Question

Physics 121 Fall 2019- Document # 22: Homework #08 & Reading Assignment page 5 of 7 Problem 4: Angles, friction: lo +o idont The figure below shows a block of given mass m on an inclined plane attached to a thin mass- less string that rolls over a frictionless massless pulley to a second equal mass m. Assume that the there is no friction in the system. Suppose that the angle of the inclined plane 0 which is given as 30 degrees. m ube a) What is the tension in the string? Explain how you calculated this. b) What is the magnitude and direction of the acceleration of block on the inclined plane? Explain your work e) Now change the problem so that there is sliding friction on the plane. What value of the coefficient of sliding (kinetic) friction will result in an acceleration that is exactly half the value that you calculated for part (b) above? Give your answer in terms of the given parameters. Explain how you determined this. d) Now change the problem yet again so that there is friction on the plane but now the friction is known to be static. What is the constraint on the value of the coefficient of static friction in terms of all of the other given parameters? You should express your answer as an inequality. In otherwords your answer should look something like: 14 .

Answer 1

= 30° mg COSO mgsino @ mg-T = ma for hanging mass) a= 9- Now, for slanted mass - T-mgsino = ma . T-mgsino = mg-t 2T = mg (1-t sino) T= mg (it sine) / 0 36, Sin 30 = 0.5 T = 1. 5mg = 0.75 mg 2 IT = 0.15 mg (6) direction :- up along the inclined plane . magnitude ! 9 8- 0.758 = 0.458 a 0.259

(C) V ng cos mgsimo 4 fk e mal- mg -t (for Hanging mass) for Slanding mass :- T-4mg cose - mg sino = mal 3-9' - HO COSO - 9 sine za Ola 0.1258 3-4 g COS 6 - 8 Sine - 0.259 1-- 0,45 - Sin (30") = MCOS 360 COS (30) = 0.29 (d) friction acceleration in above egn for static a' to 8 - US 8 COSO - 9 Sime = 0.5 = Ms COS(30)

0.45 = 0.577 COS30 | Ms = 0.58 this is the minimum possibic value that Cause zero acceleration. so it would follow inequality relation. 145 20.577
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