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A box of mass M is on a rough incline that makes an angle with the horizontal. T

ID: 1260418 • Letter: A

Question

A box of mass M is on a rough incline that makes an angle with the horizontal. The coefficient of kinetic friction between the box and the incline is ½. The box is placed against a spring whose other end is secured to a wall at the lower end of the incline. The block is used to compress the spring a distance D and is then released from rest. Derive an expression for the minimum spring constant k necessary to ensure that the box reaches a distance L up the incline from the equilibrium position of the spring. (Treat the box as a point mass.)

Explanation / Answer

when box compress restoring force is F1= - K D      In upward direction

When box release restoring force F2 = K (L-D)        In downward

Net restoring force F= F2- F1 = KL ------------1

Net force on box is ( from fig)

F net = mg sin@ + f                   f= friction force= uk* R       ( uk= cofficient of kinectic friction)

=mg sin @+ uk*mg cos@     ----2

from 1 and 2     K= mg( sin@ + uk cos@) / L