Horizontal angulation is: Select one: a. the side-to-side angulation. b. different when using the paralleling and bisecting tech
1 answer:
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a) The momentum of the coconut is 3 kg m/s
b) At first, the air resistance is negligible, so the coconut accelerates due to the force of gravity
c) The coconut reaches its terminal velocity
Explanation:
a)
The momentum of an object is given by the equation
where
m is the mass of the object
v is its velocity
For the coconut in this problem, we have:
m = 1.5 kg (mass)
v = 2 m/s (velocity)
Therefore, its momentum is
B)
There are only two forces acting on the coconut during its fall:
- The force of gravity, of magnitude
(m= mass of the coconut, g = acceleration of gravity), acting downward
- The air resistance, acting upward, whose magnitude is proportional to the speed of the coconut
During the first momentums of the fall, the speed of the coconut is still low, so the air resistance is mostly negligible, and therefore only the force of gravity is acting on the coconut. Since this force is constant, it means that the acceleration of the coconut is constant: therefore, its velocity keeps increasing during the fall, and the coconut speeds up.
C)
If the tree is very tall, the fall of the coconut lasts long, and the speed of the coconut keeps increasing. Since the air resistance is proportional to the speed, this means that at some point, the air resistance is no longer negligible, and it starts to have some effect on the fall of the coconut. In particular, at a certain point, the air resistance will become equal (in magnitude) to the force of gravity (but opposite in direction): this means that from this point, the acceleration of the coconut will be zero, and therefore the coconut will continue its motion at constant velocity. This velocity is called terminal velocity, and it occurs when the force of gravity is equal to the air resistance:
where is the air resistance.
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A) Speed in the lower section: 0.638 m/s
B) Speed in the higher section: 2.55 m/s
C) Volume flow rate:
Explanation:
A)
To solve the problem, we can use Bernoulli's equation, which states that
where
is the pressure in the lower section of the tube
is the heigth of the lower section
is the density of water
is the acceleration of gravity
is the speed of the water in the lower pipe
is the pressure in the higher section
is the height in the higher pipe
is hte speed in the higher section
We can re-write the equation as
(1)
Also we can use the continuity equation, which state that the volume flow rate is constant:
where
is the cross-section of the lower pipe, with
is the radius of the lower pipe (half the diameter)
is the cross-section of the higher pipe, with
(radius of the higher pipe)
So we get
And so
(2)
Substituting into (1), we find the speed in the lower section:
B)
Now we can use equation (2) to find the speed in the lower section:
Substituting
v1 = 0.775 m/s
And the values of the radii, we find:
C)
The volume flow rate of the water passing through the pipe is given by
where
A is the cross-sectional area
v is the speed of the water
We can take any point along the pipe since the volume flow rate is constant, so
Therefore, the volume flow rate is
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