Three beads are placed along a thin rod. The first bead, of mass m 1 = 21 g, is

Question

Three beads are placed along a thin rod. The first bead, of mass m1= 21 g, is placed a distance d1= 1.3 cm from the left end of the rod. The second bead, of mass m2= 14 g, is placed a distand d2= 2.2 cm to the right of the first bead. The third bead, of mass m3= 54 g, is placed a distand d3= 3.1 cm to the right of the second bead. Assume an x-axis that points to the right.

A.) Write a symbolic equation for the location of the center of mass of the three beads relative to the left end of the rod, in terms of the variable given in the problem statement.

B.) Find the center of mass, in centimeters, relative to the left end of the rod.

C.) Write a symbolic equation for the location of the center of mass of the three beads relative to the center bead, in terms of the variables given in the problem statement.

D.) Find the center of mass, in cenitmeters, relative to the middle bead.

Explanation / Answer

here,

m1 = 21g

m2 = 14 g

m3 = 54 g

distances from left end of the rod

dl1 = 1.3 cm

dl2 = 1.3 + 2.2

dl2 = 3.5 cm

dl3 = 3.5 + 3.1 cm

dl3 = 6.6 cm

(a)

the centre of mass from the left end , x = (m1* d1 + m2*( d1+ d2) + m3* ( d1 + d2 + d3)) /( m1 + m2 + m3)

( b)

x = (m1* d1 + m2*( d1+ d2) + m3* ( d1 + d2 + d3)) /( m1 + m2 + m3)

x = ( 21*1.3 + 14 * 3.5 + 54*6.6)/( 21 + 14 + 54)

x = 5.48 cm

the centre of mass is 5.48 cm from the left end

(c)

the centre of mass from the left end , x = (- m1* d1 + m3* (d3)) /( m1 + m2 + m3)

( b)

x = (- m1* d1 + m3* ( d3)) /( m1 + m2 + m3)

x = ( - 21*1.3 + 54* 3.1)/( 21 + 14 + 54)

x = 1.77 cm

the centre of mass is 1.77 cm from the centre bead

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