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$5.00 Spring Attached to Mass - Conceptual Problem
- From Physics: Thermodynamics , Physics: General-Physics
- Closed, but you can still post tutorials
- Due on Sep. 03, 2008
- Asked on Sep. 03, 2008 at 12:08:27AM
Q:A mass m is attached to a spring and the spring is attached to a wall. The mass is sitting on the floor. When left by itself, the system assumes a position of x0 (equilibrium position of center of mass). if m is displaced from x0, an elastic force F(e)=-kX acts on mass, where k is spring constant and X is displacement (x-x0). the work done by m against F(e)can be incorporated in the mechanical-energy equation by treating F(e) as a body force.
a) show that the sign convention for force implied by F(e)=-kX is consistent with adopted coordinate system
b) define the elastic potential function I(e) by F(e) = -dI(e)/dX. if the zero of elastic potential energy is taken at equilibrium position, show that E(p)=kX^2/2.
c)Work done by the system m against the body force F(e) as m moves away from its equilibrium position is always positive. Why?
d) write the mechanical-energy equation for the rectilinear translation of m if no forces other than F(e) act on the mass. Assume that the total energy E(t) of system is known, and make use of the relationship u=dx/dt=dX/dt=dot(X)
