SOL23
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SOL23

Course: PHY phy 303k, Spring 2010

School: University of Texas

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Thevalingam, Donald Homework 23 Due: Mar 21 2007, midnight Inst: Eslami This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Three particles are located in a coordinate system as shown in the gure below. The acceleration of gravity is 9.8 m/s2 . The mass 8 kg is...

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Donald Thevalingam, Homework 23 Due: Mar 21 2007, midnight Inst: Eslami This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Three particles are located in a coordinate system as shown in the gure below. The acceleration of gravity is 9.8 m/s2 . The mass 8 kg is located at the origin, the mass 3 kg is located on the x coordinate, and the mass 6 kg is located on the y coordinate. y 6 kg 4m 8 kg 3 kg x 13 m keywords: 1 002 (part 1 of 1) 10 points A uniform at plate of metal is situated in the reference frame shown in the gure below. 5 4 y 3 2 1 0 01 23 45 x 67 Find the distance of the center of gravity from the origin. Correct answer: 2.69371 m. Explanation: The center of gravity of the x and y components from the origin respectively are m 0 0 + m 1 x1 xc = m0 + m 1 + m 2 (3 kg) (13 m) = (8 kg) + (3 kg) + (6 kg) = 2.29412 m and m 0 0 + m 2 y2 yc = m0 + m 1 + m 2 (6 kg) (4 m) = (8 kg) + (3 kg) + (6 kg) = 1.41176 m . Then the distance of the center of gravity from the origin is d= = 2 x 2 + yc c Calculate the x coordinate of the center of mass of the metal plate. Correct answer: 2.81818 . Explanation: Basic Concept: The center of mass coordinate is x dm , x m where m dm . Solution: Let (x1 , y1 ) = (0, 0) (x2 , y2 ) = (7, 0) (x3 , y3 ) = (4, 3) (x4 , y4 ) = (0, 3) . The x-coordinate of the center of mass is Xcm = xcm rectangle Arectangle Arectangle + Atriangle xcm triangle Atriangle + Arectangle + Atriangle (2) (12) + (5) (4.5) = (12) + (4.5) 46.5 = 16.5 = 2.81818 , (2.29412 m)2 + (1.41176 m)2 where Arectangle = x3 y3 = (4) (3) = 2.69371 m . 8 9 10 Thevalingam, Donald Homework 23 Due: Mar 21 2007, midnight Inst: Eslami = 12 1 = (x 2 x 3 ) y 3 2 1 = (7 4) 3 2 = 4. 5 1 = x3 2 1 =4 2 =2 1 = x 3 + (x 2 x 3 ) 3 1 = 4 + (7 4) 3 = 5. Basic Concepts: xcm = ycm = i m i xi i mi i m i yi i mi 2 Atriangle (1) (2) xcm rectangle There is no acceleration, so ax = ay = 0 . Solution: Let: xa = 2 m , ya = 0.5 m , ma = 50.7 kg , xb = 6.5 m , yb = 0.5 m , mb = 19.7 kg , xc = 5.5 m , yc = 9 m , mc = 42.9 kg . xcm triangle xcm = Note: This problem a has dierent gure for each student. keywords: 003 (part 1 of 2) 10 points Three spherical masses are located in a plane at the positions shown in the gure below. A has mass 50.7 kg, B has mass 19.7 kg, and C has mass 42.9 kg. Three Masses in a Plane 10 C 9 8 y Distance (m) 7 6 5 4 3 2 1 0 0 1 A B 2 ycm = = = i m i xi i mi m a xa + m b xb (1) + m c xc ma + m b + m c (50.7 kg) (2 m) + (19.7 kg) (6.5 m) = (50.7 kg) + (19.7 kg) + (42.9 kg) (42.9 kg) (5.5 m) + (50.7 kg) + (19.7 kg) + (42.9 kg) (465.4 m kg) = (113.3 kg) = 4.10768 m . 004 (part 2 of 2) 10 points Calculate the y -coordinate of the center of mass. Your answer must be within 3%. Correct answer: 3.71845 m. Explanation: i m i yi i mi m a ya + m b yb (1) 3 4 5 6 7 8 9 10 x Distance (m) Figure: Drawn to scale. Calculate the x-coordinate of the center of mass. Your answer must be within 3%. Correct answer: 4.10768 m. Explanation: + m c yc ma + m b + m c (50.7 kg) (0.5 m) + (19.7 kg) (0.5 m) = (50.7 kg) + (19.7 kg) + (42.9 kg) (42.9 kg) (9 m) + (50.7 kg) + (19.7 kg) + (42.9 kg) (421.3 m kg) = (113.3 kg) = 3.71845 m . Thevalingam, Donald Homework 23 Due: Mar 21 2007, midnight Inst: Eslami keywords: 005 (part 1 of 2) 10 points Three particles are placed in the xy plane. A m1 = 30 g particle is located at (x1 , y1 ), where x1 = 8.7 m and y1 = 2.6 m and a m2 = 19 g particle is located at (x2 , y2 ), where x2 = 3.8 m and y2 = 1.4 m . What must be the x coordinate of the m3 = 30 g particle so that the center of mass of the three-particle system is at the origin? Correct answer: 6.29333 m. Explanation: We know that the x coordinate of the center of mass is dened by xCM = m 1 x1 + m 2 x2 + m 3 x3 . m1 + m 2 + m 3 3 Now, xCM is zero, and using the input values for m1 , m2 , m3 and x1 and x2 , we nd and solving for x3 : x3 = m 1 x 1 m 2 x 2 = 6.29333 m . m3 006 (part 2 of 2) 10 points What must be the y coordinate of the m3 = 30 g particle so that the center of mass of the three-particle system is at the origin? Correct answer: 1.71333 m. Explanation: Analogously, we have yCM = m 1 y1 + m 2 y2 + m 3 y3 m1 + m 2 + m 3 Since yCM is zero, using the input values for m1 , m2 , m3 and y1 , y2 : y3 = m 1 y 1 m 2 y 2 = 1.71333 m . m3 keywords:

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University of Texas - PHY - phy 303k
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University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 25 Due: Apr 3 2007, midnight Inst: Eslami This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of
University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 26 Due: Apr 10 2007, midnight Inst: Eslami This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 of
University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 27 Due: Apr 27 2007, midnight Inst: Eslami This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 28 Due: May 31 2007, midnight Inst: Eslami This print-out should have 34 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 29 Due: Apr 27 2007, midnight Inst: Eslami This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 30 Due: Apr 30 2007, midnight Inst: Eslami This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - PHY - phy 303k
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University of Texas - PHY - phy 303k
Thevalingam, Donald Homework 32 Due: May 24 2007, midnight Inst: Eslami This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. The due time is Central time. 001 (part 1 o
University of Texas - PHY - phy 303k
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