Chapter 8

# Chapter 8 - CHAPTER 8 Systems of Particles and Conservation...

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Unformatted text preview: CHAPTER 8 Systems of Particles and Conservation of Momentum 1* Â· Give an example of a three-dimensional object that has no mass at its center of mass. A hollow sphere. 2 Â· Three point masses of 2 kg each are located on the x axis at the origin, x = 0.20 m, and x = 0.50 m. Find the center of mass of the system. Use Equ. 8-4; note that y cm = 0 x cm = [(2 Ã— 0 + 2 Ã— 0.2 + 2 Ã— 0.5)/6] m = 0.233 m 3 Â· A 24-kg child is 20 m from an 86-kg adult. Where is the center of mass of this system? Take the origin at the position of the child. Use Equ. 8-4 x cm = (86 Ã— 20/110) m = 15.6 m 4 Â· Three objects of 2 kg each are located in the xy plane at points (10 cm, 0), (0, 10 cm), and (10 cm, 10 cm). Find the location of the center of mass. Use Equ. 8-4 x cm = [(10 Ã— 2 + 10 Ã— 2)/6] cm = 6.67 cm; y cm = [(10 Ã— 2 + 10 Ã— 2)/6] cm = 6.67 cm 5* Â· Find the center of mass x cm of the three masses in Figure 8-46. Use Equ. 8-4 x cm = [(1 Ã— 1 + 2 Ã— 2 + 8 Ã— 4)/11] m = 3.36 m 6 Â· Alley Oopâ€™s club-ax consists of a symmetrical 8-kg stone attached to the end of a uniform 2.5-kg stick that is 98 cm long. The dimensions of the club-ax are shown in Figure 8-47. How far is the center of mass from the handle end of the club-ax? 1. Locate CM of stick and of stone 2. Use Equ. 8-4 By symmetry, x cm (stick) = 0.49 m; x cm (stone) = 0.89 m x cm = [(2.5 Ã— 0.49 + 8 Ã— 0.89)/10.5] m = 0.795 m 7 Â· Three balls A, B, and C , with masses of 3 kg, 1 kg, and 1 kg, respectively, are connected by massless rods. The balls are located as in Figure 8-48. What are the coordinates of the center of mass? Use Equ. 8-4 x cm = [(3 Ã— 2 + 1 Ã— 1 + 1 Ã— 3)/5] m = 2 m Chapter 8 Systems of Particles and Conservation of Momentum y cm = [(3 Ã— 2 + 1 Ã— 1 + 1 Ã— 0)/5] m = 1.4 m 8 Â· By symmetry, locate the center of mass of an equilateral triangle of side length a with one vertex on the y axis and the others at (- a /2, 0) and (+ a /2, 0). 1. Draw the triangle; assume vertex at y > 0 2. Locate the intersection of the bisectors; see sketch 3. Give the coordinates of CM x cm = 0; y cm = 1/2 a tan 30 o = 0.289 a 9* Â·Â· The uniform sheet of plywood in Figure 8-49 has a mass of 20 kg. Find its center of mass. We shall consider this as two sheets, a square sheet of 3 m side length and mass m 1 and a rectangular sheet 1m Ã— 2m with a mass of - m 2 . Let coordinate origin be at lower left hand corner of the sheet. Let s be the surface density of the sheet. 1. Find x cm ( m 1 ), y cm ( m 1 ) and x cm ( m 2 ), y cm ( m 2 ) 2. Determine m 1 and m 2 3. Use Equ. 8-4 By symmetry, x cm ( m 1 ) = 1.5 m, y cm ( m 1 ) = 1.5 m and x cm ( m 2 ) = 1.5 m, y cm ( m 2 ) = 2.0 m m 1 = 9 s kg, m 2 = 2 s kg x cm = (9 s Ã— 1.5 - 2 s Ã— 1.5)/7 s = 1.5 m y cm = (9 s Ã— 1.5 - 2 s Ã— 2.0)/7 s = 1.36 m 10 Â·Â· Show that the center of mass of a uniform semicircular disk of radius R is at a point (4/3 p ) R from the center of the circle....
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## This homework help was uploaded on 04/09/2008 for the course PHYS 161,260,27 taught by Professor Staff during the Spring '08 term at Maryland.

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Chapter 8 - CHAPTER 8 Systems of Particles and Conservation...

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