# 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 =

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Our tutors have indicated that to solve this problem you will need to apply the Intro to Momentum concept. You can view video lessons to learn Intro to Momentum. Or if you need more Intro to Momentum practice, you can also practice Intro to Momentum practice problems.