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- Test #1.
(...........).
- Test #1.
( 21st March, 2000 ).
- Test #2 .
( 25 th April, 2000 ).
- Test #3 .
( 23rd May, 2000 ).
- Final Exam #1.
( Spring '99 ).
- Final Exam #2.
( 17 / 6 / 2000 ).
Question
# 1
·
The position of a particle as a function of time is give by :
x
= 3t3 +
2t2 - 5t
y
= 2t3
-
The
velocity vector ( v = ivx +
jvy ) at t = 1 sec.
-
The
acceleration vector ( a = iax
+ jay
) at t =1 sec.
-
The
angle between v and a at t = 1
sec.
Question
# 2
·
The two vectors A and B are
given by :
Find
:
-
The
constant (a) such that A and B are mutually perpendicular.
-
A
vector C such that : C = 2A -
B
-
A
vector D
perpendicular to the plane containing A and B.
Question
# 3
·
Two race cars starts from rest at the same time with constant
accelerations of :
a1
= 50 m/s2
and
a2 = 30 m/s2
Find :
a.
The position of each car after 5 seconds.
b.
When the distance between the two cars become 1000 m ?
c.
Show that the ratio between their speeds at any given time is constant.
Verify this fact for t = 5 sec.
Question
# 4
*
A small ball was thrown vertically upward from high cliff with an initial
velocity Vo = 30 m/s .
At the same time a boat starts from rest
towards the cliff with an acceleration of 2 m/s2;
a.
Find the maximum height reached by the ball.
b.
When the ball is at a height of 25 m ?
c.
What should be the position x such that the ball hits the boat?
End of test
1.
A projectile is fired with initial velocity vo = 15i + 40j
(m/s) . The speed of the projectile st the point of maximum height is :
-
0
m/s
-
40
m/s
-
43
m/s
-
15
m/s
-
none
of them
2.
A projectile is thrown with initial velocity vo =
15i + 40j (m/s). The range of
this projectile is :
-
77
m
-
240
m
-
120
m
-
154
m
-
none
of them
3.
A ball is thrown with initial velocity upwards from the top of a (50 m) high
building with initial velocity of ( 10 m/s ). The time needed for the ball to
reach a height of (10 m) above
the ground is:
-
5
s
-
2.5
s
-
4
s
-
0
s
-
none
of them
4.
A ball is kicked with initial velocity ( 50 m/s ) at an angle ( 37ْ
( above
the horizontal.. The time needed by the ball to reach the maximum height is :
-
4
s
-
5
s
-
2
s
-
3
s
-
none
of them
5.
Given two vectors A = 4i -
3j and B = -6i
+ 8j
. The direction of the vector ( A – B ) with respect to the x-axis
is:
-
37o
-
153o
-
–
65o
-
–47o
-
none
of them
6.
A car starts from rest and moves with constant acceleration. The average
velocity during the first three seconds is ( 9 m/s) . The acceleration is :
-
6
m/s2
-
18
m/s2
-
9
m/s2
-
77
m/s2
-
27
m/s2
7.
An object moves along the x-axis according to the equation : x (t) = ( 3t2
- 2t
+ 3 ) , where x is in meters and t is in seconds. The instaneous
acceleration of the car at t = 3 s is :
-
77
m/s2
-
18
m/s2
-
9
m/s2
-
6
m/s2
-
27
m/s2
8.
A car moving with initial velocity ( 20 m/s ) starts to slow down with
acceleration ( - 2
m/s2 ) The time
required for the car to stop :
-
10
s
-
2
s
-
0
s
-
8
s
-
none
of them
9.
A boy standing on the roof of a tall building throws a ball upwards with a
velocity of ( 10 m/s ). The ball
hits the ground after ( 5s ). The height of the building is :
-
175
m
-
125
m
-
250
m
-
100
m
-
none
on them
10.
A boy throws a ball vertically upwards and catches it again after ( 10 s ).
The maximum height reached by the ball is :
-
50
m
-
125
m
-
250
m
-
100
m
-
none
of them
11.
