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