Conservation of Linear Momentum in an Explosion of Particles

AI Thread Summary
In an explosion of a package on a frictionless surface, three pieces of equal mass move with specified velocities. To find the pre-explosion velocity, the conservation of linear momentum principle is applied, indicating that the total momentum before the explosion equals the total momentum after. The center of mass displacement can be calculated using the velocities of the fragments and the time elapsed post-explosion. The discussion emphasizes the importance of distinguishing between internal and external forces, noting that forces from the explosion are internal, thus conserving momentum. Understanding the center of mass is crucial for analyzing the system's overall motion and displacement.
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A suspicious package is sliding on a frictionless surface when it explodes into three pieces of equal masses and with the velocities:
(1) 7.0 m/s, north;
(2) 4.0 m/s 30 degrees south of west;
(3) 4.0 m/s 30 degrees south of east.

(a)What is the velocity(both magnitude & direction) of the package before it explodes?
(b) What is the displacement (both magnitude & direction) of the center of mass of the three-piece system (with respect to the point the explosion occurs) 3.0s after the explosion?
 
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1. What do we mean by Center of Mass?
2. How is Newton's laws formulated for C.M?
In particular, what is meant by the terms external and internal forces, and how can you use the fact that the forces associated with the explosion are to be considered internal forces?
 
another Hint: Use law of Conservation of Linear Momentum...

use vector equations and remember since therez no external forces the linear momentum component along an axis cannot change.
 

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