6.1.115 To approximate the speed of the current of a river, a circular paddle wheel with radius 4 ft. is lowered into the water
1 answer:
Answer:
1.2 ft/s or 72 ft/min
Explanation:
To solve this problem, we can use the relationship between the angular and linear speed for this particular movement (rotation). As the speed of the current is tangent to the trajectory of the wheel we can define as follows:
The speed of the current is 72 ft/min
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Answer: 7.5 rev/s
Explanation:
We are given the angular velocity a helicopter's main rotor blades:
However, we are asked to express this in the International Systrm (SI) units. In this sense, the SI unit for time is second (
):
(a) 0.448
The gravitational potential energy of a satellite in orbit is given by:
where
G is the gravitational constant
M is the Earth's mass
m is the satellite's mass
r is the distance of the satellite from the Earth's centre, which is sum of the Earth's radius (R) and the altitude of the satellite (h):
r = R + h
We can therefore write the ratio between the potentially energy of satellite B to that of satellite A as
and so, substituting:
We find
(b) 0.448
The kinetic energy of a satellite in orbit around the Earth is given by
So, the ratio between the two kinetic energies is
Which is exactly identical to the ratio of the potential energies. Therefore, this ratio is also equal to 0.448.
(c) B
The total energy of a satellite is given by the sum of the potential energy and the kinetic energy:
For satellite A, we have
For satellite B, we have
So, satellite B has the greater total energy (since the energy is negative).
(d)
The difference between the energy of the two satellites is: