Question

Prove the sum K.E and P.E of a body falling freely is always constant

Answer 1

Let a body of mass m falls from a point A, which is at a height h from the ground as shown in fig.
At A,
Kinetic energy kE = 0Potential energy Ep = mghTotal energy E = Ep + Ek = mgh + 0= mghDuring the fall, the body is at a position B. The body has moved a distance x from A.At B,velocity v2 = u2 + 2asapplying, v2 = 0 + 2ax = 2axKinetic energy Ek = 1/2 mv2 = 1/2 m x 2gx = mgxPotential energy Ep = mg (h – x)Total energy E = Ep + Ek = mg (h-x) + mgx = mgh – mgx + mgx= mgh