Find the time derivative of the x component

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Reference no: EM132104861

Question: 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?

momentum
energy
force
acceleration
inertia

Acceleration is due to which of the following physical quantities?

velocity
speed
energy
momentum
force

Since we have assumed that the system composed of blocks 1 and 2 is closed, what could be the reason for the acceleration of block 1?

the large mass of block 1

air resistance
Earth's gravitational attraction
a force exerted by block 2 on block 1
a force exerted by block 1 on block 2

Let us denote the x component of the force exerted by block 1 on block 2 by , and the x component of the force exerted by block 2 on block 1 by . Which of the following pairs equalities is a direct consequence of Newton's second law?

F12=m2a2 and F21=m1a1
F12=m1a1 and F21=m2a2
F12=m1a2 and F21=m2a1
F12=m2a1 and F21=m1a2

Let us recall that we have denoted the force exerted by block 1 on block 2 by , and the force exerted by block 2 on block 1 by . If we suppose that is greater than , which of the following statements about forces is true?

|F12|>|F21|
|F21|>|F12|

Both forces have equal magnitudes.

Now recall the expression for the time derivative of the x component of the system's total momentum: . Considering the information that you now have, choose the best alternative for an equivalent expression to .

0
nonzero constant
kt
kt2

Reference no: EM132104861

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