Gasoline is piped underground from refineries to major users. The flow rate is 3.00 × 10 − 2 m 3 /s (about 500 gal/ min), the viscosity of gasoline is 1.00 × 10 − 3 (N/m 2 ) ⋅ s, and its density is 680 kg/m 3 . (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?
Gasoline is piped underground from refineries to major users. The flow rate is 3.00 × 10 − 2 m 3 /s (about 500 gal/ min), the viscosity of gasoline is 1.00 × 10 − 3 (N/m 2 ) ⋅ s, and its density is 680 kg/m 3 . (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?
Gasoline is piped underground from refineries to major users. The flow rate is
3.00
×
10
−
2
m3/s (about 500 gal/ min), the viscosity of gasoline is
1.00
×
10
−
3
(N/m2)
⋅
s, and its density is 680 kg/m3. (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?
Two objects of masses m₁
0.48 kg and m₂ = 0.86 kg are placed on a horizontal frictionless surface and a compressed spring of force constant k 260 N/m is placed between them as in figure (a). Neglect the mass of the spring. The spring is not attached to either object and is
compressed a distance of 9.4 cm. If the objects are released from rest, find the final velocity of each object as shown in figure (b). (Let the positive direction be to the right. Indicate the direction with the sign of your answer.)
m/s
V1
V2=
m1
m/s
k
m2
a
す。
k
m2
m1
b
Sand from a stationary hopper falls on a moving conveyor belt at the rate of 4.90 kg/s as shown in the figure below. The conveyor belt is supported by frictionless rollers and moves at a constant speed of v = 0.710 m/s under the action of a constant horizontal external force F
by the motor that drives the belt.
Fext
i
(a) Find the sand's rate of change of momentum in the horizontal direction.
(b) Find the force of friction exerted by the belt on the sand.
(c) Find the external force
ext'
(d) Find the work done by F
in 1 s.
ext
(e) Find the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion.
ext supplied
An unstable atomic nucleus of mass 1.84 × 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.14 × 10-27 kg, moves in the y direction with a speed of 6.00 × 106 m/s. Another particle, of mass 8.46 × 10-27 kg, moves in the x direction with a speed of
4.00 x 106 m/s.
(a) Find the velocity of the third particle.
|Î +
i) m/s
(b) Find the total kinetic energy increase in the process.
]
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