Mass Motion under a Variable Force

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A cart of mass initially at rest at at time is attached to a mass hanging from a pulley. The pulley and the floor are assumed to be frictionless. The experiment gives a case of motion under a variable force because the angle varies with time. The resulting equation of motion has no simple analytic solution, so the solution is integrated numerically.


Plots of position , velocity , and acceleration versus time are shown.


Contributed by: Enrique Zeleny (August 2011)
Open content licensed under CC BY-NC-SA



The length of the table is and the height of the pulley is ; then, from the geometry of the problem, it can be shown that the equation of motion is


The tension is ; if , the cart does not lift off.

The initial conditions used here are , , , .

Problem taken from F. Y. Wang, Physics with MAPLE, Weinheim: Wiley-VCH, 2005.

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