This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: patel (kp9583) HW7 Mackie (20211) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points In an arcade game a 0 . 145 kg disk is shot across a frictionless horizontal surface by com- pressing it against a spring and releasing it. If the spring has a spring constant of 213 N / m and is compressed from its equi- librium position by 5 cm, find the speed with which the disk slides across the surface. Correct answer: 1 . 91635 m / s. Explanation: From conservation of mechanical energy, we have: 1 2 mv 2 f = 1 2 k x 2 i , v f = radicalBigg k x 2 i m = radicalBigg (213 N / m)(0 . 05 m) 2 . 145 kg = 1 . 91635 m / s . 002 10.0 points A 7 . 9 kg mass is attached to a light cord that passes over a massless, frictionless pulley. The other end of the cord is attached to a 3 . 8 kg mass. 4 . 6 m 7 . 9 kg 3 . 8 kg Use conservation of energy to determine the final speed of the first mass after it has fallen (starting from rest) 4 . 6 m . The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 5 . 6209 m / s. Explanation: Let : m 1 = 7 . 9 kg , m 2 = 3 . 8 kg , and = 4 . 6 m . Consider the free body diagrams 7 . 9 kg 3 . 8 kg T T m 1 g m 2 g a a Let the figure represent the initial config- uration of the pulley system (before m 1 falls down). From conservation of energy K i + U i = K f + U f 0 + m 1 g = m 2 g + 1 2 m 1 v 2 + 1 2 m 2 v 2 ( m 1- m 2 ) g = 1 2 ( m 1 + m 2 ) v 2 Therefore v = radicalBigg ( m 1- m 2 ) ( m 1 + m 2 ) 2 g = radicalBigg 7 . 9 kg- 3 . 8 kg 7 . 9 kg + 3 . 8 kg radicalBig 2 (9 . 8 m / s 2 )(4 . 6 m) = 5 . 6209 m / s . keywords: 003 10.0 points Consider a bungee cord of unstretched length patel (kp9583) HW7 Mackie (20211) 2 L = 20 m. When the cord is stretched to L > L it behaves like a spring and obeys Hookes law with the spring constant k = 38 N / m. However, unlike a spring, the cord folds instead of becoming compressed when the distance between its ends is less than the unstretched length: For L < L the cord has zero tension and zero elastic energy. To test the cords reliability, one end is tied to a high bridge (height H = 148 m above the surface of a river) and the other end is tied to a steel ball of weight mg = 130 kg 9 . 8 m / s 2 . The ball is dropped off the bridge with zero initial speed. Fortunately, the cord works and the ball stops in the air before it hits the water and then the cord pulls it back up. Calculate the balls height h bot at the lowest point of its trajectory. For simplicity, neglects the cords own weight and inertia as well as the air drag on the ball and the cord....
View Full Document