Answer :

The coefficient of friction is and the spring constant k = 1000N/m


Given


The angle of inclination of the plane is given as, a block is kept on the plane of mass 2kg and is kept from the spring at a distance of 4.8m, the compression distance of the spring is 20cm, and through the block to a distance of 1m.


Formula Used


The coefficient of friction is the ratio of the Force and reactionary forces in terms of acceleration or gravity and the using the conversation of mass, we equate the energies of spring compression and potential energy of the mass of the block, the formula of the energy stored in spring compression is



And the energy stored in the block is formulated as



where


The value of spring constant is denoted as “k”, the compression distance is “x”, the mass of the block is given as “m”, is the coefficient of friction, the gravity of the block is “g” and the height at which the block is kept is h.


Explanation


The block on the inclined plane is derived in two forms of derivatives with vertical being and horizontal as. Hence, applying conservation of energy we get the equation as





___________________1


For the upward return motion of the block we have



___________________2


Adding both the equation 1 and 2, we get the coefficient of friction as




Put the value of friction in the equation 1, we get the spring constant as


.


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