A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress

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A small block of mass 100 g is pressed against a horizontal...

A small block of mass $100 \mathrm{~g}$ is pressed against a horizontal spring fixed at one end to compress the spring through $5 \cdot 0 \mathrm{~cm}$ (figure 8-E11). The spring constant is $100 \mathrm{~N} / \mathrm{m}$. When released, the block moves horizontally till it leaves the spring. Where will it hit the ground $2 \mathrm{~m}$ below the spring?

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Key Concepts

Projectile Motion

Once the block leaves the spring, it moves as a projectile. The motion is characterized by an independent horizontal component, given by the initial speed and constant horizontal velocity (ignoring air resistance), and a vertical component governed solely by gravitational acceleration.

Spring Potential Energy

This concept involves the energy stored in a compressed or stretched spring, calculated using the formula (1/2)kx², where k is the spring constant and x is the deformation from equilibrium. It is fundamental in problems where mechanical work is converted into kinetic energy as the spring returns to its relaxed state.

Conservation of Energy

This principle states that the total energy in an isolated system remains constant, meaning that the stored energy (in this case, the spring's potential energy) is completely converted into kinetic energy of the moving block. This conversion allows determination of the block's speed when it leaves the spring.

Kinematics of Free Fall

This concept deals with the motion of objects under the influence of gravity, typically describing how an object accelerates downward at 9.8 m/s². It is used to calculate the time it takes for the block to fall a given vertical distance, which in turn is used to determine the horizontal distance traveled during free fall.

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