Answer:
a) v= 2.1 m/s
b) ω = 0.807 rad/s
Explanation
Conceptual analysis :
The dog and the merry-go- round describes a circular motion, then, the following formulas apply :
Formula (1)
v = ω *r Formula (2)
Where:
: Centripetal acceleration(m/s²)
v: linear speed or tangential (m/s)
r : radius of the circle (m)
ω : angular speed ( rad/s)
Data
r= 2.6 m
= 1.7 m/s²
Problem develpment
a) We replace data in the formula 1 to calculate the dog's linear speed(v):
v= 2.1 m/s
b)We replace data in the formula 2 to calculate the angular speed of the merry-go- round (ω).
v = ω *r
2.1 = ω *2.6
ω = 2.1/2.6
ω = 0.807 rad/s
A, C, and D all happen at different stages
of a total lunar eclipse.
I'll describe the stages of the eclipse, but before I do, I just need
to clarify: The Earth doesn't have an umbra or a penumbra, but
its shadow does.
-- the eclipse begins when the first edge of the moon
moves into the penumbra of Earth's shadow; ( C )
this part of the moon grows steadily.
-- After a while, the first edge of the moon begins to move
into the umbra of Earth's shadow ( A ), and gets very dark.
-- The total phase of the eclipse begins when the ENTIRE
moon is in the umbra of Earth's shadow.
Then everything happens in reverse.
-- Eventually, the leading edge of the moon moves out
of the shadow's umbra, into the penumbra. This part
steadily grows.
-- After a while, none of the moon is in the umbra, and
the whole thing is in the penumbra. The moon is
fully illuminated, but not quite as bright as it should be.
-- Soon, the leading edge of the moon leaves the penumbra
of Earth's shadow, and gets brighter. This portion of the moon
steadily grows, until ...
-- the moon completely leaves the penumbra, all of it is as bright
as it's supposed to be. The eclipse is completely over. ( B )
==> The whole process lasts several hours.
==> Everybody on the night side of the Earth sees the same thing
at the same time. It doesn't matter WHERE you are on the night
side ... if you can see the moon in the sky, you see the present
phase of the eclipse.
==> The lunar eclipse can only happen at the Full Moon. In fact, the
mid-point of the total phase is the exact moment of Full Moon.
The Correct answer would be D. Work equals force times distance.
Answer:
this is due to difference in speeds of sound and light
Explanation:
light has a speed of 3×10^8 m/s and it is seen at once because it takes negligible time due to very high speed and short distance that is why as soon as lightning occurs we can see it . since thundering sound travels with speed of sound which is about 330 to 340 m/s in air hence it takes some time as described in question as 6 seconds
F = 130 revs/min = 130/60 revs/s = 13/6 revs/s
t = 31s
wi = 2πf = 2π × 13/6 = 13π/3 rads/s
wf = 0 rads/s = wi + at
a = -wi/t = -13π/3 × 1/31 = -13π/93 rads/s²
wf² - wi² = 2a∅
-169π²/9 rads²/s² = 2 × -13π/93 rads/s² × ∅
∅ = 1209π/18 rads
n = ∅/2π = (1209π/18)/(2π) = 1209/36 ≈ 33.5833 revolutions.
