# Problem: 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. Part A 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). p(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 m1, m2, a1(t), and a2(t). dp(t)/dt =

###### FREE Expert Solution

Momentum:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Part A

The total momentum of the system is equal to the sum of momenta of the two particles. ###### Problem Details

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.

Part A 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). p(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 m1, m2, a1(t), and a2(t). dp(t)/dt =