This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: homework 17 – YOO, HEE – Due: Feb 28 2008, 4:00 am 1 Question 1, chap 8, sect 2. part 1 of 1 10 points The two blocks are connected by a light string that passes over a frictionless pulley with a negligible mass. The 5 kg block lies on a rough horizontal surface with a constant coefficient of kinetic friction 0 . 1. This block is connected to a spring with spring constant 7 N / m. The second block has a mass of 7 kg. The system is released from rest when the spring is unstretched, and the 7 kg block falls a distance h before it reaches the lowest point. The acceleration of gravity is 9 . 8 m / s 2 . Note: When the 7 kg block is at the lowest point, its velocity is zero. 5 kg 7 kg 7 N / m 5 kg 7 kg h h μ = 0 . 1 Calculate the mechanical energy removed by friction durning the time when the 7 kg mass falls a distance h. Correct answer: 89 . 18 J (tolerance ± 1 %). Explanation: Basic Concepts: WorkEnergy Theorem Spring Potential Energy Frictional Force according to the Work Energy Theorem m 1 m 2 k m 1 m 2 h h μ Given : m 1 = 5 kg , m 2 = 7 kg , μ = 0 . 1 , and k = 7 N / m . Solution: W ext A → B = ( K B − K A ) + ( U g B − U g A ) + ( U sp B − U sp A ) + W dis A → B . For the present case, the external work W ext A → B = 0, A corresponds to the initial state and B the state where m 2 has descended by a distance s . The sum of the kinetic energy of m 1 plus that of m 2 at B is given by K = K B = ( U g A − U g B ) + ( U sp A − U sp B ) − W dis A → B = m 2 g s − 1 2 k s 2 − μm 1 g s. (1) Based on the Eq. 1 at s = h , K B = 0, we have μm 1 g h = m 2 g h − 1 2 k h 2 . In turn, h = 2 g [ m 2 − μm 1 ] k (2) = 2 (9 . 8 m / s 2 ) [(7 kg) − (0 . 1) (5 kg)] (7 N / m) = 18 . 2 m . We know that E initial = E final + E μ , where E μ is the mechanical energy removed by fric tion. In order to solve the second part of the problem we need to calculate the initial and fi nal energies. Let y 1 be the vertical position of m 1 and y 2 the vertical position of...
View
Full
Document
This note was uploaded on 05/04/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner
 Friction, Mass, Work, Light

Click to edit the document details