on the end of that string timeter scale, draw arro scale and draw each F the force. The directic sents. Using the head-i e two vectors. (Don't f

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)...
icon
Related questions
Question

Help!!! Same question help on second page

**Part 1: Graphical Method**

Suppose you had a force table. Obviously, you do not have one in front of you, but for the sake of the problem, pretend that you do. Hypothetically, place a pulley at the 0° mark on the force table and place a total of 120 g on the end of the string. Place a second pulley at the 90° mark and place a total of 80 g on the end of that string.

Using your graph paper, a protractor, and a centimeter scale, draw arrows to represent the forces F₁ and F₂ described above. Choose a scale and draw each force vector so that its length is proportional to the magnitude of the force. The direction of each arrow must be the same direction as the force it represents. Using the head-to-tail method, draw an arrow that represents the resultant of the two vectors. (Don't forget to record the scale you chose.)

From the length of the resultant vector R, determine its magnitude according to your scale. Using the protractor, determine the resultant vector's direction (angle). Record your results in the table below.

**Graphical Determination Table**

| Force         | Angle | Mass       |
|---------------|-------|------------|
| 1             | 0°    | 120g (0.120 kg) |
| 2             | 90°   | 80g (0.08 kg)   |
| Resultant     | 323°  | 144g       |
| Equilibrant   | 213°  | 144g       |

**Diagram Description:**

The diagram shows a graphical representation of the forces and their resultant on graph paper. It features:

- An arrow representing the 120g force oriented at 0°.
- An arrow representing the 80g force oriented at 90°.
- The resultant vector is drawn using the head-to-tail method.
- The equilibrant vector is also indicated, showing balancing direction and magnitude.
Transcribed Image Text:**Part 1: Graphical Method** Suppose you had a force table. Obviously, you do not have one in front of you, but for the sake of the problem, pretend that you do. Hypothetically, place a pulley at the 0° mark on the force table and place a total of 120 g on the end of the string. Place a second pulley at the 90° mark and place a total of 80 g on the end of that string. Using your graph paper, a protractor, and a centimeter scale, draw arrows to represent the forces F₁ and F₂ described above. Choose a scale and draw each force vector so that its length is proportional to the magnitude of the force. The direction of each arrow must be the same direction as the force it represents. Using the head-to-tail method, draw an arrow that represents the resultant of the two vectors. (Don't forget to record the scale you chose.) From the length of the resultant vector R, determine its magnitude according to your scale. Using the protractor, determine the resultant vector's direction (angle). Record your results in the table below. **Graphical Determination Table** | Force | Angle | Mass | |---------------|-------|------------| | 1 | 0° | 120g (0.120 kg) | | 2 | 90° | 80g (0.08 kg) | | Resultant | 323° | 144g | | Equilibrant | 213° | 144g | **Diagram Description:** The diagram shows a graphical representation of the forces and their resultant on graph paper. It features: - An arrow representing the 120g force oriented at 0°. - An arrow representing the 80g force oriented at 90°. - The resultant vector is drawn using the head-to-tail method. - The equilibrant vector is also indicated, showing balancing direction and magnitude.
**Instruction for Vector Component Analysis**

Using your calculator, determine the x and y components of F₁ and F₂. Remember that:
- \(F_x = F \cos \theta\) 
- \(F_y = F \sin \theta\)

Find the x and y components of the resultant from the sum of x and y components. Calculate the magnitude of the resultant force from the square root of \(R_x^2 + R_y^2\). Calculate the direction of the resultant force from \(\theta = \tan^{-1} (R_y/R_x)\).

*Does this result agree with the graphical method?*

---

**Component Determination Table**

| Vector | Magnitude | X-Component | Y-Component |
|--------|-----------|-------------|-------------|
| 1      |           |             |             |
| 2      |           |             |             |

\(R_x =\)  
\(R_y =\)  

Resultant \(R =\)  
\(\theta_R =\)  

---

Fill out the table with your calculated values for each vector's magnitude, and its respective x and y components. Then, determine the resultant force using the formulas provided.
Transcribed Image Text:**Instruction for Vector Component Analysis** Using your calculator, determine the x and y components of F₁ and F₂. Remember that: - \(F_x = F \cos \theta\) - \(F_y = F \sin \theta\) Find the x and y components of the resultant from the sum of x and y components. Calculate the magnitude of the resultant force from the square root of \(R_x^2 + R_y^2\). Calculate the direction of the resultant force from \(\theta = \tan^{-1} (R_y/R_x)\). *Does this result agree with the graphical method?* --- **Component Determination Table** | Vector | Magnitude | X-Component | Y-Component | |--------|-----------|-------------|-------------| | 1 | | | | | 2 | | | | \(R_x =\) \(R_y =\) Resultant \(R =\) \(\theta_R =\) --- Fill out the table with your calculated values for each vector's magnitude, and its respective x and y components. Then, determine the resultant force using the formulas provided.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON