Explanation The figure 1 shows the center of mass of solid hemisphere. Consider elemental discs as shown in the figure. The mass of the elemental disc is, d m = ρ d V (I) Here, d m is the elemental mass of the disc, ρ is the density of the disc, and d V is the change in volume of the elemental disc. The relation between mass and density is, ρ = M V (II) Here, M is the mass of the solid hemisphere and V is the volume of the hemisphere. The volume of the hemisphere is, V = 2 3 π R 3 (III) Here, R is the radius of the hemisphere. The change in volume of the elemental disc is, d V = π r 2 d y (IV) Here, r is the radius of the elemental disc and d y is the thickness of the disc. The radius of the elemental disc is, r = R 2 − y 2 (V) The center of mass of the solid hemisphere is, y c m = ∫ d m ⋅ y ∫ d m (VI) Conclusion: Substitute the equations (II) and (III) in equation (I). d m = M V d V = M 2 3 π R 3 d V Substitute the equations (IV) and (V) in above relation

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ISBN: 9780136780984

Author: Wolfson

Publisher: PEARSON

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Chapter 9, Problem 55P

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The expression for the center of mass of solid hemisphere.

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Chapter 9, Problem 54P

Chapter 9, Problem 56P

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ESSENTIAL UNIV.PHYS.-MOD.MASTERING(18W)

Ch. 9.1 - Prob. 9.1GI Ch. 9.2 - A 500-g fireworks rocket is moving with velocity...Ch. 9.2 - Two skaters toss a basketball back and forth on...Ch. 9.3 - Which of the following systems has (1) zero...Ch. 9.4 - Which of the following qualifies as a collision?...Ch. 9.5 - Which of the following collisions qualify as...Ch. 9.6 - One ball is at rest on a level floor. A second...Ch. 9 - Prob. 1FTD Ch. 9 - Prob. 2FTD Ch. 9 - The momentum of a system of pool balls is the same...

Ch. 9 - Is it possible to have an inelastic collision in...Ch. 9 - Prob. 5FTD Ch. 9 - Why dont we need to consider external forces...Ch. 9 - How is it possible to have a collision between...Ch. 9 - A pitched baseball moves no faster than the...Ch. 9 - Two identical satellites are going in opposite...Ch. 9 - Prob. 10E Ch. 9 - Two particles of equal mass m are at the vertices...Ch. 9 - Rework Example 9.1 with the origin at the center...Ch. 9 - Three equal masses lie at the corners of an...Ch. 9 - Prob. 14E Ch. 9 - A popcorn kernel at rest in a hot pan bursts into...Ch. 9 - A 60-kg skater, at rest on frictionless ice,...Ch. 9 - A plutonium-239 nucleus at rest decays into a...Ch. 9 - A toboggan of mass 8.6 kg is moving horizontally...Ch. 9 - Prob. 19E Ch. 9 - An object with kinetic energy K explodes into two...Ch. 9 - Prob. 21E Ch. 9 - High-speed photos of a 220-g flea jumping...Ch. 9 - Youre working in mission control for an...Ch. 9 - In a railroad switchyard, a 56-ton freight car is...Ch. 9 - In a totally inelastic collision between two equal...Ch. 9 - Prob. 26E Ch. 9 - Two identical trucks have mass 5500 kg when empty,...Ch. 9 - An alpha particle (4He) strikes a stationary gold...Ch. 9 - Playing in the street, a child accidentally tosses...Ch. 9 - A block of mass m undergoes a one-dimensional...Ch. 9 - A proton moving at 6.9 Mm/s collides elastically...Ch. 9 - A head-on, elastic collision between two particles...Ch. 9 - Example 8.5: A lithium-5 nucleus (5Li) is moving...Ch. 9 - Example 9.5: A lithium-5 nucleus (’Li) decays into...Ch. 9 - Example 9.5: A space craft consists of a 549-kg...Ch. 9 - Prob. 36E Ch. 9 - Prob. 37E Ch. 9 - Prob. 38E Ch. 9 - Prob. 39E Ch. 9 - Prob. 40E Ch. 9 - Find the center of mass of a pentagon with five...Ch. 9 - Wildlife biologists fire 20-g rubber bullets to...Ch. 9 - Prob. 43P Ch. 9 - Youre with 19 other people on a boat at rest in...Ch. 9 - A hemispherical bowl is at rest on a frictionless...Ch. 9 - Physicians perform needle biopsies to sample...Ch. 9 - Find the center of mass of the uniform, solid cone...Ch. 9 - A firecracker, initially at rest, explodes into...Ch. 9 - An 11,000-kg freight car rests against a spring...Ch. 9 - On an icy road, a 1200-kg car moving at 50 km/h...Ch. 9 - Prob. 51P Ch. 9 - A 1250-kg car is moving with velocity...Ch. 9 - Masses m and 3m approach at the same speed v and...Ch. 9 - A 238U nucleus is moving in the x-direction at 5.0...Ch. 9 - Prob. 55P Ch. 9 - A 42-g firecracker is at rest at the origin when...Ch. 9 - A 60-kg astronaut floating in space simultaneously...Ch. 9 - Assuming equal-mass pieces in Exercise 24, find...Ch. 9 - A 62-kg sprinter stands on the left end of a...Ch. 9 - Youre a production engineer in a cookie factory,...Ch. 9 - Mass m, moving at speed 2v, approaches mass 4m,...Ch. 9 - Verify explicitly that kinetic energy is conserved...Ch. 9 - While standing on frictionless ice, you (mass 65.0...Ch. 9 - Youre an accident investigator at a scene where a...Ch. 9 - A fireworks rocket is launched vertically upward...Ch. 9 - Two objects moving in opposite directions with the...Ch. 9 - Explosive bolts separate a 950-kg communications...Ch. 9 - Youre working in quality control for a model...Ch. 9 - A 400-mg popcorn kernel is skittering across a...Ch. 9 - Two identical objects with the same initial speed...Ch. 9 - A proton (mass 1 u) moving at 6.90 Mm/s collides...Ch. 9 - Two objects, one initially at rest, undergo a...Ch. 9 - Blocks B and C have masses 2m and m, respectively,...Ch. 9 - Derive Equation 9.15b.Ch. 9 - An object collides elastically with an equal-mass...Ch. 9 - A proton (mass 1 u) collides elastically with a...Ch. 9 - Two identical billiard balls are initially at rest...Ch. 9 - A 114-g Frisbee is lodged on a tree branch 7.65 m...Ch. 9 - You set a small ball of mass m atop a large ball...Ch. 9 - A car moving at speed v undergoes a...Ch. 9 - A 200-g block is released from rest at a height of...Ch. 9 - Prob. 83P Ch. 9 - A block of mass m1 undergoes a one-dimensional...Ch. 9 - Two objects of unequal mass, one initially at...Ch. 9 - Prob. 86P Ch. 9 - Find the center of mass of a uniform slice of...Ch. 9 - In a ballistic pendulum demonstration gone bad, a...Ch. 9 - An 80-kg astronaut has become detached from the...Ch. 9 - Prob. 90P Ch. 9 - A thin rod extends from x = 0 to x = L. It carries...Ch. 9 - Model rocket motors are specified by giving the...Ch. 9 - A block of mass M is moving at speed r0 on a...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...Ch. 9 - Youre interested in the intersection of physics...

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