텍사스4회솔루션

텍사스4회솔루션

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: min (mm64262) – Homework 4 – lee – (GEDB00864) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A frictionless roller coaster is given an ini- tial velocity of v at height h = 22 m . The radius of curvature of the track at point A is R = 25 m. The acceleration of gravity is 9 . 8 m / s 2 . R 2 3 h h h ′ v A B Find the maximum value of v so that the roller coaster stays on the track at A solely because of gravity. Correct answer: 10 . 0631 m / s. Explanation: let : h = 22 m and R = 25 m . At point A , the weight of coaster must be just large enough to supply the centripetal acceleration. Thus m parenleftbigg v 2 A R parenrightbigg = mg , or v 2 A = Rg . Applying conservation of mechanical energy from the start to point A , 1 2 mv 2 + mg h = 1 2 mv 2 A + mg parenleftbigg 2 h 3 parenrightbigg v 2 = v 2 A- 2 g h 3 = R 2 g 2- 2 g h 3 v = radicalbigg Rg- 2 g h 3 = radicalBigg g parenleftbigg R- 2 h 3 parenrightbigg = radicalBigg (9 . 8 m / s 2 ) bracketleftbigg 25 m- 2 (22 m) 3 bracketrightbigg = 10 . 0631 m / s . 002 (part 2 of 2) 10.0 points Using the value of v calculated in question 1, determine the value of h ′ that is necessary if the roller coaster just makes it to point B. Correct answer: 27 . 1667 m. Explanation: If the speed of the coaster is to be zero at point B, conservation of mechanical energy from the start to point B gives 0 + mg h ′ = 1 2 mv 2 + mg h = 1 2 mg parenleftbigg R- 2 h 3 parenrightbigg + mg h h ′ = R 2 + 2 h 3 = 25 m 2 + 2 (22 m) 3 = 27 . 1667 m . 003 (part 1 of 3) 10.0 points A block is released from point A on a track ABCD as shown in the figure. Point A is higher than points B , C , and D . The track is frictionless except for a portion BC which has a coefficient of friction μ . The block travels down the track and hits the spring with spring constant k . The acceleration of gravity is 9 . 8 m / s 2 . A 10 kg 4 . 2m E h ′ μ B C D 3 . 3 m 2 . 8 m k = 142 kN / m F min (mm64262) – Homework 4 – lee – (GEDB00864) 2 Note: The distance h ′ is not to scale. If the spring compresses 7 cm, find the coefficient of friction μ . Correct answer: 0 . 19697. Explanation: Let : ℓ = 3 . 3 m , m = 10 kg , h = 4 . 2 m , and k = 1 . 42 × 10 5 N / m . Basic Concepts: Conservation of Energy with Dissipative Forces U spring = 1 2 k x 2 . Solution: The initial potential energy of the block is E i = mg h = (10 kg)(9 . 8 m / s 2 )(4 . 2 m) = 411 . 6 J . The friction force on the path where there is friction is F friction = μmg and so the me- chanical energy lost due to friction is E μ = μmg ℓ....
View Full Document

This note was uploaded on 05/24/2011 for the course ENGINEERIN 1 taught by Professor Lee during the Spring '11 term at Sungkyunkwan.

Page1 / 9

텍사스4회솔루션

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online