6. Mithra is an unknown planet that has two airless moons. A and B, in circular orbits around it.
1 answer:
The acceleration of gravity on Moon B is D) 0.25 m/s2
Explanation:
The data listed in the problem are not clear: find them in the table attached.
The acceleration of gravity on a planet is given by the following equation:
where:
is the gravitational constant
M is the mass of the planet
R is the radius of the planet
Here we want to find the acceleration of gravity on the surface of Moon B, which has the following data:
(mass)
(radius)
And substituting into the equation, we find:
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Answer:
a) t=10.2s
b) The 2g-cube moves first
Explanation:
Since the electric force is the same on both cubes and so is the coefficient of static friction, the first one to move will be the one with less mass.
So, on the 2g-cube the sum of forces are:
Replacing the friction on the first equation:
Thus
The electric force is:
Solving for q:
q=71.44nC
This amount divided by the rate at which they are being charged:
t = 71.44nC / 7nC/s = 10.2s
Apparent frequency heard by the staff: 389 Hz
Explanation:
The phenomenon described in this situation is called Doppler effect.
Doppler effect occurs when there is a source emitting a wave in relative motion with respect an observer. In such situation, the frequency of the wave as perceived by the observer ("apparent frequency") is shifted from the real frequency of the sound ("proper frequency"). In particular:
- The observer perceives a higher frequency if the source is moving towards them
- The observer perceives a lower frequency if the source is moving away from them
The formula to calculate the apparent frequency in the Doppler effect is
where
f is the proper frequency
f' is the apparent frequency
v is the speed of the wave
is the velocity of the observer (positive if they are moving towards the source, negative if moving away)
is the velocity of the source (positive if it is moving away, negative if moving towards the observer)
First of all, in this problem we have to calculate the proper frequency of the sound wave emitted from the ambulance; we have:
v = 343 m/s (speed of sound wave)
(wavelength)
So the proper frequency is
Now we can calculate the apparent frequency heard by the staff at the hospital when the ambulance moves away; we have:
(velocity of the ambulance)
(velocity of the staff)
Substituting,
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