HW #8-solutions

HW #8-solutions - wolz(cmw2833 HW#8 Antoniewicz(57420 This...

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

wolz (cmw2833) – HW #8 – Antoniewicz – (57420) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Three particles are placed in the xy plane. A m 1 = 36 g particle is located at ( x 1 , y 1 ), where x 1 = 3 . 1 m and y 1 = 4 . 1 m and a m 2 = 46 g particle is located at ( x 2 , y 2 ), where x 2 = - 7 . 7 m and y 2 = - 7 . 5 m. What must be the x coordinate oF the m 3 = 25 g particle so that the center oF mass oF the three-particle system is at the origin? Correct answer: 9 . 704 m. Explanation: We know that the x coordinate oF the center oF mass is defned by x CM = m 1 x 1 + m 2 x 2 + m 3 x 3 m 1 + m 2 + m 3 Now, x is zero, and using the input values For m 1 , m 2 , m 3 and x 1 and x 2 , we fnd and solving For x 3 : x 3 = - m 1 x 1 - m 2 x 2 m 3 = 9 . 704 m 002 (part 1 of 2) 5.0 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 fgure. x y 60 N 40 N 40 N 30 N (0 , 0) (2 a, 0) (0 , 2 a ) (2 a, 2 a ) ±ind the x -coordinate oF the center oF grav- ity (as a multiple oF a ). Correct answer: 0 . 911765 a . Explanation: Let : x 1 = x 2 = 1 2 a , x 3 = x 4 = 3 2 a , W 1 = 60 N , W 2 = 40 N , W 3 = 40 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 defnition 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 + 40 N) + 3 (40 N + 30 N) 2 (170 N) a = 0 . 911765 a . 003 (part 2 of 2) 5.0 points ±ind the y -coordinate oF the center oF gravity (as a multiple oF a ). Correct answer: 0 . 970588 a . Explanation: Let : y 1 = y 4 = 1 2 a and y 2 = y 3 = 3 2 a .

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

View Full Document
wolz (cmw2833) – HW #8 – Antoniewicz – (57420) 2 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 (40 N + 40 N) 2 (170 N) a = 0 . 970588 a . 004 (part 1 of 2) 5.0 points A(n) 2 . 3 kg object moving with a speed of 8 . 6 m / s collides with a(n) 4 kg object mov- ing with a velocity of 8 . 8 m / s in a direction 39 . 0135 from the initial direction of motion of the 2 . 3 kg object. 8 . 6 m / s 8 . 8 m / s 4 kg 2 . 3 kg 39 . 0135 What is the speed of the two objects after the collision if they remain stuck together? Correct answer: 8 . 26658 m / s. Explanation: Let : m 1 = 2 . 3 kg , m 2 = 4 kg , m f = m 1 + m 2 = 6 . 3 kg , v 1 = 8 . 6 m / s , v 2 = 8 . 8 m / s , p 1 = m 1 v 1 = 19 . 78 kg m / s , p 2 = m 2 v 2 = 35 . 2 kg m / s , 2 p 1 p 2 = 2 m 1 v 1 m 2 v 2 = 1392 . 51 kg 2 m 2 / s 2 , p x = p 1 + p 2 cos θ = 47 . 1303 kg m / s , p y = p 2 sin θ = 22 . 1585 kg m / s , θ = 39 . 0135 , and π - θ = 140 . 987 . v 1 v 2 m 2 m 1 θ f φ m f The Fnal momentum is p f = ( m 1 + m 2 ) v f . (1) Momentum is conserved Vp 1 + 2 = f . (2) Using the law of cosines, we have p 2 1 + p 2 2 - 2 p 1 p 2 cos( π - θ ) = p 2 f . Solving for v f , we have v f = r p 2 1 + p 2 2 - 2 p 1 p 2 cos( π - θ ) m 1 + m 2 = b 1 (2 . 3 kg) + (4 kg) B × ± (391 . 248 kg 2 m 2 / s 2 ) 2 + (1239 . 04 kg 2 m 2 / s 2 ) 2 - (1392 . 51 kg 2 m 2 / s 2 ) cos(140 . 987 ) ² 1 / 2 = 8 . 26658 m / s . Alternate Solution: Since p 2 f = p 2 x + p 2 y , we have v f = r p 2 x + p 2 y m 1 + m 2 = b 1 (2 . 3 kg) + (4 kg) B × ± (2221 . 27 kg 2 m 2 / s 2 ) + (491 kg 2 m 2 / s 2 ) ² 1 / 2 = 8 . 26658 m / s .
wolz (cmw2833) – HW #8 – Antoniewicz – (57420) 3 005 (part 2 of 2) 5.0 points How much kinetic energy is lost during this collision?

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 / 11

HW #8-solutions - wolz(cmw2833 HW#8 Antoniewicz(57420 This...

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

View Full Document
Ask a homework question - tutors are online