Name :
Roll No. :
Topic : Constraint Theory
Mohammed
Asif
Ph : 9391326657, 64606657
MECHANICS QUESTION BANK
1.
In each of the following questions, find the unknown velocity / velocities. Assume that the thread is
inextensible and taut in each case.
a)
b)
c)
d)
f)
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e)
g)
h)
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i)
j)
k)
l)
m)
n)
o)
p)
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2.
If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B
rises.
3.
If the end of the cable at A is pulled down with a speed of 2m/s, determine the speed at which block B
rises.
4.
If the hydraulic cylinder at H draws in rod BC at 2 ft/s determine the speed of the slider at A.
5.
The hoist is used lift the load at D. If the end A of the chain is traveling downward at vA = 5ft/s and the end
B is traveling upward at vB = 2ft/s, determine the velocity of the load at D.
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6.
If the end A of cable is moving upwards at vA = 14m/s, determine the speed of block B.
7.
Determine the velocity of block B at the instant when the velocity of block A is 16 in/s, directed upwards.
8.
Block C is moving up at the constant speed of 6 in/s. Given that the elevations of blocks A and B are
always equal, determine the velocity of B.
9.
The pulley arrangement shown is designed for hosing materials. If BC remains fixed while the plunger P is
pushed downward with a speed of 1 m/s, determine the speed of the load at A.
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10.
In each of the following cases, some blocks are attached to some motor/s through ideal threads and pullies.
The motors are giving out/taking in the threads at the rates shown in the figure. Find the unknown velocity
in each case. The blocks are moving such that threads are always taut.
a)
b)
c)
d)
f)
g)
11.
Determine the time needed for the load at B to attain a speed of 8 m/s, starting from rest, if the cable is
drawn into the motor with an acceleration of 0.2 m/s2.
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12.
Determine the constant speed at which the cable at A must be drawn in by the motor in order to raise the
load 6m in 1.5s.
13.
Staring form rest, the cable can be wound onto the drum of the motor at a rate of vA = (3t2) m/s, where t is
in seconds. Determine the time needed to lift the load 7m. [use of the figure of previous problem]
14.
The cylinder C is being lifted using the cable and pully system as shown. If point A on the cable is being
drawn toward the drum with a speed of 2m/s, determine the speed of the cylinder.
15.
The cylinder C can be lifted with a maximum acceleration of ac =3 m/s2 without causing the cables to fail.
Determine the speed at which point A is moving toward the drum when S = 4m if the cylinder is lifted
from rest. In the shortest time possible. [use of the figure of previous problem]
16.
The motor at C pulls in the cable with an acceleration aC = (3t2) m/s2, where t is in second. The motor at D
drawn in its cable at aD = 5m/s2. If both motors start at the same instant form rest when d = 3m, determine
(a) the time needed for d = 0 and (b) the relative velocity of block A with respect to block B when this
occur.
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17.
The motor draws in the cable at C with a constant velocity of vC = 4m/s. The motor draws in the cable at D
with a constant acceleration of aD = 8m/s2. If vD = 0 when t = 0, determine (a) the time needed for block A
to rise 3m, and (b) the relative velocity of block A with respect to block B when this occurs
18.
If motors at A and B draw in their attached cables with an acceleration of a = (0.2t) m/s2, where i is in
seconds, determine the speed of the block when it reaches a height of h = 4m, starting from rest. Also, how
much time does it take to reach this height?
19.
The mine car C is being pulled up the incline using the motor M and the rope-and-pulley arrangement
shown. Determine the speed vp at which a point P on the cable must be traveling toward the motor to move
the car up the plane with a constant speed of v = 2m/s.
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20.
Each of the following problems shows some blocks attached to each other through ideal strings. Find the
unknown velocity at the instant shown in the figure.
a)
b)
c)
d)
e)
g)
h)
f)
i)
j)
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21.
A girl flies a kite at a height of 300ft, the wind carrying the kite horizontally away from her at a rate of 25
ft/sec. How fast must she let out the string when the kite is 500 ft away form her?
22.
In each of the following questions, find the value of unknown velocity V at the instant shown in each
figure. Assume that all bodies are perfectly rigid and that they are moving without any rotation.
a)
d)
b)
c)
e)
f)
23.
Two wedges A and B are being moved with constant velocities V1 and V2 as shown in the figure. Find the
x and y components of the block C. Assume that C neither rotates nor loses contact with A and B.
24.
Block A is being moved with a constant speed V0 towards left. Find the x – y components of velocity of
sphere at the instant x = R. Assume that the sphere moves without rotating.
