(II) A 1200 -kg car rolling on a horizontal surface has speed v=65 km / h when it strikes a hori

step 1 According to energy conservation law, the potential energy of the spring should be equal to the

(II) A 1200 -kg car rolling on a horizontal surface has...

(II) A 1200 -kg car rolling on a horizontal surface has speed $v=65 \mathrm{km} / \mathrm{h}$ when it strikes a horizontal coiled spring and is brought to rest in a distance of $2.2 \mathrm{m} .$ What is the spring stiffness constant of the spring?

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Key Concepts

Conservation of Mechanical Energy

This principle states that within an isolated system free from non-conservative forces, the total mechanical energy remains constant. In problems involving collisions with springs, the kinetic energy of the moving object is transformed into the elastic potential energy stored in the spring, enabling a calculation of the spring stiffness when the object is brought to rest.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion and is expressed by the formula ½mv², where m is the mass and v is the velocity. This concept is crucial for determining how much energy is available to be absorbed or transformed in dynamic systems.

Elastic Potential Energy (Hooke’s Law)

Elastic potential energy is the energy stored in an elastic material when it is deformed, such as when a spring is compressed or stretched. According to Hooke's law, the force exerted by a spring is proportional to its displacement (F = kx), and the stored energy is given by ½kx². This relationship is essential for analyzing systems where energy is stored mechanically.

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