Uploaded by Mostafa A.

Dynamics Exam 5

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Q1
If v is the algebraic measure of the velocity vector of a particle and 𝒙 is the algebraic measure of its
position vector where 𝒗 = 𝟐 𝒙 − πŸ’, then the algebraic measure of the acceleration of the particle as a
function of the position 𝒙 is given by the relation…………………….
a) 𝒂 = 𝟐 𝒙 − πŸ’
b) 𝒂 = πŸ’ 𝒙 − 𝟐
c) 𝒂 = πŸ’ 𝒙 − πŸ–
d) 𝒂 = 𝟐
Q2
A car of mass πŸ” tons is moving along a horizontal road at full speed. If the resistances for its movement are
equal to πŸπŸ“πŸŽ π’Œπ’ˆ. π’˜π’•. for every ton of car mass, the engine force of the car equal to ………………… π’Œπ’ˆ. π’˜π’•.
a) πŸ—πŸŽ
b) πŸ—πŸŽπŸŽ
c) πŸ—πŸŽπŸŽπŸŽ
d) πŸ—πŸŽπŸŽπŸŽπŸŽ
Q3
A man of mass 65 kg. ascends up from the second floor to the seventh floor by an electric lift. If the
height of the floor is 3 meters, then the gained potential energy = …………. joule.
a) πŸ—πŸ“πŸ“πŸ“
b) πŸ—πŸ•πŸ“
c) 97.5
d) πŸ—πŸ“. πŸ“πŸ“
Q4
In the opposite figure :
It represents the (displacement - time) graph of two
particles moving in a straight line, which of the following
statement is not correct?
a) particle (2) the algebraic measure of its velocity is
negative.
b) particle (1) the algebraic measure of its velocity is
positive.
c) particle (2) moves with retarded motion.
d) particle (1) moves with accelerated motion.
Q5
A body of variable mass π’Ž = πŸπ’• + πŸ• gm. moves in a straight line, t is the time in seconds, and its velocity
v is given by the relation 𝒗 = 𝒆𝒕 cm./sec. under the action of force 𝒇 (dyne) , then the magnitude of the
force 𝒇 at 𝒕 = πŸ‘ sec. equals ............ dyne.
a) 13π’†πŸ‘
b) 15
c) 15π’†πŸ‘
d)13
Q6
A body of mass m is placed on a rough horizontal plane and
the coefficient of kinetic friction between the body and the plane
is 0.2, a horizontal force acting on it for 10 seconds and moved it
in its direction, then the force was ceased, if the body stopped
after
a distance 50 m on the plane after ceasing the force, then the ratio
between the magnitude of the friction force generated during
motion
and the magnitude of the force acting on the body =...........
a) 7:12
b) 5:7
c) 5:12
d) 12:35
Q7
In the opposite figure:
𝑭 acts on a baby stroller of mass 2 kg. moving in a straight line
parallel to 𝒙 −axis.
Calculate the work done by this force when 𝒙 changes from
𝒙 = πŸπ’Ž to 𝒙 = πŸ•π’Ž
Q8
A car moves in a straight line such that the algebraic measure of its velocity 𝒗 (m./sec.) is given as a
function in time t (sec.) as 𝒗 = πŸπ’• − πŸ’, if the average speed during the time interval 𝟎, 𝒕 equals 5 m./sec ,
then 𝒕 = β‹― seconds.
a) 1
b) 8
c) 9
d) 20
Q9
A body moves under action of a force with an acceleration 𝒂 = (πŸπ’• + 𝟏) m./π’”π’†π’„πŸ and initial velocity 5
m./sec. if the action of the force is ceased after 3 seconds from the beginning of motion and the body
remains to move with the acquires velocity, find the distance the body covers in the first 5 seconds from
the beginning of motion
a)
b)
c)
d)
Q10
If the given figure:
it represents (square of the momentum – kinetic energy)
graph of a body moving in a straight line, then the mass
of the body =…….…..π’Œπ’ˆ
a) 𝟏𝟎
b) πŸπŸ“
c) 𝟐𝟎
d) πŸ“
Q11
A particle moves in a straight line such that its position vector 𝒓 meter is given as a function in time t
sec. by the relation 𝒓 = πŸ‘ 𝒕 π’ŠΖΈ + πŸ‘ π’•πŸ 𝒋Ƹ then at 𝒕 = πŸ‘ sec. the velocity vector 𝒗 makes an angle 𝜽 with π’ŠΖΈ
where 𝜽=…
𝟐
a) 𝒕𝒂𝒏−𝟏 ( )
πŸ‘
b) 𝒕𝒂𝒏−𝟏 (πŸ‘)
𝟏
𝟐
c) 𝒕𝒂𝒏−𝟏 ( )
d) 𝒕𝒂𝒏−𝟏 (𝟐)
Q12
When a body of constant mass fell down from a certain
height on a horizontal ground, then the impulsive force
generated at the moment of contact F ∝…. (t is the contact
time).
