Mechanical Energy Formulas - Definitions & Examples
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Mechanical energy refers to the total of kinetic energy and potential energy possessed by an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both.
If K E and P E refers to the kinetic and potential energies of a body, its mechanical energy is given by, M.E = K.E + P.E For an object thrown upwards, its total mechanical energy is given by: E = ½ mv^{2} + mgh Where,m is the mass of an object, v , the velocity of that object, g, the acceleration due to gravity and htells at what height the object is from the ground.
Example: The kinetic energy of a body flying at a certain height from the ground is 4500 J and its potential energy is 8000 J. Find the total mechanical energy associated with it. Solution: KE = 4500 J, PE = 8000 J, ME=? ME = KE + PE = 4500 + 8000 = 12500 J
Example: An object of mass 2 kg has been projected vertically upwards with a kinetic energy of 100 J. Find the maximum height it can reach (take g = 10 m/s^{2} and PE of the object at the point of projection is zero). Solution: In motion under gravity, total mechanical energy is conserved. Total Mechanical energy at the point of projection = total mechanical energy at the maximum height. At the point of projection: KE_{1} = 100 J, PE_{1} = 0 At the maximum height: KE_{2} = 0, PE_{2} = mgh Now, KE_{1} + PE_{1 } = KE_{2} + PE_{2} Therefore, 100 + 0 = 0 + mgh ⇒h=100mg=1002×10=5m The object will reach upto a maximum height of 5 m.
Question: A ball thrown up with certain kinetic energy can reach a maximum height of 8 m. An identical ball thrown up with four times kinetic energy can reach a maximum height of: Options: (a) 8 m (b) 32 m (c) 64 m (d) 128 m Answer: (d)