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cddominguez63
24.09.2019 •
Physics
Why must astronauts use microphones and headphones in outer space
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Ответ:
Space is a vacuum, and this lack of a medium means sound does not carry in space. There is no atmosphere to carry the sound waves.
Astronauts therefore have to use headphones and microphones to hear each other in the vacuum of space.
Ответ:
a) SPHERE must be the winner
b) BOX is most fastest
Explanation:
For this exercise we must use conservation of energy
starting point. Highest part of the plane
Em₀ = U = m g h
final point. Lowest part of the plane
Em_f = K = ½ m v² + ½ I w²
Note that as the objects roll, the kinetic energy of rotation is included. Energy is conserved
Em₀ = Em_f
mg h = ½ m v² + ½ I w²
the linear and rotational variables are related
v = w r
w = v / r
the moment of inertia of the bodies is tabulated
ring (empty can) I = m r²
cylinder I = ½ m r²
sphere (marbles) I = 2/5 m r²
mgh = ½ m v² + ½ I v²/r² = ½ mv² (+ I / mr²)
2gh / (1 + I / mr²) = v² (1)
Let's analyze the value of I / mr2
can I / mr² = mr² / mr² = 1
cylinder I / mr² = ½ mr² / mr² = ½
sphere I / mr² = 2/5 mr² / mr² = 2/5
we substitute in equation 1
v =![\sqrt{ \frac{2gh}{ (1+ \frac{I}{m r^2}) } }](/tpl/images/1190/9268/836f0.png)
can v = √(2gh / 2) = √ gh
v = √gh
cylinder v=
= √(4gh/3)
v = 1,155 √gh
sphere v =
= √(10gh/7)
v = 1.20 √gh
therefore the object with the highest speed is the one that takes less time, consequently the SPHERE must be the cattle.
b) for a box on a frictionless surface, there is no rotational kinetic energy
mgh = ½ m v²
v = √2gh
v = 1.41 √(gh)
When comparing with the latter, this would be the one that arrives first