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Problem 2:
A box is accelerated at [tex]$2 \, \text{m/s}^2$[/tex] upward when pulled vertically by a string. Using [tex]$\vec{g} = 9.8 \, \text{m/s}^2$[/tex], what is the tension on the string?

Given:
[tex]m = \text{(mass of the box)}[/tex]

Sagot :

GinnyAnsweridn
To determine the tension in the string when a box is accelerated upward, we use the following concepts.

### Key Concepts:
1. Newton's Second Law of Motion: [tex]\( \vec{F} = m \cdot \vec{a} \)[/tex]
2. Gravitational Force: [tex]\( F_g = m \cdot g \)[/tex]
3. Tension in the String (T): The upward force exerted by the string.

### Given Data:
- Acceleration of the box, [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] (upward)
- Gravitational acceleration, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex] (downward)
- Mass of the box, [tex]\( m \)[/tex] (not provided)

### Understanding the Problem:
To find the tension [tex]\( T \)[/tex] in the string, we need to account for both the upward force required to accelerate the box and the gravitational force acting on the box. The formula for the tension in the string when the box is accelerating upward is:

[tex]\[ T = m \cdot (g + a) \][/tex]

However, in this specific problem, the mass [tex]\( m \)[/tex] of the box is not provided. Since the mass is a crucial factor in calculating the tension, without the mass value, the tension cannot be computed.

### Conclusion:
Given the lack of information regarding the mass [tex]\( m \)[/tex] of the box, it is impossible to calculate the precise tension in the string. Hence, the final answer is:

Mass not provided, unable to calculate tension.
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