Question

Read each question carefully. Show all your work for each part of the question. The parts within the question may not have equal weight. A block of mass m is placed on an inclined plane that makes an angle with the horizontal, as shown in the figure. The coefficients of static and kinetic friction between the block and the surface are , and , respectively. Express your answers in parts (b) and (c) in terms of m, 0, us, My, and physical constants, as appropriate.
Please answer all parts of the Question.

Answer 1

- - . . where : N = Normal force mg = weight of the block fs = static friction Free Body diagram of buck is given as: masinom mg cosoma where. On is the maximum angle for which the block will not slide down the in cline. For this situation equations of motion of the block in x and y direction can be written an 1 mgsinam = fs - 0 and mg cos om = N - ©

from equation 0 and © we can write N Ops Por= tan" (406) consider > Om the using free body diagram of part (6) we can write equation of motion of the block with acceleration a as: mgsins - from = ma — ☺ mg cose = N @ from equation 0 and @ we can write mg sino – lle my case = ma (: ts=dxN) or a = g [sin - 4.6058]

(i) we have equation o as mg sino = fs on increasing the value off, sing will also increase so, the value of friction increases. Thus, when angle E is slowly increased the friction acting on the block also increases. ali once the block stants sliding, we have equation f = mgsint-ma on increasing & sine and acceleration a increases resulting no change in kinetic friction fic. so on increasing angle o, force of friction acting on the blocks remain the same.