Answer:
<h2>8.0995×10^-21 kgms^-1</h2>
Explanation:
Mass of proton :
Speed of Proton:
Linear Momentum of a particle having mass (m) and velocity (v) :
Magnitude of momentum :
Frome equation (2), magnitude of linear momentum of the proton :
The situation (heat going through the ceiling) describes
conduction ... heat going from one place to another by
soaking through some material.
A). This is the one. Heat goes from from the marshmallow
to your hand by soaking through the wire. This is conduction too.
B). No. The heat in the room goes from the floor to the ceiling
because the warm air rises and carries it there. This is convection.
C). No. There's nothing for the heat to soak through between
the sun and the roof, and nothing that can move from the sun
to the roof and bring the heat with it. This is radiation.
D). No. Cold water sinks from the surface to the bottom because
warm water rose from the bottom to the surface, taking heat with it.
This is convection.
I think the key here is to be exquisitely careful at all times, and
any time we make any move, keep our units with it.
We're given two angular speeds, and we need to solve for a time.
Outer (slower) planet:
Angular speed = ω rad/sec
Time per unit angle = (1/ω) sec/rad
Angle per revolution = 2π rad
Time per revolution = (1/ω sec/rad) · (2π rad) = 2π/ω seconds .
Inner (faster) planet:
Angular speed = 2ω rad/sec
Time per unit angle = (1/2ω) sec/rad
Angle per revolution = 2π rad
Time per revolution = (1/2ω sec/rad) · (2π rad) = 2π/2ω sec = π/ω seconds.
So far so good. We have the outer planet taking 2π/ω seconds for one
complete revolution, and the inner planet doing it in only π/ω seconds ...
half the time for double the angular speed. Perfect !
At this point, I know what I'm thinking, but it's hard to explain.
I'm pretty sure that the planets are in line on the same side whenever the
total elapsed time is something like a common multiple of their periods.
What I mean is:
They're in line, SOMEwhere on the circles, when
(a fraction of one orbit) = (the same fraction of the other orbit)
AND
the total elapsed time is a common multiple of their periods.
Wait ! Ignore all of that. I'm doing a good job of confusing myself, and
probably you too. It may be simpler than that. (I hope so.) Throw away
those last few paragraphs.
The planets are in line again as soon as the faster one has 'lapped'
the slower one ... gone around one more time.
So, however many of the longer period have passed, ONE MORE
of the shorter period have passed. We're just looking for the Least
Common Multiple of the two periods.
K (2π/ω seconds) = (K+1) (π/ω seconds)
2Kπ/ω = Kπ/ω + π/ω
Subtract Kπ/ω : Kπ/ω = π/ω
Multiply by ω/π : K = 1
(Now I have a feeling that I have just finished re-inventing the wheel.)
And there we have it:
In the time it takes the slower planet to revolve once,
the faster planet revolves twice, and catches up with it.
It will be 2π/ω seconds before the planets line up again.
When they do, they are again in the same position as shown
in the drawing.
To describe it another way . . .
When Kanye has completed its first revolution ...
Bieber has made it halfway around.
Bieber is crawling the rest of the way to the starting point while ...
Kanye is doing another complete revolution.
Kanye laps Bieber just as they both reach the starting point ...
Bieber for the first time, Kanye for the second time.
You're welcome. The generous bounty of 5 points is very gracious,
and is appreciated. The warm cloudy water and green breadcrust
are also delicious.
The masses of the objects and how much distance there is between them
Answer: current I = 0.96 Ampere
Explanation:
Given that the
Resistance R = 60 Ω
Power = 55 W
Power is the product of current and voltage. That is
P = IV ...... (1)
But voltage V = IR. From ohms law.
Substitutes V in equation (1) power is now
P = I^2R
Substitute the above parameters into the formula to get current I
55 = 60 × I^2
Make I^2 the subject of formula
I^2 = 55/60
I^2 = 0.92
I = sqr(0.92)
I = 0.957 A
Therefore, 0.96 A current must be applied.