A plane flying horizontally with constant speed, drops a bag. At the instant
when the bag hits the ground :
-
The
plane is above and behind the bag.
-
The
plane is above and in front of the bag.
-
The
plane is directly above the bag.
-
The
plane is below and in front of
the bag.
12.
A ball is thrown upwards with initial velocity ( 15 m/s ) . Its acceleration
at the maximum height is :
-
0
m/s2
-
10
m/s2 down
-
5
m/s2 down
-
10
m/s2 up
-
none
of them
End
of test
Q1.
Three blocks with masses mA = 4kg., mB = 6 kg and mC
= 8 kg are connected by light string as shown in the diagram. The coefficient
of
Kinetic friction between blocks
A and B is μk1
= 0.4 . The coefficient of kinetic friction between bock B and the surface is μk2
= 0.3 .
Calculate
: 
a.
The acceleration of block B.
b.
The tension in the first string T1.
c.
The tension in the second string T2.
Q2.
A small coin on mass 20g is placed on a flat horizontal turntable at a
distance of 5 cm from the center. The turn table is observed to make
three revolution in 3.14
sec.
a.
What is the speed of the coin in it revolves without slipping ?
b.
What is the acceleration of the coin ?
c.
What is the magnitude of the frictional force acting on the coin ?
d.
Now if the coin id placed at a distance of
10 cm from the center, it observed
to be about to start sliding off the
turntable. Find the coefficient of static friction .
Q3.
A block of mass 2 kg compresses a spring with force constant k = 600 N/m, a
distance of 0.2 m as shown in the
diagram. The block is then
released from rest and moves on
a rough horizontal surface a total distance 1.2 m before coming to rest again.
Calculate:
a.
The work done by the spring.
b.
The work done by the friction force.
c.
The
coefficient of kinetic friction between the block and surface
.
Q1.
A 10 kg block is released from rest at point A on the track shown in the
diagram. The track is frictionless except the part BC , of length
5.0 m . The block slides down
the track, passes the BC region, hits a spring of force constant
k = 2500 N/m and conpresses it 0.2 m before
coming to rest.
a.
Fine the velocity of the block at point B.
b.
Calculate the maximum energy stored in the spring.
c.
Determine the coefficient of kinetic friction between the surface BC
and block.
d.
Find the velocity of the particle at point C.
Q2.
An object of mass 0.3 kg moving to the right with velocity of 0.5 m/sec
collides head-on ( in one dimension )
with another object with a
mass of 0.2 kg moving with
velocity of 1 m/sec to the left .
a.
If the two objects stick together, what is their final velocity and in
which direction ?
b.
Calculate the loss of kinetic energy during the collision in part a .
c.
If the blocks do not stick together, and the collision is completely
elastic, find the final velocity of each object.
End of test
-
Car
A is traveling along a straight road at a constant speed of ( 10 m/s ).
Just as it passes a parked police car, the police car starts to accelerate
at ( 2 m/s2 ) in
the same direction.
-
Determine
the time it takes for the police cat to reach car A.
-
Find
the speed of the police car when it reaches car A.
-
A
box of mass m, is dragged across a rough level floor, having a coefficient
of friction μk
, by a rope that pulled upward at an angle θ
above the horizontal
with a force of magnitude F.
in terms of m , θ
, μk
, F and g :
-
Show
that the normal force N = ( mg – F sin θ
).
-
Find
the frictional force.
-
Determine
the acceleration.
-
A
small sphere of mass 2 kg and radius 0.1 m is released from point A as
shown in the diagram below. The sphere rolls down without slipping along
the track and stops at point C. Find :
-
The
total energy at point A.
-
The
linear velocity of the sphere at point B(Va) , if it losses 25 J as work
against friction between A and B.
-
The
maximum height y. reached by the sphere if it losses 15 J as work
against friction between B and C.
-
The
acceleration of the sphere while moving up the incline towards C.
