Three point masses move along a horizontal -axis and interact only with each other

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

Three point masses move along a horizontal

x

-axis and interact only with each other. At an instant chosen as

t=0

, their conditions are: • Mass

M_1 = 5.0\,\text{kg}

is at

x = 0\,\text{m}

and is at rest. • Mass

M_2 = 2.0\,\text{kg}

is at

x = +2.0\,\text{m}

and moves with velocity

+3.0\,\text{m}\!\cdot\!\text{s}^{-1}

. • Mass

M_3 = 3.0\,\text{kg}

is at

x = -1.0\,\text{m}

and moves with velocity

-2.0\,\text{m}\!\cdot\!\text{s}^{-1}

. The system remains free of external horizontal forces until

t = 1.5\,\text{s}

. Then a brief external horizontal impulse delivers

+9.0\,\text{N}\!\cdot\!\text{s}

(eastward) to

M_1

only. (a) Determine the velocity of the center of mass for

0 \le t < 1.5\,\text{s}

. (b) Calculate the position of the center of mass at

t = 1.5\,\text{s}

. (c) Immediately after the impulse, find the new velocity of the center of mass. (d) Explain why the impulse applied to a single particle can alter the motion of the center of mass even though internal motions among the three masses may remain unchanged.

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