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PROBLEM 13.39
The sphere at A is given a downward velocity
0
v
of magnitude
5 m/s and swings in a vertical plane at the end of a rope of
length
2ml=
attached to a support at O. Determine the angle
θ
at which the rope will break, knowing that it can withstand a
maximum tension equal to twice the weight of the sphere.
PROBLEM 13.40
The sphere at A is given a downward velocity
0
v
and swings
in a vertical circle of radius l and center O. Determine the
smallest velocity
0
v
for which the sphere will reach Point B as
it swings about Point O (a) if AO is a rope, (b) if AO is a
slender rod of negligible mass.
PROBLEM 13.41
A bag is gently pushed off the top of a wall at A and swings in a vertical
plane at the end of a rope of length l Determine the angle
θ
for which the
rope will break, knowing that it can withstand a maximum tension equal to
twice the weight of the bag.
PROBLEM 13.42
A roller coaster starts from rest at A, rolls down the
track to B, describes a circular loop of 40-ft diameter,
and moves up and down past Point E. Knowing that h =
60 ft and assuming no energy loss due to friction,
determine (a) the force exerted by his seat on a 160-lb
rider at B and D, (b) the minimum value of the radius of
curvature at E if the roller coaster is not to leave the
track at that point.
PROBLEM 13.42 (Continued)
PROBLEM 13.43
In Problem 13.42, determine the range of values of h
for which the roller coaster will not leave the track at D
or E, knowing that the radius of curvature at E is
75 ft.
ρ
=
Assume no energy loss due to friction.
PROBLEM 13.42 A roller coaster starts from rest at A,
rolls down the track to B, describes a circular loop of
40-ft diameter, and moves up and down past Point E.
Knowing that h = 60 ft and assuming no energy loss
due to friction, determine (a) the force exerted by his
seat on a 160-lb rider at B and D, (b) the minimum
value of the radius of curvature at E if the roller coaster
is not to leave the track at that point.
PROBLEM 13.43 (Continued)
PROBLEM 13.44
A small block slides at a speed v on a horizontal surface. Knowing that
h = 0.9 m, determine the required speed of the block if it is to leave the
cylindrical surface BCD when
θ
= 30°.
PROBLEM 13.45
A small block slides at a speed
8v=
ft/s on a horizontal surface at a
height
3
h=
ft above the ground. Determine (a) the angle
θ
at which it
will leave the cylindrical surface BCD, (b) the distance x at which it
will hit the ground. Neglect friction and air resistance.
PROBLEM 13.45 (Continued)
