total momentum: The vector sum of the individual momenta of all objects constitu
ID: 1451140 • Letter: T
Question
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. 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 =
Explanation / Answer
a) at time t
total momentum = sum of momentum of two particles
P(t) = m1*V1(t) + m2*v2(t)
b) dP(t)/dt = d(m1*V1(t) + m2*v2(t))/dt
= m1*dV1(t)/dt + m2*dV2(t)/dt
= m1*a1(t) + m2*a2(t)
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