In otherwise empty space is a system of 4 particles, each of the same mass. the accelerations of the particles are as follows: a1 = ˆi a a2 = ˆj a 2 a3 = −( ˆi +ˆj) (2 a) a4 = (ˆi −ˆj) (3 a), where a > 0 is a constant. what is the acceleration of the center of mass of the system of 4 particles?

(a i - 2a j) / 2

Explanation:

a1 = a i

a2 = a j

a3 = - (i + j) (2a) = - 2a i - 2a j

a4 = (i - j) (3a) = 3a i - 3a j

Let the mass of each particle is m.

Use the formula of acceleration of centre of mass

a cm = (m1 a1 + m2 a2 + m3 a3 + m4 a4) / (m1 + m2 + m3 + m4)

a cm = (a i + aj - 2a i - 2a j + 3a i - 3a j) / 4

a cm = ( 2a i - 4a j) / 4

a cm = (a i - 2a j) / 2

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the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.