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: lim (kl9356) Homework 14 Weathers (17104) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points An Atwood machine is constructed using a hoop with spokes of negligible mass. The 2 . 4 kg mass of the pulley is concentrated on its rim, which is a distance 20 . 8 cm from the axle. The mass on the right is 1 . 06 kg and on the left is 1 . 58 kg. 2 . 5 m 2 . 4 kg 20 . 8 cm 1 . 58 kg 1 . 06 kg What is the magnitude of the linear acceler ation of the hanging masses? The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 1 . 01111 m / s 2 . Explanation: Let : M = 2 . 4 kg , R = 20 . 8 cm , m 1 = 1 . 06 kg , m 2 = 1 . 58 kg , h = 2 . 5 m , and v = R . Consider the free body diagrams 1 . 58 kg 1 . 06 kg T 2 T 1 m 2 g m 1 g a a The net acceleration a = r is in the direc tion of the heavier mass m 2 . For the mass m 1 , F net = m 1 a = m 1 g T 1 T 1 = m 1 g m 1 a and for the mass m 2 , F net = m 2 a = T 2 m 2 g T 2 = m 2 a + m 2 g . The pulleys mass is concentrated on the rim, so I = M r 2 , and net = summationdisplay ccw summationdisplay cw = I T 1 r T 2 r = ( m r 2 ) parenleftBig a r parenrightBig = m r a m a = T 1 T 2 ma = m 1 g m 1 a m 2 a m 2 g ma + m 1 a + m 2 a = m 1 g m 2 g a = ( m 1 m 2 ) g m + m 1 + m 2 = (1 . 06 kg 1 . 58 kg) (9 . 8 m / s 2 ) 2 . 4 kg + 1 . 06 kg + 1 . 58 kg = 1 . 01111 m / s 2 . 002 (part 1 of 2) 10.0 points A block of mass 2 kg and one of mass 6 kg are connected by a massless string over a pulley that is in the shape of a disk having a radius of 0 . 38 m, and a mass of 4 kg. In addition, the lim (kl9356) Homework 14 Weathers (17104) 2 blocks are allowed to move on a fixed block wedge of angle 46 , as shown. The coefficient of kinetic friction is 0 . 21 for both blocks. 2 kg 6 k g 46 . 38 m 4 kg What is the acceleration of the two blocks? The acceleration of gravity is 9 . 8 m / s 2 . As sume the positive direction is to the right. Correct answer: 2 . 96035 m / s 2 . Explanation: Let : m 1 = 2 kg , m 2 = 6 kg , M = 4 kg , and R = 0 . 38 m . m 1 m 2 M T 1 T 2 Applying Newtons law to m 1 , N 1 m 1 g = m 1 a y = 0 N 1 = m 1 g , where the force of friction on m 1 is f 1 = N 1 = m 1 g = (0 . 21) (2 kg) (9 . 8 m / s 2 ) = 4 . 116 N and T 1 f 1 = m 1 a T 1 = m 1 a + f 1 . (1) For the mass m 2 , applying Newtons law...
View Full
Document
 Fall '08
 Weathers
 Magnetism, Work

Click to edit the document details