Two blocks of masses M and 3 M are placed on a horizontal, frictionless surface.

Question

Two blocks of masses M and 3 M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them.

A cord holding them together is burned, after which the block of mass 3 M moves to the right with a speed of 2.48 m/s. What is the speed of the block of mass M? Answer in units of m/s.

Part B:

If M = 7.6 kg and the spring constant is 6200 N/m, how much was the spring originally compressed from its equilibrium length? Answer in units of m.

Explanation / Answer

Mass of one block m = M

Mass of another m ' = 3M

Speed of block first block v = ?

Speed of second block v ' = 2.48 m/s

From law of conservation of momentum , m' v ' = -mv

From this v = - m' v' / m

                 = -(3Mx2.48) / M

                 = -7.44 m/s

Answer is : 7.44 m/s

(B).M = 7.6 kg

Spring constant k = 6200 N/m

Potential energy of the spring = sum of kinetic energies

    (1/2) kA 2 = (1/2) mv 2 +(1/2)m ' v ' 2

           kA 2 = mv 2 +m ' v ' 2

                 = 7.6(7.44) 2 +(3x7.6x2.48 2)

                = 560.91

         A 2 = 560.91 / k

               = 560.91 / 6200

               = 0.0904

          A = 0.3007 m

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