{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW14.sol - homework 14 RAHMAN TARIQUE Due 3:00 am Question...

This preview shows pages 1–4. Sign up to view the full content.

homework 14 – RAHMAN, TARIQUE – Due: Mar 26 2008, 3:00 am 1 Question 1, chap 10, sect 2. part 1 of 2 10 points Three spherical masses are located in a plane at the positions shown in the figure be- low. A has mass 15 . 6 kg, B has mass 50 . 7 kg, and C has mass 46 . 7 kg. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 A B C y Distance (m) x Distance (m) Three Masses in a Plane Figure: Drawn to scale. Calculate the x -coordinate of the center of mass. Correct answer: 6 . 0323 m (tolerance ± 3 %). Explanation: Basic Concepts: x cm = i m i x i i m i (1) y cm = i m i y i i m i (2) There is no acceleration, so a x = a y = 0 . Solution: Let: x a = 2 m , y a = 8 . 5 m , m a = 15 . 6 kg , x b = 5 m , y b = 4 m , m b = 50 . 7 kg , x c = 8 . 5 m , y c = 6 m , m c = 46 . 7 kg . x cm = i m i x i i m i (1) = m a x a + m b x b + m c x c m a + m b + m c = (15 . 6 kg) (2 m) + (50 . 7 kg) (5 m) (15 . 6 kg) + (50 . 7 kg) + (46 . 7 kg) + (46 . 7 kg) (8 . 5 m) (15 . 6 kg) + (50 . 7 kg) + (46 . 7 kg) = (681 . 65 m kg) (113 kg) = 6 . 0323 m . Question 2, chap 10, sect 2. part 2 of 2 10 points Calculate the y -coordinate of the center of mass. Correct answer: 5 . 44779 m (tolerance ± 3 %). Explanation: y cm = i m i y i i m i (1) = m a y a + m b y b + m c y c m a + m b + m c = (15 . 6 kg) (8 . 5 m) + (50 . 7 kg) (4 m) (15 . 6 kg) + (50 . 7 kg) + (46 . 7 kg) + (46 . 7 kg) (6 m) (15 . 6 kg) + (50 . 7 kg) + (46 . 7 kg) = (615 . 6 m kg) (113 kg) = 5 . 44779 m . Question 3, chap 10, sect 2. part 1 of 2 10 points A square plate is produced by welding to- gether four smaller square plates, each of side a . The weight of each of the four plates is shown in the figure. x y 60 N 20 N 60 N 30 N (0 , 0) (2 a, 0) (0 , 2 a ) (2 a, 2 a )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
homework 14 – RAHMAN, TARIQUE – Due: Mar 26 2008, 3:00 am 2 Find the x -coordinate of the center of grav- ity (as a multiple of a ). Correct answer: 1 . 02941 a (tolerance ± 1 %). Explanation: Let : x 1 = x 2 = 1 2 a , x 3 = x 4 = 3 2 a , W 1 = 60 N , W 2 = 20 N , W 3 = 60 N , and W 4 = 30 N . y x W 1 W 2 W 3 W 4 a 2 3 a 2 a 2 3 a 2 The total weight is W = W 1 + W 2 + W 3 + W 4 = 170 N . Applying the definition of center of gravity, x cg = i W i x i W 1 + W 2 + W 3 + W 4 = ( W 1 + W 2 ) a 2 + ( W 3 + W 4 ) 3 a 2 W = (60 N + 20 N) + 3 (60 N + 30 N) 2 (170 N) a = 1 . 02941 a . Question 4, chap 10, sect 2. part 2 of 2 10 points Find the y -coordinate of the center of grav- ity (as a multiple of a ). Correct answer: 0 . 970588 a (tolerance ± 1 %). Explanation: Let : y 1 = y 4 = 1 2 a and y 2 = y 3 = 3 2 a . y cg = i W i y i W 1 + W 2 + W 3 + W 4 = ( W 1 + W 4 ) a 2 + ( W 2 + W 3 ) 3 a 2 W = (60 N + 30 N) + 3 (20 N + 60 N) 2 (170 N) a = 0 . 970588 a . Question 5, chap 10, sect 2. part 1 of 1 10 points A rectangular metal plate has uniform den- sity and thickness. A circular hole is cut out of the plate as shown on the figure: 10 8 6 4 2 0 2 4 6 8 10 10 8 6 4 2 0 2 4 6 8 10 Calculate the x coordinate of the remaining plate’s center of mass. Note: by reasons of symmetry, the y coor- dinate of the center of mass is zero. Correct answer: 1 . 30353 (tolerance ± 1 %). Explanation: Notations: The x coordinate of the rectangle ranges from x 1 to x 2 , the y coordinate from Y to + Y ;
homework 14 – RAHMAN, TARIQUE – Due: Mar 26 2008, 3:00 am 3 the hole has radius R and center at ( x c , 0).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 8

HW14.sol - homework 14 RAHMAN TARIQUE Due 3:00 am Question...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online