ਕੰਪੋਨੈਂਟਸ ਦੀ ਵਰਤੋਂ ਕਰਕੇ ਵੈਕਟਰ ਜੋੜਨਾ - ਸਮੱਸਿਆਵਾਂ ਅਤੇ ਹੱਲ

ਕੰਪੋਨੈਂਟਸ ਦੀ ਵਰਤੋਂ ਕਰਕੇ ਵੈਕਟਰ ਜੋੜਨਾ - ਸਮੱਸਿਆਵਾਂ ਅਤੇ ਹੱਲ

1. Three vectors as shown in the figure below.

V₁ = 30

V₂ = 30

V₃ = 40

What is the resultant ਵੈਕਟਰ.

ਜਾਣਿਆ ਜਾਂਦਾ ਹੈ:

V₁ = 30, angle between V₁ and x axis = 30^o

V₂ = 30, angle between V₂ and x axis = 30^o

V₃ = 40, angle between V₃ and x axis = 0^o

ਲੋੜੀਂਦਾ: The resultant vectors

ਹੱਲ:

The components of vectors :

V_1x = (ਵੀ₁)(cos 30^o) = (30)(0.5√3) = 15√3. Positive because this vector component points along the positive x axis (rightward).

V_1y = (ਵੀ₁)(ਪਾਪ 30^o) = (30)(0.5) = 15. Positive because this vector component points along the positive y axis (upward).

V_2x = (ਵੀ₂)(cos 30^o) = (30)(0.5√3) = -15√3. Negative because this vector component points along the negative x axis (leftward).

V_2y = (ਵੀ₂)(ਪਾਪ 30^o) = (30)(0.5) = 15. Positive because this vector component points along the positive y axis (upward).

V_3x = (ਵੀ₃)(cos 0^o) = (40)(1) = 40. Positive because this vector component points along the positive x axis (rightward).

V_3y = (ਵੀ₃)(ਪਾਪ 0^o) = (40)(0) = 0

The components of the resultant vectors :

V_x V =_1x - ਵੀ_2x + ਵੀ_3x = 15√3 – 15√3 + 40 = 40

V_y V =_1y + ਵੀ_2y + ਵੀ_3y = 15 + 15 = 30

The resultant vector :

2. Two forces perpendicular each other, F₁ = 12 N ਅਤੇ F₂ = 5 N. What is the resultant of both forces.

ਜਾਣਿਆ ਜਾਂਦਾ ਹੈ:

ਫੋਰਸ 1 (F₁) = 12 ਨਿਊਟਨ

ਫੋਰਸ 2 (F₂) = 5 ਨਿਊਟਨ

ਲੋੜੀਂਦਾ: The resultant vectors (ΣF)

ਹੱਲ:

ΣF² = ਐਫ₁² + F₂² = 12² + 5² = 144 + 25 = 169

ΣF = √169 = 13 Newton

3. Three vectors,

V₁ = 30

V₂ = 30

V₃ = 40

Determine the resultant vectors.

ਜਾਣਿਆ ਜਾਂਦਾ ਹੈ:

v₁ = 30, ਬਣਾ ਦਿੰਦਾ ਹੈ 30^o about the negative x axis

v₂ = 30, ਬਣਾ ਦਿੰਦਾ ਹੈ 30^o about the positive x axis

v₃ = 40, ਬਣਾ ਦਿੰਦਾ ਹੈ 0^o about the positive x axis

ਲੋੜੀਂਦਾ: The resultant vectors

ਹੱਲ:

The components of vectors :

v_1x =v₁ ਕੋਸ 30^o = (30)(0.5)√3) = -15√3 (Negative because this vector component points along the negative x axis (leftward))

v_1y =v₁ ਪਾਪ 30^o = (30)(0.5) = 15 (Positive because this vector component points along the positive y axis (upward))

v_2x =v₂ ਕੋਸ 30^o = (30)(0.5)√3) = 15√3 (Positive because this vector component points along the positive x axis (rightward))

v_2y =v₂ ਪਾਪ 30^o = (30)(0.5) = 15 (Positive because this vector component points along the positive y axis (upward).)

v_3x =v₃ ਕੋਸ 0^o = (40)(1) = 40 (Positive because this vector component points along the positive x axis (rightward).)

