The last stage of a rocket, which is traveling at a speed of 7600 m / s, consists of two parts

step 1 Let MC be the mass of the rocket case and MP is the mass of the payload. At first they are trave

The last stage of a rocket, which is traveling at a speed of...

The last stage of a rocket, which is traveling at a speed of $7600 \mathrm{~m} / \mathrm{s}$, consists of two parts that are clamped together: a rocket case with a mass of $290.0 \mathrm{~kg}$ and a payload capsule with a mass of $150.0 \mathrm{~kg}$. When the clamp is released, a compressed spring causes the two parts to separate with a relative speed of $910.0 \mathrm{~m} / \mathrm{s}$. What are the speeds of (a) the rocket case and (b) the payload after they have separated? Assume that all velocities are along the same line. Find the total kinetic energy of the two parts (c) before and (d) after they separate. (e) Account for the difference.

Key Concepts

Conservation of Momentum

This principle states that in an isolated system with no external forces, the total momentum remains constant before and after an event. In problems involving separation or collision, the momentum of all parts must add up to the initial momentum, which is essential in solving for individual velocities post-event.

Relative Velocity

Relative velocity is the velocity of one object as observed from another moving object. It is crucial in separation problems where the speed at which components separate is provided relative to each other, and then must be translated into absolute velocities in a common reference frame.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated by the equation (1/2)mv^2. In scenarios where objects speed up or slow down, understanding kinetic energy changes is key to analyzing the system, especially when comparing energy before and after an event like a separation.

Energy Conversion (Spring Potential Energy)

This concept involves the transformation of energy from one form to another, in this case, from the potential energy stored in a compressed spring to the kinetic energy of moving parts. Recognizing that additional kinetic energy can be allocated to the system through such stored energy explains differences in total kinetic energy before and after an event.

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