What is the work done when a force vector
(
1
0
,

0
)
N moves an object
5
m in the direction of
(
6
,

8
)
?

give the calculation step by step as like as full answer in 2 steps and explanation blo

Question

What is the work done when a force vector
(
1
0
,

0
)
﻿N moves an object
5
﻿m in the direction of
(
6
,

8
)
?

give the calculation step by step as like as full answer in 2 steps and explanation block in every steps.
And final answer summary
Definition of Parameters
Solutions are reviewed by our quality team mainly based on 6 parameters: Relevancy, Completeness, Accuracy, Clarity, Structure, and Voice.
Relevancy: This indicates how closely a solution aligns with the question asked. It evaluates whether the solution addresses the core aspects of the question and provides appropriate information.
Completeness: This indicates how thoroughly the solution addresses various asks in the question. It evaluates whether the solution has all essential information like calculations, diagrams, procedural steps, & explanatory statements in the solution.
Accuracy: It refers to how correct the provided solution is for the given question/s. This evaluates the correctness of the information/concept/method followed in the solution.
Clarity: Clarity refers to how easily the solution can be understood by the student. This evaluates the language complexity, readability, and redundancy of a solution.
S

VIPSolutions · Accepted Answer

**Definition of Parameters**

- **Force Vector:** $ \vec{F} = (10, 0) $ N  
- **Displacement Direction:** $ \vec{d}_{\text{dir}} = (6, 8) $  
- **Displacement Magnitude:** $ |\vec{d}| = 5 $ m  
- **Work Done Formula:** $ W = \vec{F} \cdot \vec{d} $  
- **Unit of Work:** Joules (J)

---

### **Step 1: Find the unit vector in the direction of displacement**

**Calculation:**  
The displacement vector must be in the direction of $ (6, 8) $ with a magnitude of 5 m.

- First, find the magnitude of $ (6, 8) $:  
  $$
  |\vec{d}_{\text{dir}}| = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10
  $$
- Unit vector in this direction:
  $$
  \vec{u} = \left( \frac{6}{10}, \frac{8}{10} \right) = (0.6, 0.8)
  $$
- Displacement vector of magnitude 5 m:
  $$
  \vec{d} = 5 \times \vec{u} = (5 \times 0.6, 5 \times 0.8) = (3, 4)
  $$

**Explanation:**  
To move 5 meters in the direction of $ (6, 8) $, scale the unit vector in that direction by 5. This gives the displacement vector $ (3, 4) $.

---

### **Step 2: Calculate the work done using the dot product**

**Calculation:**  
The work done ($ W $) is given by the dot product of the force and displacement vectors:
$$
W = \vec{F} \cdot \vec{d} = (10, 0) \cdot (3, 4) = 10 \times 3 + 0 \times 4 = 30 + 0 = 30 \text{ J}
$$

**Explanation:**  
The dot product multiplies the corresponding components and sums the results. The force has only an x-component, so only the x-component of displacement contributes to the work. The total work is 30 Joules.

---

### **Final Answer Summary**

**The work done by a force of $ (10, 0) $ N in moving an object 5 m in the direction of $ (6, 8) $ is $ \boxed{30} $ Joules.**

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Study Help, Fast Answers

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Related Answers

Study Help, Fast Answers