a body of mass 10kg on a smooth inclined plane is connected to a smooth pulley to a mass of 15kg as shown above, the acceleration of the system is
Given:
- \( m_1 = 10 \, \text{kg} \) (on incline)
- \( m_2 = 15 \, \text{kg} \) (hanging)
- \( \theta = 30^\circ \)
Inclined mass:
\( F_{\text{incline}} = m_1 g \sin(\theta) = 10g \cdot 0.5 = 5g\)
Hanging mass:
\(F_{\text{weight}} = m_2 g = 15g\)
Net Force: \(F_{\text{net}} = F_{\text{weight}} - F_{\text{incline}} = 15g - 5g = 10g\)
Total Mass
\(m_{\text{total}} = m_1 + m_2 = 25 \, \text{kg}\)
Using \( F_{\text{net}} = m_{\text{total}} \cdot a \):
\(10g = 25a \quad \Rightarrow \quad a = \frac{10g}{25} = \frac{2g}{5}\)
The acceleration is:
\(a = \frac{2g}{5} \, \text{m/s}^2\)
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