Propulsion Dynamics Lab: Verification of $F=ma$
Use the lab tools to verify **Newton's Second Law** ($F=ma$). You will calculate the required thrust for acceleration and predict the final velocity of a test mass.
Mission Briefing: Key Equations & Concepts
â–¼The net force ($\Sigma F$) acting on an object is equal to the mass ($m$) times its acceleration ($a$). $$ \Sigma F = m \cdot a $$
The final velocity ($v$) of an object accelerating uniformly is: $$ v = u + a \cdot t $$ (where $u$ is initial velocity, typically 0).
Experiment 1: Thrust Requirement Calculator ($F=ma$)
Adjust the mass and desired acceleration to find the **Required Thrust (Force)**.
Experiment 2: Final Velocity Prediction Challenge
Given the Force, Mass, and Time, calculate the final velocity ($v$) of the object (assuming $u=0$).
Newton's Second Law shows that **Force** is directly proportional to **acceleration** ($F \propto a$) and directly proportional to **mass** ($F \propto m$). If you double the force, you double the acceleration (keeping mass constant).
Momentum and Impulse (11th Std Context)
The Second Law is more accurately stated as: The rate of change of momentum of a body is directly proportional to the applied force. Momentum is defined as $$ p = m \cdot v $$.
Impulse is the change in momentum ($\Delta p$). It is also equal to the force multiplied by the time interval ($\vec{I} = \vec{F} \cdot \Delta t$). This concept is crucial in understanding safety systems like airbags.
The Second Law holds true only in **inertial frames of reference** (non-accelerating frames). In non-inertial frames (like a spinning carousel), fictitious forces must be introduced.
