In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. Two students pull with force 196 N each to the right, four students pull with force 78 N each to the left, five students pull with force 62 N each to the left, three students pull with force 150 N each to the right, and one student pulls with force 250 N to the left. Assuming the positive direction to the right, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction? net pull = Submit Question N to th✔ Select an answer Left Right

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### Tug-of-War Problem

In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. The forces applied by the students are as follows:

- **To the Left:**
  - Four students pull with a force of 78 N each.
  - Five students pull with a force of 62 N each.
  - One student pulls with a force of 250 N. 

- **To the Right:**
  - Two students pull with a force of 196 N each.
  - Three students pull with a force of 150 N each.

**Question:**
Assuming the positive direction is to the right, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction?

**Calculation:**

To find the net pull, calculate the total force exerted on each side and then find the difference.

1. **Total Force to the Left:**
   - Four students at 78 N each: \( 4 \times 78 = 312 \) N
   - Five students at 62 N each: \( 5 \times 62 = 310 \) N
   - One student at 250 N: \( 1 \times 250 = 250 \) N
   
   Combined force to the Left:
   \[ 312 + 310 + 250 = 872 \text{ N} \]

2. **Total Force to the Right:**
   - Two students at 196 N each: \( 2 \times 196 = 392 \) N
   - Three students at 150 N each: \( 3 \times 150 = 450 \) N
   
   Combined force to the Right:
   \[ 392 + 450 = 842 \text{ N} \]

3. **Net Pull (Difference in Forces):**
   \[ 872 \text{ N (Left)} - 842 \text{ N (Right)} = 30 \text{ N (Left)} \]
   
Thus, the net pull on the knot is \( 30 \) N to the left.

Please enter your answer below:
**Net pull =** [ ______ ] **N to the** [Select: Left/Right]

[Submit Question]

**Explanation:**
The net pull calculation
Transcribed Image Text:--- ### Tug-of-War Problem In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. The forces applied by the students are as follows: - **To the Left:** - Four students pull with a force of 78 N each. - Five students pull with a force of 62 N each. - One student pulls with a force of 250 N. - **To the Right:** - Two students pull with a force of 196 N each. - Three students pull with a force of 150 N each. **Question:** Assuming the positive direction is to the right, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction? **Calculation:** To find the net pull, calculate the total force exerted on each side and then find the difference. 1. **Total Force to the Left:** - Four students at 78 N each: \( 4 \times 78 = 312 \) N - Five students at 62 N each: \( 5 \times 62 = 310 \) N - One student at 250 N: \( 1 \times 250 = 250 \) N Combined force to the Left: \[ 312 + 310 + 250 = 872 \text{ N} \] 2. **Total Force to the Right:** - Two students at 196 N each: \( 2 \times 196 = 392 \) N - Three students at 150 N each: \( 3 \times 150 = 450 \) N Combined force to the Right: \[ 392 + 450 = 842 \text{ N} \] 3. **Net Pull (Difference in Forces):** \[ 872 \text{ N (Left)} - 842 \text{ N (Right)} = 30 \text{ N (Left)} \] Thus, the net pull on the knot is \( 30 \) N to the left. Please enter your answer below: **Net pull =** [ ______ ] **N to the** [Select: Left/Right] [Submit Question] **Explanation:** The net pull calculation
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