Te tāpiri i ngā whārite mā te whakamahi i ngā wāhanga – ngā raruraru me ngā otinga

Te tāpiri i ngā whārite mā te whakamahi i ngā wāhanga – ngā raruraru me ngā otinga

1. E toru ngā whārite e whakaaturia ana i te pikitia i raro nei.

V₁ = 30

V2 = ₃₀

V ₃ = 40

He aha ngā hua o ngā whārite?

Mōhiotia:

V ₁ = 30, koki i waenganui i te V ₁ me te tuaka x = 30 ^o

V ₂ = 30, koki i waenganui i te V ₂ me te tuaka x = 30 ^o

V ₃ = 40, koki i waenganui i te V ₃ me te tuaka x = 0 ^o

E hiahiatia ana: Ngā huanga whārite

Rongoā:

Ngā wāhanga o ngā whārite :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. He kino nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x kino (ki te taha mauī).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau).

V _3y = (V ₃ )(sin 0 ^o ) = (40)(0) = 0

Ngā wāhanga o ngā whārite hua:

V _x = V _1x – V _2x + V _3x = 15√3 – 15√3 + 40 = 40

V _y = V _1y + V _2y + V _3y = 15 + 15 = 30

Ko te hua o te wetere :

2. E rua ngā kaha e tū poutū ana tetahi ki tetahi, ko F ₁ = 12 N me F ₂ = 5 N. He aha te hua o ngā kaha e rua?

Mōhiotia:

Te Kaha 1 (F ₁ ) = 12 Newton

Te Kaha 2 (F ₂ ) = 5 Newton

E hiahiatia ana: Ngā huanga whārite ( ΣF)

Rongoā:

ΣF ² = F ₁ ² + F ₂ ² = 12 ² + 5 ² = 144 + 25 = 169

ΣF = √ 169 = 13 Newton

3. E toru ngā pūwero,

V₁ = 30

V ₂ = 30

V3 = ₄₀

Tāutuhia ngā hua o ngā whārite.

Mōhiotia:

v ₁ = 30, ka hanga 30 ^o te taha o te tuaka x kino

v ₂ = 30, ka hanga 30 ^o ki te taha o te tuaka x pai

v ₃ = 40, ka hanga 0 ^o ki te taha o te tuaka x pai

E hiahiatia ana: Ngā huanga whārite

Rongoā:

Ngā wāhanga o ngā whārite:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Kōraro nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x kino (ki te taha mauī) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau). )

v _3y = v ₃ hara 0 ^o = (40)(0) = 0

Ngā wāhanga o ngā whārite hua:

v _x = – v _1x + v _2x + v _3x = -15 √ 3 + 15 √ 3 + 40 = 40

v _y = v _1y + v _2y + v _3y = 15 + 15 = 30

Ko te hua o te wetere:

4. He aha te hua o ngā whārite e toru e whakaaturia ana i te pikitia i raro nei :

Mōhiotia:

F₁ = 3 Ngā Newton, ana e 60^o mō te tuaka x pai

F ₂ = 3 Newton, ka hanga 0 ^o te taha o te tuaka x kino

F ₃ = 6 Newtons , ka hanga 60 ^° ki te taha o te tuaka-y kino

E hiahiatia ana: Te hua o te wetere

Rongoā:

Ngā wāhanga o ngā whārite:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Kōraro nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x kino (ki te taha mauī) )

F _2y = F ₂ hara 0 ^o = (3)(0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Kōraro nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y kino ( ki raro ) )

Ngā wāhanga o ngā whārite hua:

ΣF _x = F _1x – F _2x + F _3x = 1.5 N – 3 N + 3 N = 1.5 N

ΣF _y = F _1y + F _2y – F _3y = 1.5√3 N + 0 N – 3√3 N = -1.5√3 N

Ko te hua o te wetere:

5. E rua ngā kaha, ko F ₁ = 15 N me F 2 ₌ 9 N. Ko te koki i waenganui i ngā whārite e rua he 60°. He aha te hua o ngā whārite?

E hiahiatia ana:

Te Kaha 1 (F ₁ ) = 15 Newton

Te Kaha 2 (F ₂ ) = 9 Newton

Koki ( θ) = 60 ^o

E hiahiatia ana: Te hua o te wetere

Rongoā:

6. He aha te hua o ngā whārite e toru e whakaaturia ana i te pikitia i raro nei?

Mōhiotia:

F₁ = 20 Newton, koki i waenganui i a F₁ ā, ko te tuaka x = 0

F ₂ = 20 Newton, koki i waenganui i te F ₂ me te tuaka x = 60

F ₃ = 24 Newton, koki i waenganui i te F ₃ me te tuaka x = 60

E hiahiatia ana: Te hua o te wetere

Rongoā:

Ngā wāhanga o ngā whārite:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x pai (ki te taha matau )

F _1y = (F ₁ )(hara 0) = (20)(0) = 0

F _2x = (F ₂ )(cos 60) = (20)(0.5) = -10. He kino nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x kino (ki te taha mauī)

F _2y = (F ₂ )(sin 60) = (20)(0.5√3) = 10√3. He pai nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y pai (ki runga)

F _3x = (F ₃ )(cos 60) = (24)(0.5) = -12. He kino nā te mea e tohu ana tēnei wāhanga whārite i te tuaka x kino (ki te taha mauī)

F _3y = (F ₃ )(sin 60) = (24)(0.5√3) = -12√3. N kino nā te mea e tohu ana tēnei wāhanga whārite i te tuaka y kino ( ki raro )

Ngā wāhanga o ngā whārite hua:

F _x = F _1x – F _2x – F _3x = 20 – 10 – 12 = -2

F _y = F _1y + F _2y – F _3y = 0 + 10√3 – 12√3 = -2√3

Ko te hua o te wetere: