When a coil spring is compressed,the work is done on the spring. The elastic potential energy:

The velocity of a body moving in a straight line is increased by applying a constant force $F$ for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

Compare the power at which each of the following is moving upwards against the force of gravity? (given $g = 10 \, m \, s^{-2}$)
$(i)$ $A$ butterfly of mass $1.0 \, g$ that flies upward at a rate of $0.5 \, m \, s^{-1}$.
$(ii)$ $A$ $250 \, g$ squirrel climbing up on a tree at a rate of $0.5 \, m \, s^{-1}$.

$A$ mass of $10 \, kg$ is dropped from a height of $50 \, cm$. Find its:
$(a)$ Potential energy just before dropping.
$(b)$ Kinetic energy just on touching the ground.
$(c)$ Velocity with which it hits the ground. (Given: $g = 10 \, m s^{-2}$)

An iron sphere of mass $30 \, kg$ has the same diameter as an aluminium sphere whose mass is $10.5 \, kg$. The spheres are dropped simultaneously from a cliff. When they are $10 \, m$ from the ground,they have the same:

State the law of conservation of energy.