Physics
Center of Mass and Momentum
Conservation of Linear Momentum
11
⚡ Quick Summary
In the absence of external forces, the total linear momentum of a system remains constant. This means the initial momentum equals the final momentum, even if internal forces cause changes within the system.
Mv = m1v1 + m2v2 (where M is the total mass, v is the initial velocity, m1 and m2 are the masses of the parts, and v1 and v2 are their respective velocities)
When a system experiences no external force, the total linear momentum is conserved. This principle applies even when internal forces act within the system, causing it to break apart or change configuration. The total momentum before and after such an event remains the same.
Impulse and Momentum
11
⚡ Quick Summary
Impulse is the change in momentum of an object. It's calculated by integrating the force acting on an object over the time interval during which it acts. The impulse on a system is related to the external forces acting on it.
['Impulse = ∫ F dt', '∫ N dt = mv - mV (Particle)', '∫ (N - T)dt = mV (Pan)', '∫ T dt = mV (Block)', 'V = v/3 (Derived relationship)']
Consider a particle and a pan with a block on top. The impulse imparted to each is related to the change in momentum:
* Particle: \( \int N dt = mv - mV \), where N is the contact force, m is the mass of the particle, v is the final velocity, and V is the initial velocity.
* Pan: \( \int (N - T)dt = mV \), where T is the tension in the string, and M is the mass of the pan.
* Block: \( \int T dt = mV \)