The toy in the Figure is made of four identical balls of mass 0.5 kg placed at d

ID: 2116062 • Letter: T

Question

The toy in the Figure is made of four identical balls of mass 0.5 kg placed at different

positions and moving with different velocities, as specified in the table (positions are noted with

respect to the origin at (0,0)).

Determine:

Ball 1: position (25,50) velocity (22.5,0)

Ball 2: position (40,35) velocity (0,-22.5)

Ball 3: position (25,20) velocity (-22.5,0)

Ball 4: position (10,35) velocity (0,22.5)

a) The position and velocity of the center of mass.

b) Its moment of inertia with respect to the center of mass.

c) The angular momentum of the system.

d) The kinetic energy of the system.

a)the position of center of mass is

(X,Y) = [(mx1 + mx2 + mx3 + mx4/4m),(my1 + my2 + my3 + my4/4m)]

where x1 = 25 cm,x2 = 40 cm,x3 = 25 cm and x4 = 10 cm

and y1 = 50 cm,y2 = 35 cm,y3 = 20 cm and y4 = 35 cm

similarly,the velocity of center of mass is

(Vx,Vy) = [(mv1x + mv2x + mv3x + mv4x/4m),(mv1y + mv2y + mv3y + mv4y/4m)]

where v1x = 22.5 cm/s,v2x = 0,v3x = -22.5 cm/s and v4y = 0

and v1y = 0,v2y = -22.5 cm/s,v3y = 0 and v4y = 22.5 cm/s

b)the moment of inertia is

I = (1/2)m x (X^2 + Y^2)

c)the angular momentum is

L = m x v x r

where v = (Vx^2 + Vy^2)^1/2

and r = (X^2 + Y^2)^1/2

d)the kinetic energy is

K = (1/2)m x v^2

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