-
A
bullet of mass 0.1 kg moving with a velocity of 400 m/s hits a wooden
block of mass 2 kg initially at rest. The bullet emerges with a velocity
of 100 m/s. The block moves up a frictionless incline and compresses a
spring of force constant k = 3200 N/m . If the final position of the block
at height of y = 1.45 m (see figure). Calculate :
-
The
velocity of the wooden block immediately after impact.
-
The
kinetic energy lost during the impact.
-
The
distance through which the spring is compressed.
-
A
bullet of mass 0.2 kg moving with a velocity of 450 m/s hits a system of
spheres as shown in the figure. The bullet is embedded in the upper sphere
of mass 1.8 kg. The system rotates after impact around an axis through the
central sphere with angular velocity ω
. Calculate :
-
The
angular momentum of the bullet before impact.
-
The
moment of inertia of the system after impact.
-
The
angular velocity ω
of the system after impact.
End of test
1.
A stone drops from a height of 100 m above the ground. At the same
time, another stone thrown upwards from the ground with a speed of 25 m/sec.
a.
At what time will the two stones be at the same height?
b.
How much time does the first stone take to reach the ground?
2.
A boy standing on the roof of a 20 m tall building throws an apple
horizontally with a velocity of 16 m/sec. At the same time, another boy
standing on the ground shoots an arrow with a velocity of 20 m/sec at an angle
θ from the horizontal
direction.
a.
What is the angle θ
that will make the arrow hit the apple.
b.
At what time will the arrow hit the apple.
3.
Block A weights 44 N, and block B weights 22 N. They are connected
together as shown in the diagram.
a.
Determine the minimum weight of block C that is necessary to prevent
block A from sliding, if coefficient of static μs
between A and the table is 0.2.
b.
If block C is suddenly lifted off block A. What is the acceleration of
block A, if the coefficient of kinetic friction between A and the table is
0.15 ?
4.
A small block with mass of 0.08 kg is tied to a cord passing through a
small hole in a frictionless horizontal surface as shown in the diagram. The
mass initially rotates in a circle of radius 0.3 m, with speed of 0.8 m/sec.
The cord is then pulled from below by force F, changing the mass to a radius
0.1 m .
a.
Find the tension in the cord when the radius is 0.3 m.
b.
What is the initial angular momentum of the block?
c.
Find the linear speed for the mass when the radius is 0.1 m.
5.
A pendulum with mass of 1
kg and length of 1.8 m is released from rest from the position shown in the
diagram. It collides with a block resting on a horizontal rough surface. The
pendulum comes to rest after the collision. The coefficient of kinetic
friction between the block and the surface is μk =
0.2.
a.
Find the velocity of the pendulum just before the collision.
b.
Fine the velocity of the block just after the collision
c.
Find the distance traveled by the block before coming to rest.
6.
A sphere of radius R = 0.1 m, mass M = 7 kg and moment of inertia I =
2/5 MR2 , starts to rolls from rest at the top of and incline as
shown in the diagram. A block having same mass is also released at the same
time top of the incline. Assume there is no friction between the block and the
incline.
a.
Calculate the velocity of the sphere at the bottom of the incline.
b.
Calculate the velocity of the block the bottom of the incline.
c.
Calculate the velocity of the block at the bottom of the incline.
Which
object reached the bottom first.
7.
A block with mass of 2 kg is pushed against spring. Compressing it a
distance 0.2 m. as shown in the diagram. Then the block is released from rest.
a.
If the spring constant K = 400 N/m . Find the speed of the block after
leaving the spring.
b.
The block then slides on a circular frictionless surface with a radius
of 2 m. Find the angle θ
at which the block leaves
the surface.
8.
A uniform ladder of length L = 15 m, and a weight 500 N , rests
against a frictionless vertical wall as shown in the diagram . The coefficient
of friction between the ladder and the ground μs
.
a.
Find the friction force on the ladder if a person weighting 800 N
stands 4 m from the bottom of the ladder.
b.
If the person stands 9 m
from the bottom. Find the coefficient of static friction needed to prevent the
ladder from slipping.
End
of Test
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