Astronomers have proposed the existence of an unexplained force that is causing the expansion of the universe to accelerate. Wha
2 answers:
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Explanation:
Below is an attachment containing the solution.
The height of the roof is <u>3.57m</u>
Let the drops fall at a rate of 1 drop per t seconds. The first drop takes 5t seconds to reach the ground. The second drop takes 4t seconds to reach the bottom of the 1.00 m window, while the 3rd drop takes 3t s to reach the top of the window.
Calculate the distances traveled by the second and the third drops s₂ and s₃, which start from rest from the roof of the building.
The length of the window s is given by,
The first drop is at the bottom and it takes 5t seconds to reach down.
The height of the roof h is the distance traveled by the first drop and is given by,
the height of the roof is 3.57 m
Answer:
a) M = 2 10³⁰ kg
, b) = 5.81 10⁷ s
Explanation:
a) For this exercise let's use Newton's second law where force is the law of universal gravitation and acceleration is centripetal
G m M / R² = m a
a = v² / R
G M / R = V²
The orbit of the two planets is approximately circular, therefore the velocity module (speed) is constant
v = d / t
The distance is the length of the circular orbit
d = 2π R
G M / R = 4π² R² / T²
G M T² = 4π² R³
Let's write this equation for each planet
For the earth
The period is T = 3.16 10⁷ s and the radius of the orbit R = 1.5 10¹¹ m, let's calculate the mass of the sun
M = 4π² R³ / G T²
M = 4π² (1.5 10¹¹)³ / (6.67 10⁻¹¹ (3.16 10⁷)²)
M = 133.24 10³³ / 66.60 10³
M = 2 10³⁰ kg
b) For this part we write this equation for the two points
For the earth
² = (4π² / G M)
³
For mars
² = (4π² / G M)
³
Let's divide the two expressions
² /
² =
³ /
³
They indicate that the orbit of Mars is = 1.5
² /
² = (1.5
/
)³
² =
² 1.5³
² = (3.16 10⁷)² 1.5³
= √ (33.70 10¹⁴)
= 5.81 10⁷ s