A 12 kg weather rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550 N/m, is anchored to the ground. (a) Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). In this scenario, the forces acting on the rocket include the thrust generated by the engine and the gravitational force acting downward due to its mass. Understanding this law is crucial for analyzing the net force and resulting motion of the rocket.

Spring Force and Hooke's Law

Hooke's Law describes the behavior of springs, stating that the force exerted by a spring is proportional to its displacement from the equilibrium position (F = -kx). Here, 'k' is the spring constant, and 'x' is the compression or extension of the spring. This concept is essential for determining how much the spring compresses when the rocket is at rest before ignition.

Equilibrium Condition

An object is in equilibrium when the net force acting on it is zero. In this case, before the rocket's engine ignites, the upward force from the spring must balance the downward gravitational force and any other forces acting on the rocket. Understanding this condition allows us to set up the equation to find the compression of the spring when the rocket is at rest.