Fundamentals of Applied Physics (GSDR2115)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 200
Year: 2016
THE UNIVERSITY OF BAMENDA UNIVERSITE DE BAMENDA
HIGHER INSTITUTE OF TRANSPORT AND INSTITU DE TRANSPORT ET LOGISTIQUE
LOGISTICS (I.S.T.L)
School: H.I.T.L Department: General Studies Lecturers(S): Dr. DADA Jean-Pierre
Course Code: TL Course Title:
Fundamentals of applied physics
OPTIONS:
LT, TL, MT and CU
Date: February, 2016 HALL:………… Time: 2hours NATURE:
CA
Instructions: Answer all questions.
Exercise 1: Vectors and applications (5 marks)
In an orthonormal basis (0, , ,
) the vector u is written as:
=
+ 2 + 4
.
1) Calculate the magnitude of
(1mark).
2) Find the magnitude of the projection of
on the XOZ plan
3) Let another vector so that =
+ 2
a) Calculate
. (1 mark)
b) Calculate
(1 mark)
c) Find two vectors
(x
A
,y
A
,0
),
(0,y
B
,z
B
) perpendicular to
(2 marks).
Exercise 2: Kinematic of particle (8 marks)
Answers should be expressed on the basis
In the basis
, a point M describes a linear movement with the equation
x=a cos(t).
M is then under the obligation to displace only on the axis
' ; 00’=R. The point 0’ of the basis
,
is in movement with the uniform rotation around
axis of the basis
(see figure) so that
the angle between vectors and
being . One will assume = =constant.
1) Give in the basis
’
in term of
1.1) The vector position components (1 mark)
1.2) The vector velocity components (2 marks)
2) Give
in the basis
’
in term of
2.1) The vector position components (1 mark)
2.2) The vector velocity components (2 marks)
3) Give the components of driven velocity' vector (2 marks)
Recall:
!
"
#
$
%
&
'
(
)*
+
,!
"
#
'%(
Exercise 3: Work done by a force (11 marks)
Let us consider an orthonormal basis (0, , ,
(and a field of force
-
defined by
-
(x, y, z) = -2xy
+ (8y -
x
2
)-
3
1) Calculate the work (circulation) of a material point moving on the action of this force from the point A(0,0,0) to the B(1,2,4) after have defined
a path (2 marks)
2) Calculer curl
-
(x, y, z) (2 marks)
3) Is
-
a conservative force? Justify your answer (2 marks)
4) Let us assume as U, a scalar function (U is called scalar potential). Let us assume
-
(
x, y,
z) = .
g/0
dU.
Give the expression of U (2 marks).
5) Calculate again, with appropriate use of scalar potential U, the work of the material point moving from point A(0,0,0) to point B(1,2,4)
(2 marks)
6) By comparing the work obtained with questions (A.1) et (A.5), what can you conclude? (1 mark)
www.schoolfaqs.net
Exercise 4: Equilibrium (6 marks)
To move heavy boxes 4i(i = 1,2, ...6) with the mass m
(
(i = 1,2, ...6), from a boat, one uses the
To move heavy boxes A
i
(i = 1,2,…,6) with the mass m
i
(i = 1,2,…6), from a boat, one uses the figure below. A long rod DB is able to rotate
U
the
point O around (1) axis. It contains a heavy solid fixed at the point B and having the fix weight
2
. The distance between the box
A
t
and (1) axis is
called3
. A small cable (with negligible mass), fixed at the variable point A, can support one box A
i
(i = 1,2,…,6) (see figure). By varying the
distance
x,
it is possible to move one box from the boat, turn horizontally at put the box on the ground (see figure).
1) List all forces applied to each element of the entire system, particularly, the cable AA
1
(3 marks)
2) By applying equilibrium condition to the system, find the relation between
x,
m
i
, 3
. and other data (3 marks)
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