Kingdom of Saudi Arabia
Ministry of higher education
Salman Bin Abdulaziz University
Faculty of science and human studies
at Al-Aflaj
Mathematics department (level 4)
Subject: Mechanics (3290Math)
Time: 3 hours
Marks=60
Number of Pages =2
Final exam of first term 1433-1434
Answer the following questions:
The first question (choose only three items)( 15 Marks)
a)- Determine the moment of the force 𝐹⃗ = 2𝑖⃗ + 3𝑗⃗ — к
⃗⃗ lb acting through the point
(3,1,1) about the point (2,5, −2) .
b)- 𝐴𝐵𝐶𝐷 is a square plate and length of the member 𝑨𝑩 = 𝟓𝟎 𝒄𝒎, 𝐸,𝐻 are respectively
middle the members 𝐴𝐷, 𝐶𝐷. The forces 𝟐𝟎, 𝟐𝟎, 𝟒𝟎, 𝟑𝟎 𝐼𝑏 act on the directions of members
𝐴𝐵, 𝐶𝐷, 𝐴𝐻, 𝐸𝐵. Determine the resultant force and the equation of its action line.
c) Three forces F1 , F2 , F3 act on the members of the triangle which is determined by: 𝒙 +
𝒚 = 𝟏, 𝒙 − 𝒚 = 𝟏, 𝒚 = 𝟐. If the forces act on one periodic direction, find the equation of
the action line of the resultant force.
d)- From the shown graph, find the length of CE.
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The second question(choose only three items)( 15 Marks)
a) - Conclude components of the velocity and acceleration by (𝑟, 𝜃)-coordinates.
b)- Determine the resultant of the concurrent force system shown in the figure:
c) - A mass of 5 units moving in the space where its position vector respect to the time is
⃗⃗. Find:
given by 𝑟 = (2𝑡 3 + 𝑡)𝑖 + (3𝑡 4 − 𝑡 2 + 8)𝑗⃗ − 12𝑡 2 𝑘
1-The velocity
2-The acceleration 3-The force 4- The power.
d) - Show that the work on an object is equal to the change in the kinetic energy.
The third question( choose only three items)( 15 Marks)
a) - Define the impulse of a variable force and prove that it is equal to the change in the
momentum.
b) - A body of mass 𝟐𝒌𝒈 moving with velocity 𝟓𝒎/𝒔𝒆𝒄 collides directly with another of
mass 𝟑 𝒌𝒈 with velocity 𝟒𝒎/𝒔𝒆𝒄 moving in the same direction. The coefficient of
restitution is 2/3. Find the velocities after collision.
c) - Conclude components of the velocity and acceleration by (𝑠, 𝜓)-coordinates.
d) - If 𝑟 and 𝜃-components of the velocity of a particle are respectively 𝜇 𝑟, 𝜃𝜃, where 𝜃, 𝜇
are constant. Find the path equation of the particle and the components of acceleration.
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The forth question(choose only three items)( 15 Marks)
a )- Prove that the following force is conservative force
⃗⃗.
𝐹⃗ = (𝑦 2 𝑧 3 − 6𝑥𝑧 2 )𝑖⃗ + 2𝑥𝑦𝑧 3 𝑗⃗ + (3𝑥𝑦 2 𝑧 2 − 6𝑥 2 𝑧)𝑘
b) – A man appeared to him that the rain falls vertically. When he doubles its velocity,
appeared to him that the rain falling at an angle α. If the velocity of the man is 20 ft/sec,
find the direction and velocity of real rain.
𝒎
c)- A car started its motion with the velocity 𝑣 = 0 and acceleration 𝑎 = 4 𝟐 for interval
𝒔𝒆𝒄
time 𝟒 𝒔𝒆𝒄 .Then it moved with constant velocity for interval time 𝟏𝟎 𝒔𝒆𝒄 , after that it
𝒎
moved with decreased acceleration 𝑎 = 8 𝟐 even the car stopped. Find the total distance
𝒔𝒆𝒄
of the motion.
d) - A particle moves in simple harmonic motion with period time is 3𝜋 𝑠𝑒𝑐. The velocity
of the particle at the points 𝑐 and 𝑑 is respectively 8, 6 𝑓𝑡 / 𝑠𝑒𝑐, where 𝑐𝑑 = 3 𝑓𝑡 and
they are in one hand side from the motion. Find the magnitude of the motion and the
maximum values of the velocity and acceleration.
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End exam
Dr\Abdel-Baset A. Mohamed
Good luck
Department’s Chairman
Dr. Ahmed Farghal