### Physics Problem: Calculating Work DoneAn object of mass 2 kg is pulled by a constant force \( F = 4 \, \text{N} \) for a horizontal distance of 2 meters. Referring to the figure below, determine the work done along the positive x-axis. Assume friction is negligible.#### Figure Description:The figure shows a block on a horizontal surface being pulled by a force \( F \). The force \( F \) is applied at an angle of 30° above the horizontal axis.#### Choices:a. 9 Jb. 8 Jc. 5 Jd. 7 Je. 2 J### Solution:To find the work done, we use the formula for work:\[ W = F \cdot d \cdot \cos(\theta) \]Where:- \( F \) is the magnitude of the applied force (4 N)- \( d \) is the distance over which the force is applied (2 m)- \( \theta \) is the angle between the force and the direction of motion (30°)Substituting the given values:\[ W = 4 \, \text{N} \times 2 \, \text{m} \times \cos(30°) \]We know that:\[ \cos(30°) = \frac{\sqrt{3}}{2} \]Thus:\[ W = 4 \, \text{N} \times 2 \, \text{m} \times \frac{\sqrt{3}}{2} \]\[ W = 8 \, \text{N} \cdot \text{m} \times \frac{\sqrt{3}}{2} \]\[ W = 8 \times 0.866 \] (approximately, since \( \sqrt{3}/2 \approx 0.866 \))\[ W \approx 6.93 \text{ J} \]Round to the nearest integer:\[ W \approx 7 \text{ J} \]Therefore, the correct answer is:**d. 7 J**

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Description: ### Physics Problem: Calculating Work DoneAn object of mass 2 kg is pulled by a constant force \( F = 4 \, \text{N} \) for a horizontal distance of 2 meters. Referring to the figure below, determine the work done along the positive x-axis. Assume fr

Given data : Mass=m Force=F Angle with horizontal=θ Find : Work done

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An object of mass = 2 kg is pulled by a constant force F = 4 N for a horizontal distance of 2 m. (Refer to Figure below) What is the work done along the +x-axis? Neglect friction. 30° Oa.gJ b.8) O c. 5) O d.7) O O e. 21

An object of mass = 2 kg is pulled by a constant force F = 4 N for a horizontal distance of 2 m. (Refer to Figure below) What is the work done along the +x-axis? Neglect friction. 30° Oa.gJ b.8) O c. 5) O d.7) O O e. 21

College Physics

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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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### Physics Problem: Calculating Work Done

An object of mass 2 kg is pulled by a constant force \( F = 4 \, \text{N} \) for a horizontal distance of 2 meters. Referring to the figure below, determine the work done along the positive x-axis. Assume friction is negligible.

#### Figure Description:
The figure shows a block on a horizontal surface being pulled by a force \( F \). The force \( F \) is applied at an angle of 30° above the horizontal axis.

#### Choices:
a. 9 J

b. 8 J

c. 5 J

d. 7 J

e. 2 J

### Solution:
To find the work done, we use the formula for work:

\[ W = F \cdot d \cdot \cos(\theta) \]

Where:
- \( F \) is the magnitude of the applied force (4 N)
- \( d \) is the distance over which the force is applied (2 m)
- \( \theta \) is the angle between the force and the direction of motion (30°)

Substituting the given values:

\[ W = 4 \, \text{N} \times 2 \, \text{m} \times \cos(30°) \]

We know that:

\[ \cos(30°) = \frac{\sqrt{3}}{2} \]

Thus:

\[ W = 4 \, \text{N} \times 2 \, \text{m} \times \frac{\sqrt{3}}{2} \]

\[ W = 8 \, \text{N} \cdot \text{m} \times \frac{\sqrt{3}}{2} \]

\[ W = 8 \times 0.866 \] (approximately, since \( \sqrt{3}/2 \approx 0.866 \))

\[ W \approx 6.93 \text{ J} \]

Round to the nearest integer:

\[ W \approx 7 \text{ J} \]

Therefore, the correct answer is:

**d. 7 J**

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