Which of the following is the most effective relaxation technique?
2 answers:
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Answer:
a. 15.4 seconds
b. 0.455 m/s
Explanation:
a. The carousel rotates at 0.13 rev/s.
This means that it takes the carousel 1 sec to make 0.13 of an entire revolution.
This means that time it will take to make a complete revolution is:
1 / 0.13 = 7.7 seconds
Therefore, the time it will take to make 2 revolutions is:
2 * 7.7 = 15.4 seconds
b. Let us calculate the linear velocity. Angular velocity is given as:
where v = linear velocity and r = radius
The radius of the circle is 3.5 m and the angular velocity is 0.13 rev/s, therefore:
0.13 = v / 3.5
v = 3.5 * 0.13 = 0.455 m/s
Linear velocity is 0.455 m/s
(a) 198 g
When the rock is submerged into the water, there are two forces acting on the rock:
- its weight, equal to (m=mass, g=acceleration of gravity), downward
- the buoyant force, equal to (
=mass of water displaced), upward
So the resultant force, which is the apparent weight of the rock (W'), is
which can be rewritten as
where m' is the apparent mass of the rock. Using:
m = 540 g
m' = 342 g
we find the mass of water displaced
(b)
If the rock is completely submerged, the volume of the rock corresponds to the volume of water displaced.
The volume of water displaced is given by
where
is the mass of the water displaced
is the density of the water
Substituting,
And so this is also the volume of the rock.
(c)
The average density of the rock is given by
where
m = 540 g = 0.540 kg is the mass of the rock
is its volume
Substituting into the equation, we find