constraint motion (two bodies)

Question

Two blocks connected by an inextensible string over a frictionless pulley: m1 = 8 kg on a frictionless horizontal table, m2 = 2 kg hanging. Find the acceleration of the system (g = 10 m/s²).

RankGuru · Accepted Answer

1. **Identify Forces**:
   - On $m_1$ (Table): Tension ($T$) pulls it forward.
   - On $m_2$ (Hanging): Weight ($m_2g$) pulls it down, Tension ($T$) resists.
2. **Write Equations** ($F = ma$):
   - Table block: $T = m_1 a \implies T = 8a$.
   - Hanging block: $m_2g - T = m_2 a \implies 20 - T = 2a$.
3. **Substitute $T$**:
   - $20 - (8a) = 2a$
   - $20 = 10a$
   - $a = 2 	ext{ m/s}^2$.
4. **Common Trick**: The hanging weight is the ONLY external force driving the whole system mass: $a = \frac{m_2 g}{m_1 + m_2} = \frac{20}{10} = 2$ m/s².

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constraint motion (two bodies)

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