v_3y =v₃ ਪਾਪ 0^o = (40)(0) = 0

The components of the resultant vectors :

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

ਨਤੀਜਾ ਵੈਕਟਰ:

4. What is the resultant of three vectors as shown in figure below :

ਜਾਣਿਆ ਜਾਂਦਾ ਹੈ:

F₁ = 3 Newton, ਬਣਾ ਦਿੰਦਾ ਹੈ 60^o about the positive x axis

F₂ = 3 Newton, ਬਣਾ ਦਿੰਦਾ ਹੈ 0^o about the negative x axis

F₃ = 6 Newton, makes 60^o about the negative y axis

ਲੋੜੀਂਦਾ: The resultant vector

ਹੱਲ:

The components of vectors :

F_1x = ਐਫ₁ ਕੋਸ 60^o = (3)(0.5) = 1.5 N (Positive because this vector component points along the positive x axis (rightward))

F_1y = ਐਫ₁ ਪਾਪ 60^o = (3)(0.5√3) = 1.5√3 N (Positive because this vector component points along the positive y axis (upward))

F_2x = ਐਫ₂ ਕੋਸ 0^o = (3)(1) = -3 N (Negative because this vector component points along the negative x axis (leftward))

F_2y = ਐਫ₂ ਪਾਪ 0^o = (3)(0) = 0

F_3x = ਐਫ₃ ਕੋਸ 60^o = (6)(0.5) = 3 N (Positive because this vector component points along the positive x axis (rightward))

F_3y = ਐਫ₃ ਪਾਪ 60^o = (6)(0.5√3) = -3√3 N (Negative because this vector component points along the negative y axis (ਥੱਲੇward))

The components of the resultant vectors :

ΣF_x = ਐਫ_1x - ਐਫ_2x + F_3x = 1.5 N – 3 N + 3 N = 1.5 N

ΣF_y = ਐਫ_1y + F_2y - ਐਫ_3y = 1.5√3 N + 0 N – 3√3 N = -1.5√3 N

ਨਤੀਜਾ ਵੈਕਟਰ:

5. Two forces, F₁ = 15 N ਅਤੇ F₂ = 9 N. The angle between both vectors is 60°. What is the resultant of vectors.

ਲੋੜੀਂਦਾ:

ਫੋਰਸ 1 (F₁) = 15 ਨਿਊਟਨ

ਫੋਰਸ 2 (F₂) = 9 ਨਿਊਟਨ

ਕੋਣ (θ) = 60^o

ਲੋੜੀਂਦਾ: The resultant vector

ਹੱਲ:

6. What is the resultant of three vectors as shown in the figure below?

ਜਾਣਿਆ ਜਾਂਦਾ ਹੈ:

F₁ = 20 Newton, angle between F₁ and x axis = 0

F₂ = 20 Newton, angle between F₂ and x axis = 60

F₃ = 24 Newton, angle between F₃ and x axis = 60

ਲੋੜੀਂਦਾ: The resultant vector

ਹੱਲ:

The components of vectors :

F_1x = (ਐਫ₁)(cos 0) = (20)(1) = 20. Positive because this vector component points along the positive x axis (rightward)

F_1y = (ਐਫ₁)(sin 0) = (20)(0) = 0

F_2x = (ਐਫ₂)(cos 60) = (20)(0.5) = -10. Negative because this vector component points along the negative x axis (leftward)

F_2y = (ਐਫ₂)(sin 60) = (20)(0.5√3) = 10√3. Positive because this vector component points along the positive y axis (upward)

F_3x = (ਐਫ₃)(cos 60) = (24)(0.5) = -12. Negative because this vector component points along the negative x axis (leftward)

F_3y = (ਐਫ₃)(sin 60) = (24)(0.5√3) = -12√3. Negative because this vector component points along the negative y axis (ਥੱਲੇward)

The components of the resultant vectors :

F_x = ਐਫ_1x - ਐਫ_2x - ਐਫ_3x = 20 – 10 – 12 = -2

F_y = ਐਫ_1y + F_2y - ਐਫ_3y = 0 + 10√3 – 12√3 = -2√3

ਨਤੀਜਾ ਵੈਕਟਰ: