An object of mass 3 M , moving in the + x direction at speed v 0, breaks into tw

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=42.0 and 2=27.0, 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.)

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

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

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

Explanation / Answer

1 = 42.0 and 2 = 27.0  

using horizontally conservation of momentum

3 m vo = 2 m v2 cos2 + m v1 cos1

3 vo = 2 v2 cos2 + v1 cos1   

3 vo = 2 v2 cos27+ v1 cos42

3 vo = 2 v2 0.891+ v1 0.743

3 vo = 1.782 v2 + 0.743 v1 ------- 1

vertically

2 mv2 sin2 = m v1 sin1

2 v2 sin27= v1 sin42

v2 = 0.736 v1 ------- 2

using equations 1 and 2

3 vo = 1.782 v2 + 0.743 v1

3 vo = 1.782 X 0.736 v1 + 0.743 X v1

v1 = 1.46 vo

and

v2 = 0.736 v1

= 0.736 X 1.46 X vo

= 1.0749 vo

now v1x = v1 cos42

= 1.46 vo X 0.743

v1x = 1.084 vo  

v1y = v1 sin42

v1y = 0.976 vo  

v2x = v2 cos27

= 1.0749 vo X cos27

v2x = 0.9577 vo

v2y = v2 sin27

v2y = 0.5696 vo

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.