In Fig. 9-63, block 1( mass 2.0 kg ) is moving rightward at 10 m / s and block 2 (mass 5.0 kg )

step 1 In this question, log 1 is moving at 10 meters per second to the right. And block 2 is moving to

In Fig. 9-63, block 1( mass 2.0 kg ) is moving rightward at...

In Fig. $9-63,$ block 1$($ mass 2.0 $\mathrm{kg}$ ) is moving rightward at 10 $\mathrm{m} / \mathrm{s}$ and block 2 (mass 5.0 $\mathrm{kg} )$ is moving rightward at 3.0 $\mathrm{m} / \mathrm{s}$ . The surface is frictionless, and a spring with a spring constant of 1120 $\mathrm{N} / \mathrm{m}$ is fixed to block $2 .$ When the blocks collide, the compression of the spring is maximum at the instant the blocks have the same velocity. Find the maximum compression.

Key Concepts

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object, calculated by (1/2)mv². In problems involving collisions and spring compression, evaluating the kinetic energy of each object before and after the interaction helps in determining how much energy is converted into potential energy during the collision.

Spring Potential Energy

Spring potential energy is the energy stored when a spring is compressed or stretched, and it is given by the formula (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position. This concept is crucial in understanding how the mechanical energy of a moving system is temporarily stored during the collision.

Conservation of Energy

This principle states that energy cannot be created or destroyed but can change forms. In collision problems involving springs, some of the kinetic energy of the moving objects is converted into the elastic potential energy stored in the compressed spring. Analyzing energy transformations allows for the calculation of maximum compression.

Conservation of Momentum

In any collision or interaction where external forces are negligible, the total momentum of the system is conserved. This principle is used to determine the common velocity of colliding objects at the moment when their relative motion ceases, such as during maximum spring compression when the blocks move together.

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