Chapter 6, Problem 66AP

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# A 0.400-kg blue bead slides on a frictionless, curved wire, starting from rest at point Ⓐ in Figure P6.66, where h = 1.50 m. At point Ⓑ. the bead collides elastically with a 0.600-kg green bead at rest. Find the maximum height the green bead rises as it moves up the wire.Figure P6.66

To determine
The height to which mg rises after collision.

Explanation

Explanation

Given Info:

Mass of the blue bead at position A is 0.400â€‰kg , the mass of the green bead at B is 0.600â€‰kg , initial speed of green mass at position B is zero.

Formula to calculate the potential energy of the blue bead at position A is,

PEbA=mbgh (I)

• PEbA is the potential energy of the blue bead at position A
• mb is the mass of the blue bead
• g is the acceleration due to gravity
• h is the height of the position A from the B

Formula to calculate the kinetic energy of the blue bead at position B is,

• KEbB=12mbvb2 (II)
• KEbB is the kinetic energy of the blue bead at point B
• vb is the speed of blue bead at point B just before collision

According to conservation of energy, Potential energy of the blue bead at position A will be equal to the kinetic energy of the blue bead at position B.

Equate (I) and (II) to find vb .

12mbvb2=mbghvb2=2ghvb=2gh

Substitute 9.8â€‰mâ‹…sâˆ’2 for g and 1.50â€‰m for h to calculate vb

vb=2(9.8â€‰mâ‹…sâˆ’2)(1.50â€‰m)=98â€‰mâ‹…sâˆ’2=5.42â€‰mâ‹…sâˆ’1

Collisions conserves momentum. Momentum before collision is equal to momentum after collision.

mbvb+mgvg=mbvbâ€²+mgvgâ€² (III)

• vg is the velocity of the green bead before collision
• vbâ€² is the velocity of the blue bead after collision
• vgâ€² is the velocity of the green bead after collision
• mg is the mass of the green bead

For elastic collision,

vbâˆ’vg=âˆ’(vbâ€²âˆ’vgâ€²)

Initial velocity of m2 is zero vg=0 .

Use 0 for vg in the above equation and rewrite the above equation in terms of vgâ€² .

vbâˆ’(0)=âˆ’(vbâ€²âˆ’vgâ€²)vgâ€²=vb+vbâ€² (IV)

Substitute equation (IV) in equation (III) to calculate vbâ€²

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