Calculate the center of mass of the following system: A mass of 5 kg lies at x = 1, a mass of 3 kg lies at x = 4 and a mass of 2 kg lies at x = 0.

Calculate the center of mass of the following system: A mass of 10 kg lies at the point (1,0), a mass of 2 kg lies at the point (2,1) and a mass of 5 kg lies at the point (0,1), as shown in the figure below.

Consider the system from problem 2, but now with forces acting upon the system. On the 10 kg mass, there is a force of 10 N in the positive x direction. On the 2 kg mass, there is a force of 5 N inclined 45^o above horizontal. Finally, on the 5 kg mass, there is a force of 2 N in the negative y direction. Find the resultant acceleration of the system.

Two masses, m₁ and m₂, m₁ being larger, are connected by a spring. They are placed on a frictionless surface and separated so as to stretch the spring. They are then released from rest. In what direction does the system travel?

A 50 kg man stands at the edge of a raft of mass 10 kg that is 10 meters long. The edge of the raft is against the shore of the lake. The man walks toward the shore, the entire length of the raft. How far from the shore does the raft move?