Genesis Crash. On September 8,2004 , the Genesis space-craft...

Genesis Crash. On September $8,2004$ , the Genesis space-craft crashed in the Utah desert because its parachute did not open. The $210-k g$ capsule hit the ground at 311 $\mathrm{km} / \mathrm{h}$ and penetrated the soil to a depth of 81.0 $\mathrm{cm} .$ (a) Assuming it to be constant, what was its acceleration $\left(\text { in } \mathrm{m} / \mathrm{s}^{2} \text { and in } g^{\prime} \mathrm{s}\right)$ during the crash? (b) What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight. (c) For how long did this force last?

Key Concepts

Impulse and Momentum

Impulse, defined as the product of force and the time interval over which it acts, is equal to the change in momentum of an object. This concept is instrumental in understanding how forces applied over short durations affect the motion of an object during collisions.

Work-Energy Principle

The work-energy principle connects the work done by forces to the change in kinetic energy of an object. It is useful in analyzing impacts by relating the distance over which a force is applied to the reduction in kinetic energy, thereby helping to determine the deceleration.

Unit Conversion

Unit conversion is a critical practice in physics to ensure consistency across calculations. Converting all quantities to a standardized set of units, such as the International System of Units (SI), is necessary to correctly apply formulas and compute meaningful results.

Kinematic Equations

Kinematic equations describe the motion of objects moving with constant acceleration. They provide relationships between displacement, initial and final velocities, acceleration, and time, which are essential for determining unknown parameters in collision or deceleration scenarios.

Newton's Second Law

Newton's second law establishes that the net force acting on an object is equal to the product of its mass and acceleration. This principle is fundamental in calculating impact forces when the acceleration and mass of an object are known.

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