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Moving a Sliding Dresser

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Sam is trying to move a dresser of mass m and dimensions of length L and height H by pushing it with a horizontal force F applied at a height h above the floor. The coefficient of kinetic friction between the dresser and the floor is k and g is the magnitude of the acceleration due to gravity. The ground exerts upward normal forces of magnitudes Np and Nq at the two ends of the dresser. Note that this problem is two-dimensional.

A. If the dresser is sliding with constant velocity, find F, the magnitude of the force that Sam applies.
B. Find the magnitude of the normal force.
C. Find the magnitude of the normal force.
D. Find the maximum height at which Sam can push the dresser without causing it to topple over.

See the attached file.

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Solution Summary

This solution shows steps for rearranging needed expressions and includes calculations and answers (see the attached file).

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A. SUM Fx = F + (-fK) = 0 ---- (1)
SUM Fy = Np + NQ - mg = 0 ---- (2)
fk = uk(Np + NQ) ---- (3)

from equation (2), Np + NQ = mg ...

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