(a) What\'s the difference between stable and unstable equilibrium? What feature
ID: 2077073 • Letter: #
Question
(a) What's the difference between stable and unstable equilibrium? What features of a potential energy function do they correspond to? (b) 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. What is the stiffness (spring constant) of the spring? What is the total potential energy of the system? How much work does the force of gravity the crate if it gets disconnected and falls to the ground? Is the work positive or negative?Explanation / Answer
Stable and unstable equilibriums can be intuitively understood by considering the behavior of a ball placed on the top of a hill versus one placed at the bottom of a valley. At the top of the hill, there is a flat point where the ball remains stable and does not roll down the hill. However, if the ball is placed anywhere surrounding the stable point, gravity causes it to roll down the hill and lowers the ball's potential energy. Therefore, the top of the hill represents an unstable equilibrium. Conversely, the potential energy, due to gravity, of a ball at the bottom of a valley is lower than that of the ball at any surrounding point in the valley, so the bottom of the valley represents a stable equilibrium.
In both equilibrium, If potential energy of a body changes with change in its configuration then the body will have maximum potential energy at unstable equilibrium and minimum potential energy at stable equilibrium.
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