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Solving problems is an essential part of the understanding process.

Questions and their answers are presented here in the module text format as if it were an extension of the treatment of the topic. The idea is to provide a verbose explanation, detailing the application of theory. Solution presented is, therefore, treated as the part of the understanding process – not merely a Q/A session. The emphasis is to enforce ideas and concepts, which can not be completely absorbed unless they are put to real time situation.

Hints on solving problems

The incline plane has two contact or interface surfaces. One is the incline surface, where the block is placed and the other is the base of the incline, which is in contact with the surface underneath. The motion of the block, therefore, may depend on the motion of the incline itself.

We must understand here that there are two ways to look at such situation, which involves motion of the incline itself. We can analyze the motion of the elements of "block and incline" system in either the inertial frame (ground reference) or in the accelerated frame. The two techniques have relative merits in particular situations. As pointed out earlier in the course, we should stick to the analysis from inertial frame to the extent possible unless analysis in accelerated frame gives distinct advantage.

In this module, however, our objective is to learn analysis of motion in accelerated frame. As such, we have selected questions which are better suited to analysis in non-inertial frame of reference.

Representative problems and their solutions

We discuss problems, which highlight certain aspects of the study leading to the motion on accelerated incline plane. The questions are categorized in terms of the characterizing features of the subject matter :

  • Coefficient of friction in accelerated frame
  • Incline on a smooth horizontal surface
  • Incline in an accelerated lift

Coefficient of friction in accelerated frame

Problem 1 : A block is placed on a rough incline plane placed on the floor of a lift, which is moving up with acceleration “a”. The incline plane is raised at one end to increase the angle of incline slowly till the block is about to move down. Find angle of repose (this is the angle of incline for which block begins to slide).

Solution : Let the angle of incline, when block is about to move down, is “θ”. To analyze the forces, we select a coordinate system with axes in horizontal and vertical directions. This orientation of axes takes advantage of the fact that acceleration of the lift is in vertical direction.

The context of motion here is peculiar, in which inertial or non-inertial considerations for force analysis do not make any difference. The reason is that angle of repose is obtained by considering motion in horizontal direction only (as we shall see soon). It does not matter whether we analyze forces without pseudo force (inertial ground reference) or with pseudo force (non-inertial lift reference). Note that if we consider non-inertial analysis, then the pseudo force would be in vertically downward direction and as such would not come in consideration for force analysis in horizontal direction.

Questions & Answers

What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
Amar
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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