Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule. Fig. P2.1

Question

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Answer 1

Textbook Question

Chapter 2.1, Problem 2.1P

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Chapter 2.1, Problem 2.1P, Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of

Fig. P2.1

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

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Students have asked these similar questions

Q1/ A vertical, circular gate with water on one side as shown. Determine the total resultant force acting on the gate and the location of the center of pressure, use water specific weight 9.81 kN/m³ 1 m 4 m

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Answer 2

Textbook Question

Chapter 2.1, Problem 2.1P

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Chapter 2.1, Problem 2.1P, Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of

Fig. P2.1

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

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Answer 3

Textbook Question

Chapter 2.1, Problem 2.1P

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Chapter 2.1, Problem 2.1P, Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of

Fig. P2.1

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

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Answer 4

Textbook Question

Chapter 2.1, Problem 2.1P

Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of their resultant using (a) the parallelogram law, (b) the triangle rule.

Chapter 2.1, Problem 2.1P, Two forces are applied as shown to a hook. Determine graphically the magnitude and direction of

Fig. P2.1

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Answer 8

(a)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The magnitude and direction of the resultant force on the hook graphically using the parallelogram law.

Answer 13

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Answer 14

Explanation of Solution

Force is a vector and the addition of vectors can be done using parallelogram law. The parallelogram law of vector addition says that if a parallelogram is constructed using two vectors by taking them as the adjacent sides of the parallelogram by attaching them on the same point, then the diagonal passing through that point gives the sum of the two vectors.

The forces acting on the hook are taken as the adjacent sides of the parallelogram. The diagram is shown in figure 1. In the figure, α is the angle the diagonal makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 1

The length of the diagonal of the parallelogram gives the magnitude of the resultant vector and the angle the diagonal makes with the horizontal gives the direction.

Conclusion:

The length of the diagonal is measured to be 1,391 N and the value of α is found to be 47.8° .

Thus, the magnitude of the resultant force on the hook determined graphically using the parallelogram law is 1,391 N and it is at 47.8° with the horizontal.

Answer 15

(b)

Expert Solution

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The magnitude and direction of the resultant force on the hook graphically using the triangle rule.

Answer 20

Answer to Problem 2.1P

The magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.

Answer 21

Explanation of Solution

Force is a vector and one of the graphical methods to obtain the resultant of two vectors is triangle rule. The triangle rule says that the sum of two vectors can be found by arranging the vectors in tip-to-tail fashion and then connecting the tail of the first vector with the tip of the second.

The forces acting on the hook are arranged in tip-to-tail fashion by placing the tail of 900 N at the tip of 600 N. The diagram is shown in figure 2. In the figure, α is the angle the resultant makes with the horizontal and R is the resultant force.

Vector Mechanics for Engineers: Statics and Dynamics, Chapter 2.1, Problem 2.1P , additional homework tip 2

The length of the third side of the triangle formed gives the magnitude of the resultant force. The direction of the resultant force is specified by the angle the third side of the triangle makes with the horizontal.

Conclusion:

The length of the third side of the triangle is measured to be 1,391 N and the value of α is found to be 47.8°.

Thus, the magnitude of the resultant force on the hook determined graphically using the triangle rule is 1,391 N and it is at 47.8° with the horizontal.