unit 6 - week 5 lectures

24/07/2018 Engineering Mechanics - - Unit 6 - Week 5 Lectures

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Unit 6 - Week 5 Lectures

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Week 5 Lectures

Motion of aparticle in aplane in termsof planar polarcoordinates

Planar polarcoordinates:solvedexamples

Description ofmotion incylindrical andsphericalcoordinatesystems

Using planarpolar, cylindricaland sphericalcoordinatesystems: solvedexamples

Motion withconstraints,constraintforces and freebody diagram

Motion withconstraints –solvedexamples

Motion with dryfriction – solvedexamples

Due on 2016-08-23, 23:59 IST.

1 point1)

1 point2)

Assignment 5The due date for submitting this assignment has passed.

Submitted assignment

A projectile is launched from the origin with a speed of 2 at the angle of from thehorizontal. Assume that ground to be flat and plane of trajectory to be x-y plane with x-axis alonghorizontal. The radial and tangential components of its velocity at its highest point are given by.

No, the answer is incorrect. Score: 0

Accepted Answers:

A particle is moving along the line y = 2 at a speed of 5 towards the positive x-axis. Assume that it starts from the y-axis at t=0. The radial and tangential component of the velocityas a function of time are


Accepted Answers:

ms−1 60∘

and −2

7√

1

7

‾‾√

and −2

7√

3

7

‾‾√

and −2

7√

2

7

‾‾√

and −1

7√

3

7

‾‾√

and −2

7√

3

7

‾‾√ms−1

,−25t

25 +4t2√

10

25 +4t2√

,25t

25 +4t2√

10

25 +4t2√

,−25t

25 +4t2√

20

25 +4t2√

,−10t

25 +4t2√

25

25 +4t2√

,−25t

25 +4t2√

10

25 +4t2√Loading [MathJax]/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GreekAndCoptic.js

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Review Problems

Quiz :Assignment 5

1 point3)

1 point4)

1 point5)

A particle moves in a plane with . Its angular speed is constant. Itstarts from and at . For this particle, radial distance r(t) as function of time t and the time at which the velocity makes angle to the radius vector are given by

and 1s

and 1s

and 2s

and 1s


Accepted Answers: and 1s

A mass attached to a string is swung in circular path on a horizontal plane (see fig below).Seen directly from above, which path would the mass most closely follow if string breaks suddenly atpoint T ?

P Q R S


Accepted Answers:Q

A small block of mass m sliding down on a cylindrical surface starting from its top as shownin Fig. below. The Normal reaction of surface on the block at the position shown in Fig. will be

greater than

less than


= 2t mr˙ s−1 = 1 rad/sφ˙

r = 1 m ϕ = 0 t = 0

45∘

r(t) = t + 1

r(t) = + 1t2

r(t) = + 1t2

r(t) = + 1t3

r(t) = + 1t2

mg cos(ϕ)

mg sin(ϕ)

mg sin(ϕ)

mg sin(ϕ)

Loading [MathJax]/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GreekAndCoptic.js

https://onlinecourses.nptel.ac.in/noc16_ph02/assessment?name=84



1 point6)

1 point7)

1 point8)

Accepted Answers:less than

Consider the motion of a small block of mass m on a wedge of mass M that is free to moveon a horizontal surface, as shown in Fig. The coordinates of right lower corner wedge are andthat of block are . The constraint equations for their motion in the plane are (the block issmall enough so that one does not not have to worry about is toppling)


Accepted Answers:

A 5-kg mass is on a frictionless table with a 1-kg block on top of it with the coefficient offriction between the blocks being 0.1 . The 5-kg mass is connected to another mass M by a masslessstring passing over a frictionless pulley. The maximum value of M so that 1-kg mass does not slide onthe 5-kg mass is


Accepted Answers:

A lift originally moving downwards at velocity is brought to rest with a constantacceleration in a distance of 25 m. The force with which the feet of a passenger of mass 80 kg (take

) press downwards on the floor of the lift is

160 N

mg sin(ϕ)

( , )x1 y1( , )x2 y2 x − y

( − ) = const; = 0x1 x2 y1

( − ) = const × ; = 0x1 x2 y2 y1

= const; = 0x2 y1

= const; = constx1 y1

( − ) = const × ; = 0x1 x2 y2 y1

kg3

5

kg2

3

kg3

4

kg5

6

kg2

3

10 m/s

g = 9.8 m 2s−




1 point9)

1 point10)

1 point11)

784 N 944 N 1000


Accepted Answers:944 N

A block of mass M is released from point P on a rough inclined plane with inclination angle shown in the Fig. below. The coefficient of friction is . If , then the time taken by the block toreach another point Q on the inclined plane, where PQ=s, is


Accepted Answers:

A bead of mass is at the top of a fixed vertical ring of radius . It is pushed gently so that itstarts sliding on the ring. There is no friction between the bead and the ring. The equation of motion ofthe bead in polar coordinates are given as


Accepted Answers:

A particle, tied to a string, is moving on a smooth frictionless table in a circle of radius with anangular velocity . The string is pulled in slowly through a hole in the middle of the table with constant

θ

μ μ < tan θ

2s

g cos θ(tan θ−μ)‾ ‾‾‾‾‾‾‾‾‾‾‾√

2s

g cos θ(tan θ+μ)‾ ‾‾‾‾‾‾‾‾‾‾‾√

2s

g sin θ(tan θ−μ)‾ ‾‾‾‾‾‾‾‾‾‾√




1 point12)

1 point13)

1 point14)

1 point15)

speed (See the Fig. below). The force required for the string to be pulled at time t is given by


Accepted Answers:

A heavy rope of length L with linear mass density being pulled with constant speed on arough plane. The coefficient of friction between the rope and plane is . Find the tension in the rope asfunction of distance from its end which being pulled.


Accepted Answers:

A particle is moving along the line in plane with constant velocity passing through the originat t= 0. the radial and tangential component of its velocity at time t are


Accepted Answers:

Expression for change in the unit vector of spherical polar coordinates if is kept fixed and ischanged to is


Accepted Answers:

A particle is moving in a circle of radius 1 m with angular speed . Its acceleration at time t is





Accepted Answers:

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unit 6 - week 5 lectures

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