# Vectors - Lab**Name:** **Lab Partner:** **Lab Partner:** **Date:** **Lab day & time:** ---**Question:** When an object is pushed several ways at once, what is the net effect?**Apparatus:** Grid paper, ruler, protractor---## Part L-1:Another way to use the parallelogram rule is to draw the forces in sequence, the tail of one force lying on the head of the other, as shown in Figure 3.**Example:** Suppose the sailboat we have been considering has an outboard motor. The boat is acted on by the forces of wind (\( W \)), lake current (\( C \)), and the current produced by the propeller (\( P \)). These forces are drawn head-to-tail in Figure 4B.### 1. Draw the resultant of the three forces. (Sketch this directly on Figure 4B.)---**Figure 4A:** Illustration showing three forces acting on a boat:- **\( W \):** Force of wind on the boat- **\( C \):** Lake current- **\( P \):** Current produced by the propeller**Figure 4B:** Diagram showing the three forces drawn head-to-tail:- The diagram illustrates the sequential drawing of forces. The head of one vector aligns with the tail of the next, visualizing the vector addition process.**Figure 3:** - This figure demonstrates drawing the forces head-to-tail. The resultant force can be drawn from the tail of the first force to the head of the second, creating a vector that combines all original forces.--- ### Force Vectors - Lesson 2#### Transcription:2. **Activity:** Use the head-to-tail method, as shown in the previous example, to find the resultant force acting on the box with three forces acting on it as shown below. Draw and label the head-to-tail solution and the resultant in the space next to the figure below. ![Diagram Showing Forces](#) (Three forces labeled as \( F_1, F_2, \) and \( F_3 \) act on a box.)#### Part L-2:Applying the parallelogram rule directly can become tedious, especially if more than two forces are involved. Fortunately, the parallelogram rule can be used indirectly to simplify these calculations, using the **method of components**.![Diagram: Decomposition of Force](#) **Figure 5:** \( F_x \) and \( F_y \) are the x and y components of a particular force. For this force, the x-component is negative and the y-component is positive.#### Notes on Components:- The **component** of a force in a given direction is the projection of that force onto a straight line in that direction.- A component is considered positive when the force is drawn with its tail at the coordinate origin, and the component lies along the positive direction of the axis. (See Figure 5)- By Pythagoras's theorem, the magnitude of a vector can be determined from its components: \[ \text{magnitude of } F = \sqrt{F_x^2 + F_y^2} \]#### 3. Activity:Fill in the below chart, specifying whether the three forces on the boat in Figure 4A have components that are positive, negative, or zero.| Force | East component | North component ||-------|----------------|-----------------|| W | | || P | | || C | | |*Last Revised 07/17/2015*

Answered: 1. Draw the resultant of the three…

1. Draw the resultant of the three forces. (Sketch this directly on Figure 4B.) Figure 4A: Three forces acting on a boat Figure 4B: The three forces drawn head-to-tail

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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Newton’s Third Law of Motion

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### Force Vectors - Lesson 2

#### Transcription:

2. **Activity:**
Use the head-to-tail method, as shown in the previous example, to find the resultant force acting on the box with three forces acting on it as shown below. Draw and label the head-to-tail solution and the resultant in the space next to the figure below.

![Diagram Showing Forces](#)
(Three forces labeled as \( F_1, F_2, \) and \( F_3 \) act on a box.)

#### Part L-2:

Applying the parallelogram rule directly can become tedious, especially if more than two forces are involved. Fortunately, the parallelogram rule can be used indirectly to simplify these calculations, using the **method of components**.

![Diagram: Decomposition of Force](#)
**Figure 5:** \( F_x \) and \( F_y \) are the x and y components of a particular force. For this force, the x-component is negative and the y-component is positive.

#### Notes on Components:

- The **component** of a force in a given direction is the projection of that force onto a straight line in that direction.
- A component is considered positive when the force is drawn with its tail at the coordinate origin, and the component lies along the positive direction of the axis. (See Figure 5)
- By Pythagoras's theorem, the magnitude of a vector can be determined from its components:

\[
\text{magnitude of } F = \sqrt{F_x^2 + F_y^2}
\]

#### 3. Activity:

Fill in the below chart, specifying whether the three forces on the boat in Figure 4A have components that are positive, negative, or zero.

| Force | East component | North component |
|-------|----------------|-----------------|
| W | | |
| P | | |
| C | | |

*Last Revised 07/17/2015*

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