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

ID: 1260421 • 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 µ. 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.)

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 mu. 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

Potential energy stored due to spring=Work done due to friction

1/2*K*D^2=u*M*g*cos(theta)*L

K=2*u*M*g*cos(theta)*L/D^2 ans