Question

To what height would a 3.0 kg object have to be raised such that its gravitational potential energy would equal the kinetic energy it would possess if it were moving at 3.0 m/s?

Answer 1

Lets,first understand what the terms gravitational potential energy and kinetic energy mean.

Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object.  More massive the object or higher it is elevated, the greater the gravitational potential energy. These relationships are expressed by the following equation :

PE_grav = m * g * h

where m = mass, h= height, g= 9.8 = gravitational acceleration

Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy.The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

KE = 0.5 * m * v²
where m = mass of object v = speed of object

We need the gravitational potential energy to be equal to the kinetic energy, i.e

m* g * h  = 0.5 *m * v²

g * h = 0.5 * v²

9.8 * h = 0.5 * 3²

h = 0.4591 m

Thus, the object must be raised to a height of 0.4591 m or 45.9 cm such that its gravitational potential energy would equal the kinetic energy it would possess if it were moving at 3.0 m/s