tension in strings

Question

Two masses 3 kg and 5 kg connected by a light inextensible string are pulled on a frictionless surface by a 32 N force applied on the 5 kg mass. Find the tension (N).

RankGuru · Accepted Answer

1. **System Analysis**: Both masses move with the same acceleration ($a$).
2. **Calculate Acceleration**: 
   - $a = \frac{F}{m_1 + m_2} = \frac{32}{3 + 5} = \frac{32}{8} = 4 	ext{ m/s}^2$.
3. **Free Body Diagram of 3 kg block**: The only horizontal force on the $3$ kg block is the tension ($T$) in the string.
4. **Equation**: $T = m_1 a$.
5. **Substitution**:
   - $T = 3 	ext{ kg} 	imes 4 	ext{ m/s}^2 = 12$ N.
6. **Final Result**: The tension is **$12$ N**.

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tension in strings

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