Explanation Sketch the semicircle thick wire as in Figure 1. Consider the radius of the semicircle as r = 2 m . Consider the thickness of the wire is t . The equation for the semicircle is x 2 + y 2 = r 2 . Consider the distance x and y are as follows; x = r sin t = 2 sin t y = r cos t = 2 cos t Find the distance x ¯ using the equation; x ¯ = 1 2 π k ∫ − π / 2 π / 2 x k d s Here, the density constant is k . Substitute 2 sin t for x and integrate the equation. x ¯ = 1 2 π k ∫ − π / 2 π / 2 2 sin t ( 2 ) k d t = 2 π [ cos t ] − π 2 π / 2 = 2 π [ cos π 2 − cos ( π 2 ) ] = 0 Find the distance y ¯ using the equation

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition)

3rd Edition

ISBN: 9780134197319

Author: Richard Wolfson

Publisher: PEARSON

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Chapter 9.1, Problem 9.1GI

To determine

To find: the point of the center of mass for a thick wire bent into a semicircle.

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Chapter 8, Problem 75PP

Chapter 9.2, Problem 9.2GI

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Chapter 9 Solutions

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition)

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 - Roughly where is your center of mass when youre...Ch. 9 - Prob. 2FTD Ch. 9 - Prob. 3FTD

Ch. 9 - The momentum of a system of pool balls is the same...Ch. 9 - An hourglass is inverted and placed on a scale....Ch. 9 - Why are cars designed so that their front ends...Ch. 9 - Give three everyday examples of inelastic...Ch. 9 - Is it possible to have an inelastic collision in...Ch. 9 - Prob. 9FTD 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. 14E 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. 18E 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 - A 150-g trick baseball is thrown at 60 km/h. It...Ch. 9 - An object with kinetic energy K explodes into two...Ch. 9 - Two 140-kg satellites collide at an altitude where...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. 30E 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 - Find the center of mass of a pentagon with five...Ch. 9 - Wildlife biologists fire 20-g rubber bullets to...Ch. 9 - Consider a system of three equal-mass particles...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 - 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 - A cylindrical concrete silo is 4.0 m in diameter...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 - Youre investigating an accident in which a 1040-kg...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 - Find an expression for the impulse imparted by a...Ch. 9 - A 32-u oxygen molecule (O2) moving in the...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 - A 14-kg projectile is launched at 380 m/s at a 55...Ch. 9 - During a crash test, a car moving at 50 km/h...Ch. 9 - Use numerical or graphical techniques to estimate...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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the point of the center of mass for a thick wire bent into a semicircle.

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To find: the point of the center of mass for a thick wire bent into a semicircle.

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Chapter 9 Solutions