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Let's go through the problem step by step:

### Part a:
**Find the mass of a box with weight 268 N.**

We know the relationship between weight \( W \), mass \( m \), and gravitational acceleration \( g \):
\[
W = m \cdot g
\]
where \( W = 268 \, \text{N} \) and \( g = 9.8 \, \text{m/s}^2 \).

We can rearrange the formula to solve for the mass \( m \):
\[
m = \frac{W}{g}
\]
\[
m = \frac{268}{9.8} \approx 27.35 \, \text{kg}
\]

So, the mass of the box is approximately **27.35 kg**.

---

### Part b:
**The box is being pulled vertically upwards with an acceleration of \( 0.9 \, \text{m/s}^2 \). Find the tension in the rope.**

To find the tension \( T \) in the rope, we can use Newton's second law:
\[
F = m \cdot a
\]
The total force acting on the box in the upward direction is the tension in the rope, and the forces acting against it are the gravitational force. So, the equation for the forces in this case is:
\[
T - W = m \cdot a
\]
Rearranging to find \( T \):
\[
T = W + m \cdot a
\]
Substitute the known values:
\[
T = 268 \, \text{N} + 27.35 \, \text{kg} \times 0.9 \, \text{m/s}^2
\]
\[
T = 268 \, \text{N} + 24.62 \, \text{N} \approx 292.62 \, \text{N}
\]

So, the tension in the rope is approximately **292.62 N**.

---

### Part c:
**The box is now lowered at a constant speed. Find the tension in the rope.**

When the box is moving at a constant speed, there is no acceleration (\( a = 0 \)). Therefore, the tension in the rope must exactly balance the weight of the box, as there is no net force acting on it.

So, the tension \( T \) is equal to the weight \( W \):
\[
T = W = 268 \, \text{N}
\]

Thus, the tension in the rope is **268 N**.

---

### Part d:
**Explain how you have used the modelling assumptions that the rope is:**
- **i) Light:** 
   - A light rope means the rope's mass is negligible, so it does not contribute any additional weight to the system. We do not need to account for the rope's weight when calculating the forces.
  
- **ii) Inextensible:** 
   - An inextensible rope does not stretch, meaning the tension is the same throughout the rope, and the box and rope move with the same acceleration. There is no need to consider changes in length or elastic forces when modeling the system.

---

Let me know if you need more details or have any questions. 

Here are five related questions for further understanding:
1. How would the problem change if the rope were extensible?
2. What happens to the tension if the rope has a significant mass?
3. How does the tension in the rope change if the box is accelerating downwards?
4. What forces act on the box when it is at rest and held by the rope?
5. Can we model the forces differently if the box is pulled up with variable acceleration?

**Tip**: Always clearly define and label the forces acting on an object when applying Newton's second law.

A box has weight 268 N. Find its mass. The box is being pulled vertically upwards using a light inextensible rope and accelerates uniformly with a = 0.9 m/s². Find the tension in the rope. The box is now lowered at a constant speed. Find the tension in the rope. Explain how you have used the modeling assumption that the rope is: i) light ii) inextensible.

Learn how to calculate the mass of a box given its weight (268 N) and the tension in a rope when the box is pulled upward with acceleration (0.9 m/s²) and lowered at constant speed. Understand the role of light and inextensible rope assumptions. Suitable for Grades 11-12 physics students.

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