Answer:
r = 3.787 10¹¹ m
Explanation:
We can solve this exercise using Newton's second law, where force is the force of universal attraction and centripetal acceleration
F = ma
G m M / r² = m a
The centripetal acceleration is given by
a = v² / r
For the case of an orbit the speed circulates (velocity module is constant), let's use the relationship
v = d / t
The distance traveled Esla orbits, in a circle the distance is
d = 2 π r
Time in time to complete the orbit, called period
v = 2π r / T
Let's replace
G m M / r² = m a
G M / r² = (2π r / T)² / r
G M / r² = 4π² r / T²
G M T² = 4π² r3
r = ∛ (G M T² / 4π²)
Let's reduce the magnitudes to the SI system
T = 3.27 and (365 d / 1 y) (24 h / 1 day) (3600s / 1h)
T = 1.03 10⁸ s
Let's calculate
r = ∛[6.67 10⁻¹¹ 3.03 10³⁰ (1.03 10⁸) 2) / 4π²2]
r = ∛ (21.44 10³⁵ / 39.478)
r = ∛(0.0543087 10 36)
r = 0.3787 10¹² m
r = 3.787 10¹¹ m
Answer:
0.2 J
Explanation:
The pendulum forms a right triangle, with hypotenuse of 50 cm and base of 30 cm. The height of this triangle can be found with Pythagorean theorem:
c² = a² + b²
(50 cm)² = a² + (30 cm)²
a = 40 cm
The height of the triangle is 40 cm. The height of the pendulum when it is at the bottom is 50 cm. So the end of the pendulum is lifted by 10 cm. Assuming the mass is concentrated at the end of the pendulum, the potential energy is:
PE = mgh
PE = (0.200 kg) (9.8 N/kg) (0.10 m)
PE = 0.196 J
Rounding to one significant figure, the potential energy is 0.2 J.
Answer:
1). 
2). Toward us
3). 
4). Toward us
5). 
6). Away from us
7). 
8). Away from us
Explanation:
Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when it is moving away from the observer (that is known as the Doppler effect).
The wavelength at rest is 121.6 nm (
)
Then, for this particular case it is gotten:
Star 1: 
Star 2: 
Star 3: 
Star 4: 
Star 1:
Toward us
Star 2:
Toward us
Star 3:
Away from us
Star 4:
Away from us
Due to that shift the velocity of the star can be determine by means of Doppler velocity.
(1)
Where 
is the wavelength shift, 
is the wavelength at rest, v is the velocity of the source and c is the speed of light.
(2)
<em>Case for star 1 
:</em>
<em></em>
Notice that the negative velocity means that is approaching to the observer.
<em>Case for star 2 
:</em>
<em>Case for star 3 
:</em>
<em>Case for star 4 
:</em>
