Learning Goal: To learn the definition of the center of mass for systems of particles anda be able to locate it.

Imagine throwing a rock upward and away from you. With neglible air resistance, the rock will follow a parabolic path before hitting the ground. Now imagine throwing a stick (or any other extended object). The stick will tend to rotate as it travels through the air, and the motion of each point of the stick (taken individually) will be fairly complex. However, there will be one point that will follow a simple parabolic path: the point about which the stick rotates. No matter how the is thrown, this special point will always be located at the same position within the stick. The motion of the entire stick can then be described as a combination of the translation of that single point (as if the entire mass of the stick were concentrated there) and the rotation of the stick about that point. Such a point, it turns out, exists for every rigid object or system of mssive particles. It is called the center of mass.

To calculate the center of mass for a system of massive point particles that have coordinates (x, y) and masses m4, the following equations are used.

Xcm = m1 + x1 +m2x2 +m3x3+ .../ m1 + m2 + m3 + ...

Ycm = m1y1 + m2y2 + m3y3 + .../m1 + m2 + m3 +

Part A: Two particles of masses m1 and m2 (m1 < m2) are located 10 meters apart. Where is the center of mass of the system located ?

Correct - more than 5 meters but less than 10 meters from the particle of mass m1

Part B: For the system of three particles shown, which have masses M, 2M, and 3M as indicated, where is the center of mass located :

Correct - between the particle of mass 2M and the particle of mass 3M

NEED !!! Part C: For the system of particles described in Part B, find the x coordinate Xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right.

Express your answer in terms of L.