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Practice Exercise 2.2 A balloon is rising vertically at 4.0 m/s. Wind is blowing from east to west at 3.0 m/s. Find the resultant velocity of the balloon. The parallelogram method may also be used to add more than two vectors. However, the process is tedious. The steps when adding more than two vectors using the parallelogram method are outlined below and demonstrated in Sample Problem 2.3. 1. 2. 3. 4. After drawing the resultant of the first two vectors, construct a second parallelogram using this resultant and the third vector as sides. Draw the diagonal of the parallelogram from the common point. This is now the new resultant. The process is continued until all vectors have been added. The magnitude of the final resultant is determined from the scale used. The direction is measured by a protractor. Sample Problem 2.3 A particle is being acted upon by the following forces: F₁ = 4.0 N, east; F₂ = 6.0 N, northeast; and F3 = 8.0 N, south. Find the resultant using the parallelogram method. You may add the forces according to the following grouping (F+F₂)+F₂. Solution: As shown in the figure, R₁ = F₁+F₂ while R₂ = R₁ +F₂. The resultant vector in the figure has nine scale units corresponding to 9 N. Using a protractor, the angle that the resultant makes with the horizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east. W F₂ 0 R₁ F₁ F₁+F₂ -E R₂ = (F₁+F₂) + F3 F3 scale: HIN S

Practice Exercise 2.2 A balloon is rising vertically at 4.0 m/s. Wind is blowing from east to west at 3.0 m/s. Find the resultant velocity of the balloon. The parallelogram method may also be used to add more than two vectors. However, the process is tedious. The steps when adding more than two vectors using the parallelogram method are outlined below and demonstrated in Sample Problem 2.3. 1. 2. 3. 4. After drawing the resultant of the first two vectors, construct a second parallelogram using this resultant and the third vector as sides. Draw the diagonal of the parallelogram from the common point. This is now the new resultant. The process is continued until all vectors have been added. The magnitude of the final resultant is determined from the scale used. The direction is measured by a protractor. Sample Problem 2.3 A particle is being acted upon by the following forces: F₁ = 4.0 N, east; F₂ = 6.0 N, northeast; and F3 = 8.0 N, south. Find the resultant using the parallelogram method. You may add the forces according to the following grouping (F+F₂)+F₂. Solution: As shown in the figure, R₁ = F₁+F₂ while R₂ = R₁ +F₂. The resultant vector in the figure has nine scale units corresponding to 9 N. Using a protractor, the angle that the resultant makes with the horizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east. W F₂ 0 R₁ F₁ F₁+F₂ -E R₂ = (F₁+F₂) + F3 F3 scale: HIN S

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Practice Exercise 2.2 ged A balloon is rising vertically at 4.0 m/s. Wind is blowing from east to west at 3.0 m/s. Find the resultant velocity of the balloon. The parallelogram method may also be used to add more than two vectors. However, the process is tedious. The steps when adding more than two vectors using the parallelogram method are outlined below and demonstrated in Sample Problem 2.3. al After drawing the resultant of the first two vectors, construct a second parallelogram using this resultant and the third vector as sides. 1. 2. Draw the diagonal of the parallelogram from the common point. This is now the new resultant. 3. The process is continued until all vectors have been added. 4. The magnitude of the final resultant is determined from the scale used. The direction is measured by a protractor. Sample Problem 2.3 N. A particle is being acted upon by the following forces: F = 4.0 N, east; F,= 6.0 N, northeast; and F = 8.0 N, south. Find the resultant using the parallelogram method. You may add the forces according to the following grouping (F +F,)+F, . F2 R= F, + F2 W R2 = (F, + F) + F, Solution: As shown in the figure, R, = F+F, while R, =R, +F, . The resultant vector in the figure has nine scale units corresponding to 9 N. Using a protractor, the angle that the resultant makes with the horizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east. F scale: H 1N
Transcribed Image Text:Practice Exercise 2.2 ged A balloon is rising vertically at 4.0 m/s. Wind is blowing from east to west at 3.0 m/s. Find the resultant velocity of the balloon. The parallelogram method may also be used to add more than two vectors. However, the process is tedious. The steps when adding more than two vectors using the parallelogram method are outlined below and demonstrated in Sample Problem 2.3. al After drawing the resultant of the first two vectors, construct a second parallelogram using this resultant and the third vector as sides. 1. 2. Draw the diagonal of the parallelogram from the common point. This is now the new resultant. 3. The process is continued until all vectors have been added. 4. The magnitude of the final resultant is determined from the scale used. The direction is measured by a protractor. Sample Problem 2.3 N. A particle is being acted upon by the following forces: F = 4.0 N, east; F,= 6.0 N, northeast; and F = 8.0 N, south. Find the resultant using the parallelogram method. You may add the forces according to the following grouping (F +F,)+F, . F2 R= F, + F2 W R2 = (F, + F) + F, Solution: As shown in the figure, R, = F+F, while R, =R, +F, . The resultant vector in the figure has nine scale units corresponding to 9 N. Using a protractor, the angle that the resultant makes with the horizontal axis is 25°. Thus, the resultant is 9 N, 25° south of east. F scale: H 1N
Proctice Exercise 2.3 Using the same forces in Sample Problem 2.3, find F+(F,+F). Compare your answer with the resultant obtained in Sample Problem 2.3. Polygon Method The polygon method is otherwise known as the tip-to-tail method. This method is more convenient than the parallelogram method when more than two vectors are to be added graphically. The following are the steps to be followed using the polygon method. 1. Represent each vector quantity by an arrow drawn to scale. Starting from the origin, draw the first vector on the rectangular coordinate system, accounting properly its direction. 2. Connect the tail of the second vector to the head of the first vector. Then, connect the tail of the third vector to the head of the second vector. You may continue drawing the vectors head to tail 3. until you draw the last vector to be added. The resultant will close the figure formed by connecting the vectors. This resultant is drawn from the tail of the first vector to the head of the last vector. 4. 5. Measure the length of the arrow representing the resultant. Determine the magnitude of the resultant from the scale used. 6. Use a protractor to determine the direction of the resultant. If there are only two vectors to added, the polygon that will be formed is a triangle. In this case, the polygon method is otherwise known as the triangle method.
Transcribed Image Text:Proctice Exercise 2.3 Using the same forces in Sample Problem 2.3, find F+(F,+F). Compare your answer with the resultant obtained in Sample Problem 2.3. Polygon Method The polygon method is otherwise known as the tip-to-tail method. This method is more convenient than the parallelogram method when more than two vectors are to be added graphically. The following are the steps to be followed using the polygon method. 1. Represent each vector quantity by an arrow drawn to scale. Starting from the origin, draw the first vector on the rectangular coordinate system, accounting properly its direction. 2. Connect the tail of the second vector to the head of the first vector. Then, connect the tail of the third vector to the head of the second vector. You may continue drawing the vectors head to tail 3. until you draw the last vector to be added. The resultant will close the figure formed by connecting the vectors. This resultant is drawn from the tail of the first vector to the head of the last vector. 4. 5. Measure the length of the arrow representing the resultant. Determine the magnitude of the resultant from the scale used. 6. Use a protractor to determine the direction of the resultant. If there are only two vectors to added, the polygon that will be formed is a triangle. In this case, the polygon method is otherwise known as the triangle method.
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