A spring of force constant k is set into a hole in a table and a light platform is attached to the top. The spring extends a distance D out of the table’s surface. A mass m is set on the platform and the spring is compressed so that the platform is initially at the same height as the table’s surface. When the mass is released, the mass is projected directly upward and reaches a maximum height of 4D. (a) Write an expression for D in terms of m, g, and k. (b) From the instant that the mass is released until the mass reaches its highest height, the mechanical energy of the mass-Earth-spring system is E. This is taking the table’s surface as the zero-point for gravitational potential energy and the spring’s natural length as the zero-point for elastic potential energy. Sketch graphs of the following quantities as functions of the mass’s height above the table’s surface as it is projected. i. Ug, the gravitational potential energy of the mass-Earth system ii. Us, the elastic potential energy of the spring iii. K, the ki
A spring of force constant k is set into a hole in a
table and a light platform is attached to the top.
The spring extends a distance D out of the table’s
surface. A mass m is set on the platform and the
spring is compressed so that the platform is
initially at the same height as the table’s surface.
When the mass is released, the mass is projected
directly upward and reaches a maximum height
of 4D.
(a) Write an expression for D in terms of m, g, and k.
(b) From the instant that the mass is released until the mass reaches its highest height, the mechanical energy of
the mass-Earth-spring system is E. This is taking the table’s surface as the zero-point for gravitational
potential energy and the spring’s natural length as the zero-point for elastic potential energy. Sketch graphs
of the following quantities as functions of the mass’s height above the table’s surface as it is projected.
i. Ug, the gravitational potential
energy of the mass-Earth
system
ii. Us, the elastic potential energy
of the spring
iii. K, the ki
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