a)
𝟏
𝒕
𝟐
c) 𝒕
b) t
d)
𝟏
π’•πŸ
Q13
A bullet is fired horizontally with speed 200 m/sec. at a vertical fixed barrier of thickness 32 cm. it
penetrates the barrier and lose
bullet = ……………. gm.
a) πŸ“
a) 𝟏𝟎
πŸ’
πŸ“
of its speed. If the barrier resistance = 900 N , then the mass of the
c) 𝟏𝟐
a) πŸπŸ“
−πŸ—πŸŽπŸŽ
∴π’Ž=
= 𝟎. πŸŽπŸπŸ“ π’Œπ’ˆ = πŸπŸ“ π’ˆπ’Ž
−πŸ”πŸŽπŸŽπŸŽπŸŽ
Q14
𝟏
A smooth ball of mass π’Œπ’ˆ moves with speed 𝒗 . It collided with another smooth ball of mass 𝟏 π’Œπ’ˆ at
𝟐
rest, if the first ball rebounded after collision with speed equals quarter of its speed before collision and
the second ball gained a kinetic energy of magnitude πŸ’πŸ“πŸŽ 𝒋𝒐𝒖𝒍𝒆𝒔, then the speed of the first ball directly
after collision =……….π’Ž/𝒔𝒆𝒄
a) πŸ’πŸ–
b) 𝟏𝟐
c) πŸ‘πŸŽ
d) πŸ•. πŸ“
Q15
If the power of a machine at any time 𝒕 𝒔𝒆𝒄 equals (πŸ‘π’•πŸ + π’Œπ’•) watt and the work done during the 5th
second equals πŸ•πŸŽ 𝒋𝒐𝒖𝒍𝒆𝒔, then the work done during the first four seconds equals……….joule.
a) πŸ“πŸŽ
b) πŸ•πŸŽ
c) πŸ”πŸŽ
d) πŸ–πŸŽ
Q16
In the opposite figure:
The (force - time) graph for a body moves in a straight line under the
action of a force F (Newton). If the impulse of this force during the first
four seconds equals its impulse during the time interval[πŸ’, 𝒂] , then a =
.....
a) 8.5
b) 8.3
c) 8.6
d) 8.4
Q17
In the opposite figure, two masses of πŸ’πŸŽ π’ˆπ’Ž, πŸ‘πŸŽ π’ˆπ’Ž connected by the
two ends of a light string passing over a smooth small pulley fixed at the
top of two smooth opposite planes inclined at πŸ‘πŸŽ° and πŸ’πŸŽ° to horizontal
respectively, then the system……..
a) Moves in direction of mass πŸ’πŸŽ π’ˆπ’Ž. Downwards with acceleration .
b) Moves in direction of mass 3𝟎 π’ˆπ’Ž. Downwards with acceleration
c) Moves in direction of mass 4𝟎 π’ˆπ’Ž. Downwards with uniform vecloity
d) at rest
Q18
A body moves in a straight line under the action of a force 𝑭 (π’π’†π’˜π’•π’π’) is given as a function in time (𝒔𝒆𝒄)
by the relation 𝑭 = π’Œπ’• ∢ π’Œ ∈ ℝ+ and its displacement 𝒔 (π’Žπ’†π’•π’†π’“) is given as a function in time 𝒕 (𝒔𝒆𝒄) by the
relation 𝒔 = π’•πŸ‘ , where the force acts in the same direction of the displacement, if the work done during the
time interval 𝟎, 𝟐 equals πŸ–πŸ’ 𝒋𝒐𝒖𝒍𝒆, then π’Œ =……..
a) πŸ“
b) πŸ”
c) πŸ•
d) πŸ–
Q19
A sphere of mass 500 gm. fells from a height of 2.5 m. to a liquid and it is embedded in it and
stopped after one second from the moment it penetrates the liquid. Given that the magnitude
of the impulse of the liquid to the sphere is 1.5 newton. sec. Find the liquid resistance to the
motion of the sphere.
Q20
πŸ’
The mass of a cyclist and the bike together is 80 kg, and the greatest power to the cyclist is of a horse. If
πŸ“
the maximum velocity for this cyclist on horizontal road is 18 km/h.
calculate the road resistance in kg.wt. If given that the cyclist ascends a slope inclined road with the
πŸ‘
same resistance inclines at an angle of sine to the horizontal with maximum velocity, calculate this
πŸ’πŸŽ
velocity in km/h.
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