma waena o ka poloka a me ka mokulele hilig he 0,2√3 a me g = 10 ms^-2, a laila ʻo ka hopena o ka ikaika e hoʻoneʻe ai i ka mea he...

Pahana
Ua ʻike ʻia:
m = 2 kg, g = 10 m/s², = 30^o, μ_s = 0,2√3
Nīnau ʻia: ʻO ka hopena o ka ikaika e hoʻoneʻe ai i kahi mea?

Pane:

Hoʻopaʻa mau ka haʻalulu i ka neʻe ʻana o kahi mea, no laila ua hōʻike ʻia ke kuhikuhi o ka ikaika haʻalulu e kūʻē i ke kuhikuhi o ka neʻe ʻana o ka mea. Manaʻo ʻia e neʻe ana ka mea i lalo, no laila ua hōʻike ʻia ka ikaika haʻalulu e piʻi ana i luna. Manaʻo ʻia e neʻe ana ka mea i lalo no ka mea ʻaʻohe ikaika e huki ana iā ia i luna.
w = mg = (2)(10) = 20 Newtons
w_x = w sin 30^o = (20)( ½ ) = 10 Newton
w_y = w cos 30^o = (20)( ½ √3) = 10√3 Newtons
N = w_y = 10√3 Newton
f_s = μ_s N = (0,2√3)(10√3) = (2)(3) = 6 Newtons
ʻO ka hopena o ka ikaika e hoʻoneʻe ai i kahi mea:
F = w_x - f_s = 10 – 6 = 4 Newton
w_x ʻoi aku ma mua o f_s no laila neʻe ka mea i lalo, ma ke kuhikuhi o w_x.
ʻO A ka pane pololei.

Puna nīnau:

Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana