Question

1. Compare the kinetic energies of two objects, A and B, identical in every respect except one.  Assume that the single difference is:
   1. Object A has twice the velocity of B.
   2. Object A moves north, B south.
   3. Object A moves in a circle, B in a straight line.
   4. Object A is a projectile falling vertically downward; B is a projectile moving vertically upward at the same speed.
   5. Object A consists of two separate pieces attached by a light string, each equal in mass to the mass of B.

Answer 1

here,

the two objects A and B are indentical in every respect except one

a)

as vA = 2 vB

the kinetic energy ratio , R = 0.5 * ( mb * vb^2 )/(0.5 * ma * vA^2)

R = (vB /vA)^2 = (vB /2vB)^2 = 1/4

b)

as |vA| = |vB|

the kinetic energy ratio , R = 0.5 * ( mb * vb^2 )/(0.5 * ma * vA^2)

R = (vB /vA)^2 = (vB /vB)^2 = 1

c)

as vA = vB

the kinetic energy ratio , R = 0.5 * ( mb * vb^2 )/(0.5 * ma * vA^2)

R = (vB /vA)^2 = (vB /vB)^2 = 1

d)

as vA = vB

the kinetic energy ratio , R = 0.5 * ( mb * vb^2 )/(0.5 * ma * vA^2)

R = (vB /vA)^2 = (vB /vB)^2 = 1

e)

as vA = vB

the kinetic energy ratio , R = 0.5 * ( mb * vb^2 )/(0.5 * ma * vA^2)

R = (vB /vA)^2 = (vB /vB)^2 = 1