Problem 6. Assume that a force field f is given in the (z, y)-plane, and consider a mass m is moving under the influence of f. The total energy of the mass is defined by the following expression E =m lu?+V(z, y), where v= is the velocity vector of the mass along the curve y (r(), y(t)), and V is the potential of the mass defined by the relation f -vv, where V is the gradient operator defined as VV = av Show that 0 assuming the NEWTON's second law m =f, and conclude that the mass moves along the solution to the following differential equation %3D dt DE dz+ dy =0.
Problem 6. Assume that a force field f is given in the (z, y)-plane, and consider a mass m is moving under the influence of f. The total energy of the mass is defined by the following expression E =m lu?+V(z, y), where v= is the velocity vector of the mass along the curve y (r(), y(t)), and V is the potential of the mass defined by the relation f -vv, where V is the gradient operator defined as VV = av Show that 0 assuming the NEWTON's second law m =f, and conclude that the mass moves along the solution to the following differential equation %3D dt DE dz+ dy =0.
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Transcribed Image Text:Problem 6. Assume that a force field f is given in the (r, y)-plane, and consider a mass m is moving under
the influence of f. The total energy of the mass is defined by the following expression
E=m lu?+V(z, y),
where v=
is the velocity vector of the mass along the curve y= (#(t), y(t)), and V is the potential of
the mass defined by the relation f=-vV, where V is the gradient operator defined as
VV =
Ae
dE
du
Show that
dt
=0 assuming the NEWTON's second law m=f, and conclude that the mass moves along
dt
the solution to the following differential equation
dr+
dy-0.
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