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Answer :
To solve this problem, we need to determine if the force of 115 N is sufficient to accelerate a 210 kg sofa at a rate of [tex]\(0.15 \, \text{m/s}^2\)[/tex].
1. Understand the Problem:
- We have a sofa with a mass of 210 kg.
- We are applying a force of 115 N.
- The required acceleration is [tex]\(0.15 \, \text{m/s}^2\)[/tex].
2. Apply Newton’s Second Law of Motion:
- Newton’s Second Law states that force ([tex]\(F\)[/tex]) is equal to mass ([tex]\(m\)[/tex]) multiplied by acceleration ([tex]\(a\)[/tex]).
- The formula is [tex]\( F = m \times a \)[/tex].
3. Calculate the Required Force:
- With the given mass [tex]\(m = 210 \, \text{kg}\)[/tex] and the required acceleration [tex]\(a = 0.15 \, \text{m/s}^2\)[/tex], we use the formula:
[tex]\[
F = 210 \, \text{kg} \times 0.15 \, \text{m/s}^2 = 31.5 \, \text{N}
\][/tex]
4. Compare the Forces:
- The force needed to achieve the acceleration is 31.5 N.
- We are applying a force of 115 N.
- Since 115 N is greater than 31.5 N, the applied force is sufficient to move the sofa.
5. Conclusion:
- The force of 115 N is indeed enough to accelerate the 210 kg sofa at the desired rate of [tex]\(0.15 \, \text{m/s}^2\)[/tex].
- Therefore, the answer to the problem is that the force is sufficient to move the sofa.
1. Understand the Problem:
- We have a sofa with a mass of 210 kg.
- We are applying a force of 115 N.
- The required acceleration is [tex]\(0.15 \, \text{m/s}^2\)[/tex].
2. Apply Newton’s Second Law of Motion:
- Newton’s Second Law states that force ([tex]\(F\)[/tex]) is equal to mass ([tex]\(m\)[/tex]) multiplied by acceleration ([tex]\(a\)[/tex]).
- The formula is [tex]\( F = m \times a \)[/tex].
3. Calculate the Required Force:
- With the given mass [tex]\(m = 210 \, \text{kg}\)[/tex] and the required acceleration [tex]\(a = 0.15 \, \text{m/s}^2\)[/tex], we use the formula:
[tex]\[
F = 210 \, \text{kg} \times 0.15 \, \text{m/s}^2 = 31.5 \, \text{N}
\][/tex]
4. Compare the Forces:
- The force needed to achieve the acceleration is 31.5 N.
- We are applying a force of 115 N.
- Since 115 N is greater than 31.5 N, the applied force is sufficient to move the sofa.
5. Conclusion:
- The force of 115 N is indeed enough to accelerate the 210 kg sofa at the desired rate of [tex]\(0.15 \, \text{m/s}^2\)[/tex].
- Therefore, the answer to the problem is that the force is sufficient to move the sofa.
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