calculate the redshift gh/c^2 if h is the distance from the ground to a satellite in low-Earth orbit, 300km. Suppose the "light" is actually a radio wave with a frequency of 10^11 Hz. How many cycles would the transmitter emit if it ran for one day? How many fewer would be received in one day by the satellite? How long did it take the transmitter to generate these "extra" cycles?
Since gh/c^2 is dimensionless, it must be the RELATIVE change is wavelength (or frequency). g is the acceleration of gravity at the earth's surface. Plug in the numbers and you get
(delta f)/f = 9.8 m/s^2*300m/(9*10^16) m^2/s^2 = 3.27*10^-14.
The red-shifted frequency will be that times 10^11 Hz, or 3.27*10^-3 Hz. Use that to answer the other questions.
A hydraulic lift office chair has it's seat attached to a piston with an area of 11.2cm squared. The chair is raised by exerting force on another piston, with an area of 4.12 cm squared. If a person sitting on the chair exerts a downward force of 219 N, what force needs to be exerted on the small piston to lift the seat?
Please use "Post a New Question" for new questions.
Questions about hydraulic lifts can always be solved by using the fact the
(force)/(piston area0 is a constant for all pistons in contact with the same fluid
where did u get 9*10^16 and how can i answer the questions??? im still confused.. sorry
To calculate the redshift, we need to determine the relative velocity between the satellite and the transmitter. Given the distance from the ground to the satellite in low-Earth orbit (h = 300 km), we can assume the satellite is stationary compared to the ground.
To find the relative velocity, we can calculate the speed of light (c) and the gravitational constant (G). The speed of light is approximately 3 x 10^8 meters per second (m/s), and the gravitational constant is approximately 6.67430 x 10^-11 m^3/(kg s^2).
Now, let's proceed with the calculations:
1. Relative Velocity:
The relative velocity (v) is given by v = h * (G / c^2).
Since h is in kilometers, we need to convert it to meters: h = 300,000 meters.
Plugging in the values, we get v = 300,000 * (6.67430 x 10^-11 / (3 x 10^8)^2).
2. Redshift:
The redshift (z) can be calculated using the formula z = Δf / f, where Δf is the change in frequency, and f is the initial frequency.
Here, Δf = v * f, where v is the relative velocity we calculated earlier.
Plugging in the values, we get Δf = v * f = v * 10^11 Hz.
Now, we can calculate the redshift:
z = Δf / f = (v * 10^11 Hz) / (10^11 Hz) = v.
Therefore, the redshift (z) is equal to the relative velocity (v).
Now, moving onto the next part of the question:
3. Cycles Emitted:
To calculate the number of cycles emitted by the transmitter in one day, we need to multiply the frequency (f = 10^11 Hz) by the time (t) in seconds.
Since one day has 24 hours and each hour has 60 minutes, we have:
t = 24 hours * 60 minutes * 60 seconds.
The number of cycles emitted (N) is given by N = f * t.
4. Cycles Received:
The number of cycles received by the satellite will be lower due to the redshift effect. We need to multiply the number of cycles emitted (N) by (1 - z) since the satellite observes a redshifted frequency.
Therefore, the number of cycles received (N_r) is given by N_r = N * (1 - z).
5. Time to Generate Extra Cycles:
To calculate the time it takes to generate the "extra" cycles, we need to divide the number of cycles emitted (N) by the frequency (f).
Therefore, the time (T) is given by T = N / f.
By applying these formulas and performing the calculations, you can find the values for the number of cycles emitted, number of cycles received, and the time taken to generate these "extra" cycles.
Please note that the accurate result may require inputting the exact values for constants like G and c, which are given here with reasonable approximations.