91Ó°ÊÓ

Kinetic energy is the energy an object possesses due to its motion. When a block is released from rest on a spring, its kinetic energy increases as it moves downward. The block begins to accelerate due to gravity and the force exerted by the spring. The equation for kinetic energy is given by: \[\ K = \frac{1}{2}mv^2\ \] where \( m \) is the mass and \( v \) is the velocity of the block.
As the block oscillates on the spring, its kinetic energy fluctuates. At its release point, \( y = 0 \), the kinetic energy is zero because the block hasn’t moved yet. When the block reaches a lower point, like \( y = -5 \text{ cm} \), it speeds up, increasing its kinetic energy.
Kinetic energy changes throughout the motion, reaching its maximum when the gravitational pull and elastic force combine optimally. Tracking kinetic energy helps us understand how energy transforms from potential forms (gravitational and elastic) into motion.

Gravitational potential energy is the energy held by an object because of its position relative to a gravitational field. For our block and spring system, it is determined by the height of the block above its equilibrium position. The equation is:\[ \Delta U_g = mg \Delta y \],
where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( \Delta y \) is the change in height.
When the block is attached to the spring at position \( y = 0 \), it is at its maximum height during the motion cycle, so its gravitational potential energy is at the maximum relative to lower positions. When the block moves downwards to positions like \( y = -5 \text{ cm} \), its gravitational potential energy decreases.

Elastic potential energy is stored in spring systems when the spring is either compressed or stretched from its natural length. The energy stored in a spring is described by Hooke’s law:
\[ \Delta U_e = \frac{1}{2}k(\Delta y)^2\]
Here, \( k \) is the spring constant, and \( \Delta y \) is the displacement from its unstressed position.
As the block descends and stretches the spring, elastic potential energy accumulates. For instance, at \( y = -5 \text{ cm} \), the elastic energy starts increasing because the spring is stretched. This energy can be transformed back into kinetic energy and gravitational potential energy, showcasing the interplay of forces and energy conservation in spring-block systems.