Mechanics tutorial_2
1
1.
A box of mass m is lowered by means of a rope, which passes over a fixed cylinder, the
angle of embrace being
. The stretch in the rope and its mass can both be ignored. If the
coefficient of friction between the rope and the cylinder is
, show that the tension at B and
C are governed by the relationship,
e
T
T
B
c
If the downward acceleration of the box is
a
, determine the tension
T
B
.
mg
A
B
C
D
ans:
e
a
g
m
T
B
)
(
2.
The same vehicle in question 7 of tutorial 1 is under consideration. The arm is now carrying
a mass of 3.0kg. Determine the force exerted by the arm on the body for the position
shown.
ans:
(55.62i+47.31j)N
3.
A particle is projected from P which lies in a horizontal plane with a velocity of 5m/s at an
angle of 30
above the plane. Find
(a) maximum height reached,
(b) the horizontal distance travelled before the particle hit the ground,
(c) the length of the curved path traced by the particle.
ans:
(a)
0.319m
(b)
2.21m
(c)
2.349m
4.
An escalator has a mass of 500kg. It is raised through a height of 130m by cable. The
initial upward acceleration is 1.65m/s
2
and this remains constant until a speed of 10m/s is
reached. The speed remains constant until, during the final stage of motion, the lift has a
constant retardation that brings it to rest. The total time taken is 16.7s. Determine
(a) tension in the cable at each stage
(b) total work done by the tensile force on the lift
(c) the maximum required for such system.
ans:
(a)
5730N, 4905N, 1170N
(b)
637.6kNm
(c)
57.3kW
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Mechanics tutorial_2
2
5.
Two coaxial shafts are connected together by a coupling, which is fastened by a number of
0.3kg bolts at 100mm radius. At a particular moment the angular velocity is 15rev/s and the
angular acceleration is 200rev/s
2
. Find the magnitude of the forces acting on the bolts due
to the rotation.
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 Spring '09
 GXXY
 Acceleration, Force, Friction, Mass

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