Learning Goal:

To understand the concept of total momentum for a system of objects and the effect of the internal forces on the total momentum.

We begin by introducing the following terms:

System: Any collection of objects, either pointlike or extended. In many momentum-related problems, you have a certain freedom in choosing the objects to be considered as your system. Making a wise choice is often a crucial step in solving the problem.

Internal force: Any force interaction between two objects belonging to the chosen system. Let us stress that both interacting objects must belong to the system.

External force: Any force interaction between objects at least one of which does not belong to the chosen system; in other words, at least one of the objects is external to the system.

Closed system: a system that is not subject to any external forces.

Total momentum: The vector sum of the individual momenta of all objects constituting the system.

In this problem, you will analyze a system composed of two blocks, 1 and 2, of respective masses m1 and m2. To simplify the analysis, we will make several assumptions:

The blocks can move in only one dimension, namely, along the x axis.

The masses of the blocks remain constant.

The system is closed.

At time t, the x components of the velocity and the acceleration of block 1 are denoted by v1(t) and a1(t). Similarly, the x components of the velocity and acceleration of block 2 are denoted by v2(t)and a2(t). In this problem, you will show that the total momentum of the system is not changed by the presence of internal forces.

Find p(t), the x component of the total momentum of the system at time t. Express your answer in terms of m1, m2, v1(t), and v2(t).

Part B
Find the time derivative dp(t)/dt of the x component of the system's total momentum.

Express your answer in terms of a1(t), a2(t), m1, and m2.
Part C

The quantity ma (mass times acceleration) is dimensionally equivalent to which of the following?

a. momentum
b. energy
c. force
d. acceleration
e. inertia