An object of mass 3M, moving in the +x direction at speed v0, breaks into two pi

Question

An object of mass 3M, moving in the +x direction at speed v0, breaks into two pieces of mass M and 2M as shown in the figure below. 1=49.0 and 2=34.0, determine the final velocities of the resulting pieces in terms of v0.

1) Determine the x component of the velosity of the smaller piece v1x in terms of v0. (Express your answer to three significant figures.) v0

2) Determine the y component of the velosity of the smaller piece v1y in terms of v0. (Express your answer to three significant figures.) v0

3) Determine the x component of the velosity of the larger piece v2x in terms of v0. (Express your answer to three significant figures.) v0

4) Determine the y component of the velosity of the larger piece v2y in terms of v0. (Express your answer to three significant figures.) v0

Explanation / Answer

1) 2M with 34 degree above the axis and M 49 deg below the axis.

Using momentum conservation,

3M (v0 i)   = 2Mv2(cos34i + sin34j) + Mv1(cos49i + sin49j)

3Mv0i + 0j = (1.66Mv2 + 0.656Mv1)i + (1.12Mv2 - 0.755Mv1) j

so

1.66Mv2 + 0.656Mv1 = 3M

0.656v1 + 1.66v2 = 3v0 ..........(i)

and 1.12Mv2 - 0.755Mv1 = 0

1.12v2 - 0.755v1 = 0

v2 = 0.675v1

putting in (i)

0.656v1 + 1.66(0.675v1) = 3v0

v1 = 1.689v0

v2 = 1.139v0

1) v1x = v1cos49 = 1.108v0

2) v1y = v1sin49 = 1.274v0

3) v2x = v2cos34 = 0.944v0

4)v2y = v2sin34 =   0.637v0

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