(a) What\'s the difference between stable and unstable equilibrium? What feature

Question

(a) What's the difference between stable and unstable equilibrium? What features of a potential energy function do they correspond to? You hang a 4 kg crate from the ceiling using a spring. The unstretched length of the spring is 10 cm. With the crate connected, the spring stretches out to a length of 15 cm. The system is at rest, with the crate hanging 2 meters above the ground. (b1) What is the stiffness (spring constant) of the spring? (b2) What is the total potential energy of the system? (b3) How much work does the force of gravity do on the crate if it gets disconnected and falls to the ground? Is the work positive or negative?

Explanation / Answer

Q1.

When the center of gravity of a body lies below point of suspension or support, the body is said to be in STABLE EQUILIBRIUM.
When the center of gravity of a body lies above the point of suspension or support, the body is said to be in unstable equilibrium

Second derivative < 0: The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state.

Second derivative > 0: The potential energy is at a local minimum. This is a stable equilibrium.

Please post other question separately.

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