Ntxiv cov vectors siv cov khoom sib xyaw - teeb meem thiab kev daws teeb meem

Ntxiv cov vectors siv cov khoom sib xyaw - teeb meem thiab kev daws teeb meem

1. Peb lub vectors raws li qhia hauv daim duab hauv qab no.

V₁ = 30

V2 = ₃₀

V3 = ₄₀

Cov vectors uas tau los ntawm qhov no yog dab tsi.

Paub:

V ₁ = 30, lub kaum sab xis ntawm V ₁ thiab x axis = 30 ^o

V ₂ = 30, lub kaum sab xis ntawm V ₂ thiab x axis = 30 ^o

V ₃ = 40, lub kaum sab xis ntawm V ₃ thiab x axis = 0 ^o

Xav tau: Cov vectors tshwm sim

Tshuaj:

Cov khoom ntawm vectors :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. Zoo vim tias cov vector no taw tes raws txoj kab x zoo (sab xis).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. Tsis zoo vim tias qhov vector no taw tes raws txoj kab x tsis zoo (sab laug).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis).

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

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim :

2. Ob lub zog uas sib ncaj nraim rau ib leeg, F ₁ = 12 N thiab F ₂ = 5 N. Qhov tshwm sim ntawm ob lub zog yog dab tsi.

Paub:

Lub zog 1 (F1 ₎ = 12 Newton

Lub zog 2 (F2 ₎ = 5 Newton

Xav tau: Cov vectors tshwm sim ( ΣF)

Tshuaj:

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

ΣF = √ 169 = 13 Newton

3. Peb lub vectors,

V₁ = 30

V ₂ = 30

V3 = ₄₀

Txheeb xyuas cov vectors uas tau los.

Paub:

v ₁ = 30, ua rau 30 ^o nyob ib ncig ntawm qhov tsis zoo ntawm x axis

v ₂ = 30, ua rau 30 ^o nyob ib ncig ntawm lub x axis zoo

v ₃ = 40, ua rau 0 ^o nyob ib ncig ntawm lub x axis zoo

Xav tau: Cov vectors tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Tsis zoo vim tias cov vector no taw tes raws txoj kab x tsis zoo (sab laug) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis). )

v _3y = v ₃ sin 0 ^o = (40)(0) = 0

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim:

4. Qhov tshwm sim ntawm peb lub vectors raws li qhia hauv daim duab hauv qab no yog dab tsi :

Paub:

F₁ = 3 Newtons, ua 60^o txog qhov x axis zoo

F2 = 3 Newtons, ua rau 0 ^o nyob ib ncig ntawm qhov tsis zoo ntawm x _axis

F3 = ₆ Newtons , ua rau 60 ^o ncig lub y axis tsis zoo

Xav tau: Tus vector tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug) )

F _2y = F ₂ sin 0 ^o = (3)(0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Tsis zoo vim tias cov vector no taw tes raws txoj kab y tsis zoo ( downward ) )

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim:

5. Ob lub zog, F ₁ = 15 N thiab F 2 ₌ 9 N. Lub kaum sab xis ntawm ob lub vectors yog 60°. Qhov tshwm sim ntawm cov vectors yog dab tsi.

Xav tau:

Lub zog 1 (F ₁ ) = 15 Newton

Lub zog 2 (F2 ₎ = 9 Newton

Lub kaum sab xis ( θ) = 60 ^o

Xav tau: Tus vector tshwm sim

Tshuaj:

6. Qhov tshwm sim ntawm peb lub vectors raws li qhia hauv daim duab hauv qab no yog dab tsi?

Paub:

F₁ = 20 Newton, lub kaum sab xis ntawm F₁ thiab x axis = 0

F ₂ = 20 Newtons, lub kaum sab xis ntawm F ₂ thiab x axis = 60

F ₃ = 24 Newtons, lub kaum sab xis ntawm F ₃ thiab x axis = 60

Xav tau: Tus vector tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis )

F _1y = (F ₁ )(sin 0) = (20)(0) = 0

F _2x = (F ₂ )(cos 60) = (20)(0.5) = -10. Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug)

F _2y = (F ₂ )(sin 60) = (20)(0.5√3) = 10√3. Zoo vim tias cov vector no taw tes raws txoj kab y zoo (sab saud)

F _3x = (F ₃ )(cos 60) = (24)(0.5) = -12. Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug)

F _3y = (F ₃ )(sin 60) = (24)(0.5√3) = -12√3. N tsis zoo vim tias cov vector no taw tes raws txoj kab y tsis zoo ( downward )

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim: