## Linear Momentum of Various Objects

When the linear momentum of various object is considered, still a single linear momentum can be assigned to the entire group of objects. This linear momentum is called the total linear momentum and it is calculated using the vector addition rules. In fact, the total linear momentum associated to a group of objects is obtaining solving the vector addition of the linear momentum associated with the individual objects. Therefore, if are the linear momenta of N objects, the total linear momentum of the system is .

 The sequence of drawings presented at the left correspond to an illustration of how the total linear momentum of a configuration of objects is calculated. The first drawing of the sequence shows a set of pool balls moving in all direction just after the break, . Since the mass of the pool balls are all the same, the difference in the length of the vectors representing the linear momentum of the individual balls is a consequence of their velocities being different. The drawing of just the vector representing the linear momentum is shown in the second drawing of the sequence . The vector addition is a commutative operation; therefore, the addition of the linear momentum can be done in any order. In this case, the order selected has for only purpose to maintain the clarity of the drawing . The next drawing of the sequence shows the result of the addition of vectors; that is, the linear momentum of the system. This vector is obtained following the usual rules for drawing it: ... from the tail of the first vector placed, in the addition sequence, to the tip of the last vector added to the addition it is drown the vector representing the vector addition. The last drawing of the sequence shows the vector linear momentum of the system alone .

 Examples

The picture on the left shows an intersection in downtown Dallas. Only five vehicles are actually in motion while the remainder are at rest (can you calculate the linear momentum for those vehicles at rest?). The arrows are the graphical representation of the linear momentum for those vehicles in motion. The cardinal points are also represented in the picture. If the masses and velocities are given in the following table,

 Mass (Kg) Velocity (m/s) 1 1600 5 west 2 700 8 west 3 500 6 west 4 5000 1 south 5 700 3 south

 1) J

Find the total linear momentum for vehicles one, two, and three.

 N a) 16600 Kg-m/s due west b) 7100 Kg-m/s due west c) 18055 Kg-m/s due east d) 23700 Kg-m/s e) None of the above.

 2) J

What is the magnitude of the total linear momentum for the vehicles at the corner?

 a) 16600 Kg-m/s b) 7100 Kg-m/s N c) 18055 Kg-m/s d) 23700 Kg-m/s e) None of the above.

 3) J

What is the direction of the total linear momentum for the vehicles at the corner?

 a) 670 south of west b) 230 west of south c) 670 east of south N d) 230 south of west e) None of the above.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com
 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com