Download entrance examination at the school of petroleum - ISA-EMT

ENTRANCE EXAMINATION AT THE SCHOOL OF PETROLEUM
ENGINEERS OF ISA - EMT
Paper: PHYSICS
Duration : 2 Hours
/20mks
A
Exercise 1. Simple pendulum
In all the exercise, frictions are neglected.
We studies a simple pendulum made up of a specific mass m,
attached to one ends of an inextensible wire,
of negligible mass and length L. This pendulum is studied
in the terrestrial reference frame considered as Galilean.
The other end of the wire is attached in a fixed point A.
Drawn aside of its equilibrium position Go, the pendulum oscillates
without frictions with an amplitude m. Gi is the initial position from
which the pendulum is abandoned without speed. An unspecified
position G is defined by , angular elongation measured from
equilibrium position. Its speed is then noted V.
1. Energy study.
1.1. Give the expression of the kinetic energy of the mass m at the point G.
1.2. Show that the potential energy at point G can express as: EP = mgL(1 - cos).
In which point the origin of the potential energies was selected?
1.3. Give the expression of the mechanical energy according to m, g, L, V and .
Explain why the mechanical energy is preserved (keep the same value) during the motion?
1.4. Give the expression of the speed at the position of equilibrium according to g, L and m.
Calculate its value. Data: g = 10 m.s -2; L = 1,0 m; cosm = 0,95.
2. Isochronism.
2.1. State the law of isochronism of the small oscillations.
2.2. Choose the correct expression of the period among those proposed below:
Check its accuracy by a dimensional analysis.
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Situé à Makèpe à 500 m de l’Hôpital Général
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Exercise 2. Motion of a particle charged in a uniform field
D = 40 cm ; ℓ = 1 cm ; d = 10 cm ; m = 9,1.10-31 kg ; E = 5.104 V.m-1.
In all the exercise, we will neglect the weight of the electron in relation to the other forces which act
on him.
1. Electrons of mass m and electric load q are emitted without initial speed by cathode (C).They
undergo over the length D, the action of the uniform electric field E (see figure below).
a) What is the nature of the motion of the electron between cathode (C) and anode (A)?
b) What is the speed value V0 of an electron at the point O1?
2. When reached point O1, the electrons undergo along the distance ℓ the action of a uniform
⃗ perpendicular to the plan of the figure (the domain where this field 𝐵
⃗ acts is hatched
magnetic field 𝐵
⃗ so that the electrons describe the arc of
in the figure).What must be the direction of the vector 𝐵
circle O1N? Justify the answer. Establish the expression of the radius R = O'O1 = O'N of this arc of
circle and calculate the value of R for B = 2.10-3 T.
3. What is the nature of the motion of the electron in the domain III where the field does not exist?
4. Domain III is limited by a screen (E) on which the electrons arrive. Express according to m, E, B, D,
ℓ and Vo the magnetic deflection O3I = Y undergone by an electron when crossing the system II+III.
The line IN cut the axis O1O2 at the point M. The screen E is at the distance D of this point M. Let’s
assume the following simplifications:
- in the domain II of the space, we consider the length of the arc equal to the length O1O2 = ℓ
- we will suppose that the angular deviation is weak. Knowing that Y = 3.35 cm, find again the speed
value Vo of the electron at the point O1.
The Direction of Exams
September 2014
BP : 1215 Douala
Situé à Makèpe à 500 m de l’Hôpital Général
Tél : 33 78 85 87 / 74 18 94 40
Site web : www.a-eim.com
E-mail : [email protected]