25.
Find the speed of sphere C at instant x =2 3 R . Where R is the radius of each sphere. Assume that all
the spheres are always in contact and that they move without rotating.
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26.
Each of the following problems shows an arrangement of identical frictionless spheres placed on a
horizontal table. Each sphere is moving such that it is always in contact with neighboring spheres. Find the
unknown velocities at the instant shown in each figure.
a)
27.
b)
c)
d)
In each of the arrangements shown on next page, some particles are connected to each other via ideal
threads and pullies. Some of the pullies are step pullies. Find the magnitude and direction of unknown
velocity in each case.
a)
b)
c)
d)
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e)
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f)
h)
g)
i)
j)
k)
28.
In the given arrangement find x and y components of velocity of rod B at the instant rod A makes an angle
θ with vertical. Rod A is being rotated at constant angular speed ω and length of each rod is l.
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29.
In the given arrangement, find the speed of block C at the instant shown in the figure.
30.
In the given arrangement, block A is being moved downward with a constant speed VA. At the instant
shown in figure, find i) speed of B
ii) Angular speed of rod AB.
31.
Point B of bar BD is being pushed to the right with constant velocity VA. At the instant shown in the
figure. find
i) angular speed of rod BD
ii) velocity of point B
iii) speed of point D
32.
The wheel is rolling without slipping. Its centre has a constant velocity of 0.6m/s to the left. Compute the
angular velocity of bar BD and the velocity of end D when θ = 0.
33.
A block A is attached to the rim of a circular disk as shown in the figure. The wheel is rotating with a
constant angular speed ω . Find the velocity of block A at the instant shown in the figure.
34.
In the given arrangement, find the speed of point C at the instant shown in figure.
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KEY
1)
2)
7)
10
)
11
)
16
)
20
)
a) -1m/s, b) 14m/s, c) 2m/s, d) 10m/s, e) 8m/s, f) 5m/s, g) 14m/s, h) 4/3 m/s, i) 7/4 m/s, j) 12m/s
k) 16m/s, l) 4m/s, m) 12m/s, n) 10m/s, o) 10m/s, p) 2m/s
0.5m/s ↑
3) 0.5m/s ↑
4) 4 ft/s ↓
5)
32 in/s ↓
8) 4 in/s ↓
a) 2m/s, b) 4m/s, c) 6m/s, d) 1m/s, e) 6 m/s, f) 8m/s, g) 6m/s
9)
160s
13
)
1.07s, 5.93 m/s
→
32 m/s ↓
3.83s
14
)
0.667
m/s
15
)
↑
a) 1.22s,
18
19 6 m/s
b) 2.90m/s ↑
)
)
10 cos θ 2
10 cos θ1
20
m / s , e) 10 cot θm / s , f)
m/s ,
m / s , b) 5 2m / s , c) 10 sec θm / s , d)
a)
cos θ2
3
cos (θ1 − θ 2 )
10 tan θ 2
m / s , i) V1 =10 m / s, V2 =10 cos θ m / s ,
g) 4(1 −cos ec θ) m / s , h) V1 =10 tan θ2 , V1 =
tan θ1
j)
21
)
23
)
12
)
6)
17
)
10
m/s
(1 + cos θ )
20 ft /sec
Vx =
(V2 −V1 ) sin θ ,
22
)
24
)
10
10
m / s , b) 10 3m / s , c) 5m/s, d)
m / s , e) 10 3m / s f) 5 m/s
3
3
V
V0
25
V 3
3 3
Vx = 0 , V y =
,
Vx =
, Vy =
,V
)
4
2
2
2 tan θ
a)
2
(V +V2 ) sin θ
Vy = 1
2
a) V = 10/s, b) 5 3m / s , c) VB =VC = 5 3 m / s , d) V A = 5 3 m / s, VB = 7.5m / s
26
)
27. a) 5m/s, b) 2.5m/s, c) 40/9 m/s, d) 15m/s, e) 20/9 m/s, f) 65/6 m/s, g) 16 m/s, h) Thread cannot remain taut. Henc
fall down with acceleration g.
28 Vx = rωcos θ( rightward ),
29 2lωcos θ righwards
30 i)
)
)
)
VB =V A ωtθ rightwards
V y = rωcos θ( downward ),
VA
ii) ω =
i sin θ
V A2
iii) a B =
L sin 3 θ
rightwards
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33
)
V = rω
2+ 3
(rightwards
3
)
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