PROBLEM 14.55 (Continued)
PROBLEM 14.56
Three small identical spheres A, B, and C, which can slide on a horizontal, frictionless surface, are attached
to three strings of length l which are tied to a ring G. Initially, the spheres rotate clockwise about the ring
which moves along the x axis with a velocity
v
0
. Suddenly the ring breaks and the three spheres move freely in
the xy plane. Knowing that
(3.5 ft/s) ,
A
vj
(6.0 ft/s) ,
C
vi
16 in.a
and
9in.,d
determine (a) the initial
velocity of the ring, (b) the length l of the strings, (c) the rate in rad/s at which the spheres were rotating
about G.
PROBLEM 14.56 (Continued)
PROBLEM 14.57
A stream of water with density
= 1000 kg/m
3
is
discharged from a nozzle at the rate of 0.06 m
3
/s. Using
Bernoulli’s equation the gage pressure P in the pipe just
upstream from the nozzle is
2
1
2
2
2vvP
. Knowing
the nozzle is held to the pipe by six flange bolts, determine
the tension in each bolt, neglecting the initial tension
caused by the tightening of the nuts.
PROBLEM 14.58
A jet ski is placed in a channel and
is tethered so that it is stationary.
Water enters the jet ski with
velocity
v
1
and exits with velocity
v
2
. Knowing the inlet area is A
1
and the exit area is A
2
, determine
the tension in the tether.
PROBLEM 14.59
The nozzle shown discharges a stream of water at a flow rate
Q 475 gal/min with a velocity v of magnitude 60 ft/s. The stream is split
into two streams with equal flow rates by a wedge that is kept in a fixed
position. Determine the components (drag and lift) of the force exerted by the
stream on the wedge. (1 ft3 7.48 gal.)
PROBLEM 14.60
The nozzle shown discharges a stream of water at a flow rate
Q 500 gal/min with a velocity v of magnitude 48 ft/s. The stream is split
into two streams of equal flow rates by a wedge that is moving to the left at a
constant speed of 12 ft/s. Determine the components (drag and lift) of the
force exerted by the stream on the wedge. (1ft3 = 7.48 gal.)
PROBLEM 14.61
A rotary power plow is used to remove snow
from a level section of railroad track. The plow
car is placed ahead of an engine that propels it
at a constant speed of 20 km/h. The plow car
clears 160 Mg of snow per minute, projecting it
in the direction shown with a velocity of 12 m/s
relative to the plow car. Neglecting friction,
determine (a) the force exerted by the engine
on the plow car, (b) the lateral force exerted by
the track on the plow.
PROBLEM 14.62
Tree limbs and branches are being fed at A at the rate of
5 kg/s into a shredder which spews the resulting wood
chips at C with a velocity of 20 m/s. Determine the
horizontal component of the force exerted by the shredder
on the truck hitch at D.
PROBLEM 14.63
Sand falls from three hoppers onto
a conveyor belt at a rate of 90 lb/s
for each hopper. The sand hits the
belt with a vertical velocity 1
v 10
ft/s and is discharged at A with a
horizontal velocity 2
v 13 ft/s.
Knowing that the combined mass
of the beam, belt system, and the
sand it supports is 1300 lb with a
mass center at G, determine the
reaction at E.