a) Kinetic and gravitational potential energy

a) kinetic energy of an object; E_k = ½mv²

b) gravitational potential energy of an object in a uniform gravitational field; E_p = mgh

c) the exchange between gravitational potential energy and kinetic energy

kinetic energy = energy resulting from an object’s motion

E_k = ½mv²

• kinetic energy of an object (J) = ½ × mass of the object (kg) × velocity of the object² (ms^-1)

gravitational potential energy = energy resulting from an object’s position in a gravitational field

E_p = mgΔh

• gravitational potential energy of an object (J) = mass of the object (kg) × acceleration of free fall (ms^-2) × change in height (m)

when E_k and E_p are exchanged

• ½mv² = mgΔh

  • loss/gain in E_k = loss/gain in E_p

• v = √2gh

  • velocity of the object (ms^-1) = √ 2 × acceleration of free fall (ms^-2) × change in height (m)