Fundamentals of Applied Physics (GSDR2115)
Higher Institute of Transport and Logistics (HITL)
Semester: First Semester
Level: 200
Year: 2017
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 DEPARTEMHNT: General Studies LECTURERSR(S): Dr. DADA Jean-Pierre
COURSE CODE: TLG COURSE TITLE: Fundamentals of applied physics OPTIONS: LT, TL, MT and CU
DATE: March 16
th
, 2017 HALL: .... TIME: 2 hours NATURE; CA2
Instructions: Answer all questions.
Exercise 1: Vectors and applications (6 marks)
In an orthonomal basis
,
the vector
is written as:
= 2 + 4k
1) Calculate the magnitude of
(1 mark).
2) Find the magnitude of the projection of
on the YOZ plan (1 mark).
3) Let another vector so that =
a) Calculate
(1 mark)
b) Calculate
(1 mark)
c) Find two vectors
(x
A
,y
A
,0),
( 0 , y
B
, z
B
) perpendicular to
(1 mark).
4) Let us consider the vectors
and
.
Demonstrate that if
+
=
, then
x
=
x = x
Exercise 2 (6 makes): Let us consider two scalar functions f(x, y, z) and g(x, y, z) defined by: f(x, y, z) = x
2
yz + x
3
yz
and g(x, y, z) = z
3
1. Calculate the gradients of f(x ,y, z) and g(x, y, z) (2 marks)
2. Demonstrate that g
d(f.g) = f.g
dg + g g
df ( 2 marks)
3. Let: us consider the function
(x, y, z) = -2xy + (8y x
1
) 3k.
3.1 Calculate div
(x,y,z) (1 mark)
3.2 Calculate curl
(x,y,z) (1 mark)
Exercise 3: Effects of rebounding, crumpling vehicles (8 marks)
A car (A) with a mass (m
1
) moving with the velocity !
"
, collides with another car (B) having a mass (m
2
). The
car (B) is also in movement with the velocity V
2
. The mass of the driver driving the car (A) is ( m
3
) while (m
4
) is the
mass of the driver of the car (B). After the frontal collision, the two cars become a single solid moving with the
velocity #
(see the figure).
1. Answer by Yes or No:
1.1. This collision corresponds to the non conservation of kinetic energy
1.2. This collision corresponds to the conservation of kinetic energy
1.3. This collision corresponds to the non conservation of total momentum
1.4. This collision corresponds to the conservation of total momentum
1.5. This is an elastic collision
1.6. This is an inelastic collision
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2. Give the expression of momentum and kinetic energy before the collision in terms of m
1
, m
2
, m
3
, m
4
, !
3. Give the expression of momentum and kinetic energy before the collision in terms of m
1
, m
2
, m
3
, m
4
, !
4. Give the expression of the velocity V after collision
5. Give the expression of the force F created on the driver after if this collision happened in 2 seconds
6. In car collision, do you think tat the mass of the driver can be a parameter of safety? What do you prefer between
a fat driver and a tiny driver as safety is concerned after collision
7.Some automobiles have crumpled zones or sections in cars which are designed to crumple up when the car
encounters a collision. Answer by YES or NO:
7.1) The figure above shows that the two cars were crumpled
7.2) By crumpling, the car is less likely to rebound upon impact
7.3) By crumpling, the momentum changes and impulse is minimized
7.4) The crumpling of the car lengthens the time over which the car’s momentum is changed
7.5) By crumpling, the time of the collision is increasing
7.6) By crumpling, the force of the collision is greatly reduced
7.7) By crumpling, the time of the collision is reducing
7.8) By crumpling, the force of the collision is greatly increased
8. According to this exercise, answer by Yes or No:
8.1) Crumpling a vehicle helps to protect the driver during accident
8.2) Crumpling a vehicle helps to protect the vehicle during accident
8.3) Not crumpling a vehicle helps to protect the driver during accident
8.4) Not crumpling a vehicle helps to protect the vehicle during accident
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