Topic: Engineering Mechanics
The uniform link shown in the following figure has a mass of 12 kg. If the spring is un-stretched at theta = 0 deg, determine the angle theta for stable equilibrium. Neglect the surface friction and assume g = 10 m/s² (k = 200 N/m, l = 0.6 m)
- A. 0 deg
- B. 60 deg
- C. 90 deg
- D. 30 deg
Answer: B. 60 deg
Explanation: Taking moments about the pivot or using the potential energy method: The restoring force of the spring balances the overturning moment of the link's weight. The equilibrium condition yields 1 - cos(theta) = (m*g) / (2*k*l). Substituting values: 1 - cos(theta) = (12 * 10) / (2 * 200 * 0.6) = 120 / 240 = 0.5. Thus, cos(theta) = 0.5, which gives theta = 60 deg.