A $$2kg$$ Block slides on a horizontal floor with speed of $$4$$ $$m/s$$. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is $$15N$$ and spring constant is $$10$$,$$000$$ $$N/m$$. The spring compressed by

Question

A $$2kg$$ Block slides on a horizontal floor with speed of $$4$$ $$m/s$$.   It strikes a uncompressed spring and compresses it till the block is motionless.  The kinetic friction force is $$15N$$ and spring constant is $$10$$,$$000$$ $$N/m$$.   The spring compressed by

Infinity Learn · Accepted Answer

Let the spring compresses by x  Initial K.E. of the mass  $$=$$   P.E. of the spring $$+$$ work done                               due to friction   $$KE$$ of the $$mass=$$   $$12mv2$$;  $$PE$$ of $$spring=$$   $$12kx2$$;work done by $$friction=friction$$ force . displacement substitute  $$12mv2=$$   $$12kx2+f$$.x substitute the given values ∴    $$12$$ ×$$2$$ ×$$42$$  $$=$$   $$12$$×$$10000$$× $$x2+15x$$ solve the quadratic equation $$x=0.055$$ m spring is compressed by $$5.5$$ cm

A 2kg Block slides on a horizontal floor with speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compressed by

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