https://file.aiquickdraw.com/mathbot/file/1726683884352sj1vfp84.jpg

The problem provided in the image can be broken down as follows:

### Problem Statement:
A boy pulls a sled along level ground using a rope. The tension in the rope is 78 N, and it makes an angle of 37° with the horizontal.

**Questions:**
1. **Part (a):** What is the magnitude of the component of the tension responsible for actually moving the sled?
2. **Part (b):** What is the magnitude of the component of the tension that is wasted?

---

### Part (a): Finding the horizontal component of the tension responsible for moving the sled:

The tension force can be split into two components:
- A horizontal component that is responsible for moving the sled.
- A vertical component that is not useful for moving the sled.

To find the horizontal component \(T_x\), we use the formula:
\[
T_x = T \cdot \cos(\theta)
\]
Where:
- \(T = 78 \, \text{N}\) is the total tension.
- \(\theta = 37^\circ\) is the angle with the horizontal.

### Part (b): Finding the vertical component of the tension that is wasted:

The vertical component \(T_y\) can be found using the formula:
\[
T_y = T \cdot \sin(\theta)
\]

Now, let's calculate both components.### Solution:

- **Part (a):** The magnitude of the horizontal component of the tension responsible for moving the sled is approximately **62.29 N**.
- **Part (b):** The magnitude of the vertical component of the tension that is wasted is approximately **46.94 N**.

Would you like further details or have any other questions?

Here are five related questions for practice:
1. What happens to the horizontal and vertical components if the angle increases?
2. How would the components change if the tension in the rope increased?
3. What would be the horizontal force if the angle were 0°?
4. How much work is done if the sled moves a certain distance with this tension force?
5. What role does friction play in this type of problem?

**Tip:** To maximize the horizontal component of a force while pulling an object, try to minimize the angle of the applied force relative to the horizontal direction.

A boy pulls a sled along level ground by means of a rope under 78 N of tension. The rope with which he pulls the sled makes an angle of 37° with the horizontal.

a) What is the magnitude of the component of the tension responsible for actually moving the sled?
b) What is the magnitude of the component of the tension that is wasted?

Learn how to decompose a tension force of 78 N at a 37° angle into horizontal and vertical components. Find out the magnitude of the tension responsible for moving the sled and the wasted vertical component. Suitable for high school physics students.

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