A ball of mass 2 kg is dropped from a height of 0.4 m above the free end of a vertically fixed

step 1 number 118 in which it is given that a ball of mass 2k is being dropped from high 0 .4 meter abo

A ball of mass 2 kg is dropped from a height of 0.4 m...

A ball of mass $2 \mathrm{~kg}$ is dropped from a height of $0.4 \mathrm{~m}$ above the free end of a vertically fixed spring of constant $\mathrm{k}=200 \mathrm{~N} \mathrm{~m}^{-1}$ (a) The maximum $\mathrm{K} . \mathrm{E}$ attained by the ball is $9 \mathrm{~J}$ (b) The maximum K.E is attained $0.5 \mathrm{~m}$ below original position $\mathrm{P}$. (c) The maximum potential energy attained by the spring is $16 \mathrm{~J}$ (d) The maximum potential energy attained by the spring is 9 J

A ball of mass $2 \mathrm{~kg}$ is dropped from a height of $0.4 \mathrm{~m}$ above the free end of a vertically fixed spring of constant $\mathrm{k}=200 \mathrm{~N} \mathrm{~m}^{-1}$
(a) The maximum $\mathrm{K} . \mathrm{E}$ attained by the ball is $9 \mathrm{~J}$
(b) The maximum K.E is attained $0.5 \mathrm{~m}$ below original position $\mathrm{P}$.
(c) The maximum potential energy attained by the spring is $16 \mathrm{~J}$
(d) The maximum potential energy attained by the spring is 9 J

Key Concepts

Elastic Potential Energy

Elastic potential energy is stored when mechanical work is done to deform an elastic object, like a spring. It is expressed as 1/2 k x², with k being the spring constant and x the displacement. This concept is fundamental in analyzing systems where springs are compressed or stretched.

Kinetic Energy

Kinetic energy is the energy an object has due to its motion, calculated using the formula 1/2 mv². In dynamic systems, such as a ball in free fall or during impact, kinetic energy is a measure of the work the object can do due to its velocity.

Hooke's Law

Hooke's Law states that the force needed to extend or compress a spring by some distance is proportional to that distance. This relationship, expressed as F = -kx, underpins the behavior of elastic materials and is essential for calculating elastic potential energy in spring systems.

Energy Conservation

This concept refers to the principle that energy cannot be created or destroyed, only transformed from one form to another. In mechanical systems like a falling ball and a spring, gravitational potential energy converts into kinetic energy and then into elastic potential energy, and vice versa, as the system evolves.

Gravitational Potential Energy

This is the energy an object possesses because of its position in a gravitational field. It is calculated as the product of mass, gravitational acceleration, and height, and plays a key role when an object is lifted or dropped, converting into kinetic energy as the object falls.

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