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Sagot :
Certainly! Let's address the problem of determining the tension in each string in the given scenarios, step by step:
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### Case (i): Zero Newton (0 N)
Given Information:
- Surface: Smooth
- String: Massless
- Additional details suggest the tension is zero
Step-by-Step Explanation:
1. The surface being smooth implies there is no friction.
2. The string being massless suggests its contribution to the tension calculation is negligible.
3. Given the tension in the scenario is provided as 0 N, it indicates no external force is causing tension in the string.
Thus, the tension in the string for this case is:
[tex]\[ \text{Tension} = 0 \, \text{N} \][/tex]
---
### Case (ii): 20 Newton (20 N)
Given Information:
- Surface: Smooth
- String: Massless
- Tension is stated to be 20 N
Step-by-Step Explanation:
1. A smooth surface ensures there is no friction force acting on the body.
2. A massless string does not affect the tension calculation.
3. The given tension in this case is directly stated as 20 N, meaning the force causing tension in the string is 20 Newtons.
Therefore, the tension in the string for this case is:
[tex]\[ \text{Tension} = 20 \, \text{N} \][/tex]
---
### Case (iii): 10 Newton (10 N)
Given Information:
- Surface: Smooth
- String: Massless
- Tension is indicated as 10 N
Step-by-Step Explanation:
1. Again, a smooth surface implies no frictional force.
2. The masslessness of the string signifies that it does not affect the tension calculation.
3. The provided tension in this case is 10 N, indicating a force of 10 Newtons is present within the string.
Thus, the tension in the string for this case is:
[tex]\[ \text{Tension} = 10 \, \text{N} \][/tex]
---
### Case (iv): Cannot be determined
Given Information:
- Surface: Smooth
- String: Massless
- Insufficient detail to determine tension
Step-by-Step Explanation:
1. With a smooth surface, friction is not a concern.
2. A massless string simplifies the tension calculations.
3. However, the question does not provide enough specific information to calculate or determine the tension in this particular scenario comprehensively.
Therefore, for this case:
[tex]\[ \text{Tension} = \text{Cannot be determined} \][/tex]
---
In summary:
1. For Case (i), the tension is 0 N.
2. For Case (ii), the tension is 20 N.
3. For Case (iii), the tension is 10 N.
4. For Case (iv), the tension cannot be determined with the given information.
---
### Case (i): Zero Newton (0 N)
Given Information:
- Surface: Smooth
- String: Massless
- Additional details suggest the tension is zero
Step-by-Step Explanation:
1. The surface being smooth implies there is no friction.
2. The string being massless suggests its contribution to the tension calculation is negligible.
3. Given the tension in the scenario is provided as 0 N, it indicates no external force is causing tension in the string.
Thus, the tension in the string for this case is:
[tex]\[ \text{Tension} = 0 \, \text{N} \][/tex]
---
### Case (ii): 20 Newton (20 N)
Given Information:
- Surface: Smooth
- String: Massless
- Tension is stated to be 20 N
Step-by-Step Explanation:
1. A smooth surface ensures there is no friction force acting on the body.
2. A massless string does not affect the tension calculation.
3. The given tension in this case is directly stated as 20 N, meaning the force causing tension in the string is 20 Newtons.
Therefore, the tension in the string for this case is:
[tex]\[ \text{Tension} = 20 \, \text{N} \][/tex]
---
### Case (iii): 10 Newton (10 N)
Given Information:
- Surface: Smooth
- String: Massless
- Tension is indicated as 10 N
Step-by-Step Explanation:
1. Again, a smooth surface implies no frictional force.
2. The masslessness of the string signifies that it does not affect the tension calculation.
3. The provided tension in this case is 10 N, indicating a force of 10 Newtons is present within the string.
Thus, the tension in the string for this case is:
[tex]\[ \text{Tension} = 10 \, \text{N} \][/tex]
---
### Case (iv): Cannot be determined
Given Information:
- Surface: Smooth
- String: Massless
- Insufficient detail to determine tension
Step-by-Step Explanation:
1. With a smooth surface, friction is not a concern.
2. A massless string simplifies the tension calculations.
3. However, the question does not provide enough specific information to calculate or determine the tension in this particular scenario comprehensively.
Therefore, for this case:
[tex]\[ \text{Tension} = \text{Cannot be determined} \][/tex]
---
In summary:
1. For Case (i), the tension is 0 N.
2. For Case (ii), the tension is 20 N.
3. For Case (iii), the tension is 10 N.
4. For Case (iv), the tension cannot be determined with the given information.
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