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) Determine the truth sets for the following predicates
(i) x, y ∈ Z such that x ≤ y
(ii) x, y ∈ Z such that (x + y = 0) ∨ (xy = 0).
The following particulars relate to a symmetrical tangent cam operating a roller follower :-
Least radius = 36 mm, nose radius = 30 mm, roller radius = 21 mm, distance between cam
shaft and nose centre = 28 mm, angle of action of cam = 150°, cam shaft speed = 750 r.p.m.
Assuming that there is no dwell between ascent and descent, determine the lift of the valve
and the acceleration of the follower at a point where straight flank merges into the circular
nose.
The external and internal radii of a friction clutch of disc type are 120 mm and 70 mm
respectively. Both sides of the friction clutch are effective and co-efficient of friction is
equal to 0.25. The friction clutch is used to rotate a machine from a shaft which is rotating
at a constant speed of 320 r.p.m. The moment of inertia of the rotating parts of the machine
is 5.5 kg m2
. The intensity of pressure is not to exceed 80,000 N/m2
. Assuming uniform
wear, determine the time required for the machine to attain the full speed when the clutch is
suddenly applied. Also determine the energy lost in slipping of the clutch.
100 rpm in the counter-clockwise direction. Lengths of various links are OP = 90 mm,
OA = 300 mm, AR = 480 mm and RS = 330 mm. The slider move along an axis
perpendicular to AO and is 120 mm from O. Determine the velocity of the slider during
cutting and return strokes.
Least radius = 36 mm, nose radius = 30 mm, roller radius = 21 mm, distance between cam
shaft and nose centre = 28 mm, angle of action of cam = 150
The following particulars relate to a symmetrical tangent cam operating a roller follower :-
Least radius = 36 mm, nose radius = 30 mm, roller radius = 21 mm, distance between cam
shaft and nose centre = 28 mm, angle of action of cam = 150°, cam shaft speed = 750 r.p.m.
Assuming that there is no dwell between ascent and descent, determine the lift of the valve
and the acceleration of the follower at a point where straight flank merges into the circular
nose.
3. The following particulars relate to a symmetrical tangent cam operating a roller follower :-
Least radius = 36 mm, nose radius = 30 mm, roller radius = 21 mm, distance between cam
shaft and nose centre = 28 mm, angle of action of cam = 150°, cam shaft speed = 750 r.p.m.
Assuming that there is no dwell between ascent and descent, determine the lift of the valve
and the acceleration of the follower at a point where straight flank merges into the circular
nose.
Least radius = 36 mm, nose radius = 30 mm, roller radius = 21 mm, distance between cam
shaft and nose centre = 28 mm, angle of action of cam = 150
A spherical pressure vessel is constructed by bolting two hemispheres together along rigid flanges as shown in the sketch. The sphere has an internal diameter of 1.5 m and the plate thickness is 5 mm. Allowable tensile stresses are 45 MPa in the shell and 80 MPa in the bolts.
1 Calculate the allowable gauge pressure.
2 Determine the number of bolts required if the bolt diameter is 25 mm
(Note: bolt root diameter = 0.84 × nominal bolt diameter)
A safety valve (pressure relieve valve) on top of a pressure vessel containing steam under pressure p = 2 MPa, has a discharge hole of diameter d = 10 mm as shown in the figure below. The valve is designed to release the steam when the pressure reaches the maximum allowable value pmax = 2.23 MPa. If the free height (i.e., uncompressed height) of the spring hfree = 135 mm and its spring stiffness k = 5 kN/m, what should be the dimension h of the valve?
