Solution 1:
Drawing the free body diagram of the entire beam we get that there are three unknown
reactions at A and one unknown reaction at B.
MA
HA
15 kN/m
VC
A
Segment AC
C
HC HC
VC
C
Segment CB
B
RB
RA
x
x
For solving, the entire beam is divided into t
Answers of Tutorial 4
ME101 (Engineering Mechanics) 2014-2015 Sem II
Problem-1
Solution: We shall start by drawing the FBD for the BEAM:
2 kN/m
1.5 kN
1.5 kN
Y
X
(4+3) kN-m
RB
RA
Finding Reaction Forces RA and RB:Equation for Half-Sine wave: = 2 sin [
(+1
Indian Institute of Technology Guwahati
ME 101: Engineering Mechanics (2014-2015, Sem II)
Answers of Mid-Semester Examination
Ans 1.
To determine the force in members DG and FI of the truss, a section a-a is passed through members DG,
DE, EF and FI as sho
Indian Institute of Technology Guwahati
ME101 Engineering Mechanics (2014-2015, Sem II)
End-Semester Examination
Time: 3 hours
Full marks: 160
It is a closed-book and closed-note examination
Mention clearly the free-body diagram and sign convention wher
3-D Kinetics of Rigid Bodies
Angular Momentum
Generalized Newtons second law for the motion for a 3-D mass system
Moment eqn for 3-D motion will be different than that obtained for plane
motion
Consider a rigid body in general motion in space
: x-y-z ar
Indian Institute of Technology Guwahati
ME 101: Engineering Mechanics (2014-2015, Sem II)
Answers of Quiz 1
P
Ans 1.
A
B
F
C
G
D
E
H
The FBD for the given frame is drawn by showing the forces on each of the members.
Member AC
Member AF
Ay
Ax = 0
Ax = 0
A
ME101: Engineering Mechanics
IIT Guwahati
1
Solutions to tutorial 6
18th of February, 2015
Problem 1
10 points
Consider the semicircular area and X-Y coordinate axes shown in figure (1). FromR basic definitions
and integration,
find (i) the coordinates of
Kinetics of Particles: Force-Mass-Acceleration method
Rectilinear Motion
Motion of a particle along a straight line
For motion along x-direction, accelerations along y- and z-direction will be zero
Fx = max
Fy = 0
Fz = 0
For a general case:
Fx = max
Fy
Indian Institute of Technology Guwahati
ME 101: Engineering Mechanics (2014-2015, Sem II)
Mid-Semester Examination
Time: 2 hours
It is a closed-book and closed-note examination
Mention clearly the free-body diagram and sign convention wherever applicabl
Plane Kinetics of Rigid Bodies
: Relates external forces acting on a body with the translational and
rotational motions of the body
: Discussion restricted to motion in a single plane (for this course)
Body treated as a thin slab whose motion is confined
W
(4)
N2
F2
N1
G
P
= 15o
F1
F3
N3
F2
N2
Consider a situation where the pipe and the wedge are in static equilibrium. Both of them have to satisfy
equations of equlibrium given next.
N1 N2 sin F2 cos = 0
F1 W + N2 cos F2 sin = 0
R(F1 F2 ) = 0
F3 + N2 sin
INDIAN INSTITUTE OF TECHNOLOGY - GUWAHATI
ME 101 : Engineering Mechanics
2014-2015, IInd semester
Quiz - 2 (25.03.2015)
Total Marks: 45
Question 1 Two automobiles A and B, Fig. (1), are approaching each other in adjacent highway
lanes. At t = 0, A and B a
Answers of Tutorial 1
ME101 (Engineering Mechanics) 2014-2015 Sem II
Vectors and Force Resultants
Ans 1.
The two set of forces form 2 couples as they are equal in magnitude and opposite in direction.
Hence, the resultant force = 0 ,
Each of the couple so
Tutorial 9
ME101 (Engineering Mechanics) 2014-2015 Sem II
Time: 8:00- 8:55 am
Note: Each question carries 10 Marks
Ans. 1. Looking at d and as polar coordinates with = 0
= = ,
= = 0
= + =
= + 2 = 0,
= 2 = 2
From geometry, at = 60, =
120
=
30
180120
3D Kinetics of Rigid Bodies
Angular Momentum
HG [ ( )] dm
Expression for H:
Inertia Matrix
HO [ r ( r)] dm
Components of H:
Principal axes of inertia
Kinetic Energy
ME101 - Division III
Kaustubh Dasgupta
1
3-D Kinetics of Rigid Bodies
General Momentum Equ
INDIAN INSTITUTE OF TECHNOLOGY - GUWAHATI
ME 101 : Engineering Mechanics
2014-2015, IInd semester
Tutorial - 12 (22.04.2015)
Total Marks: 50
Question 1 The 7.5-kg rod BC, see Fig. (1), connects a disk centered at A to crank CD. Knowing that the disk is ma
A ball is thrown at an inclined wall. Just before the impact on the wall, the ball has a
height of 1.2 m and a velocity v 0 that is horizontal with a magnitude of 15 m/s. The
coefficient of restitution between the ball and the wall is 0.9 and there is no
Tutorial 11
ME101: Engineering Mechanics
Note: This is an open book and open notes exercise. While students can consult tutors
and TAs, consultaion among students during tutorials is discouraged.
1) Link OA has a constant counter-clokwise angular velocity
3-D Dynamics of Rigid Bodies
Introduction of third dimension
: Third component of vectors representing force, linear velocity, linear
acceleration, and linear momentum
: Two additional components for vectors representing angular quantities:
moments of for
3-D Kinematics of Rigid Bodies
Rotation about a Fixed Point
Instantaneous Axis of Rotation
: Rotation of solid rotor with black particles
embedded on its surface
: 1 and 2 are steady angular velocities
: Along line O-n, velocity of particles will be
momen
Rigid Body Kinetics : Force/Mass/Acc
General Equations of Motion
G is the mass center of the body
Dynamic
Response
Action
ME101 - Division III
Kaustubh Dasgupta
1
Rigid Body Kinetics : Force/Mass/Acc
Fixed Axis Rotation
All points in body move in a circu
Answers of Tutorial 3
ME101 (Engineering Mechanics) 2014-2015 Sem II
Time: 8:00- 8:55 am
Note: Each question carries 10 Marks
Ans 1.
We shall begin by determining the co-ordinates of the points A, B, C and D. Through
simple geometry analysis the co-ordina
Rigid Body Kinetics : Virtual Work
Work-energy relation for an infinitesimal displacement:
dU = dT + dV (dU : total work done by all active forces)
For interconnected systems, differential change in KE for the entire system:
For each body:
dsi : infinites
Tutorial 2
ME101 (Engineering Mechanics) 2014-2015 Sem II
Ans 1. The reactions at A and B will act normally to the respective surfaces of contact. The
forces acting are the weight, W acting downwards, NA and NB acting at 150 and 600 to the
horizontal resp
Tutorial - 12 (solutions)
Question 1 The 7.5-kg rod BC, see Fig. (1), connects a disk centered at A to crank CD. Knowing that the disk is made to rotate at the constant speed of 180 rpm, determine
for the position shown the vertical components of the forc
Tutorial 8
ME101 (Engineering Mechanics) 2014-2015 Sem II
Time: 8:00- 8:30 am
Note: Each question carries 10 Marks
Ans 1.
y
A
5
B
12
At t=0,
0 = 0
Initial Condition
0 = 5
The equation of the path is,
12
+5=1
12
=
=
5
12
5
The velocity along the path i