Answer: 8.1 x 10^24
Explanation:
I(t) = (0.6 A) e^(-t/6 hr)
I'll leave out units for neatness: I(t) = 0.6e^(-t/6)
If t is in seconds then since 1hr = 3600s: I(t) = 0.6e^(-t/(6 x 3600) ).
For neatness let k = 1/(6x3600) = 4.63x10^-5, then:
I(t) = 0.6e^(-kt)
Providing t is in seconds, total charge Q in coulombs is
Q= ∫ I(t).dt evaluated from t=0 to t=∞.
Q = ∫(0.6e^(-kt)
= (0.6/-k)e^(-kt) evaluated from t=0 to t=∞.
= -(0.6/k)[e^-∞ - e^-0]
= -0.6/k[0 - 1]
= 0.6/k
= 0.6/(4.63x10^-5)
= 12958 C
Since the magnitude of the charge on an electron = 1.6x10⁻¹⁹ C, the number of electrons is 12958/(1.6x10^-19) = 8.1x10^24 to two significant figures.
<span>It's pretty easy problem once you set it up.
Earth------------P--------------Moon
"P" is where the gravitational forces from both bodies are acting equally on a mass m
Let's define a few distances.
Rep = distance from center of earth to P
Rpm = distance from P to center of moon
Rem = distance from center of earth to center of moon
You are correct to use that equation. If the gravitational forces are equal then
GMearth*m/Rep² = Gm*Mmoon/Rpm²
Mearth/Mmoon = Rep² / Rpm²
Since Rep is what you're looking for we can't touch that. We can however rewrite Rpm to be
Rpm = Rem - Rep
Mearth / Mmoon = Rep² / (Rem - Rep)²
Since Mmoon = 1/81 * Mearth
81 = Rep² / (Rem - Rep)²
Everything is done now. The most complicated part now is the algebra,
so bear with me as we solve for Rep. I may skip some obvious or
too-long-to-type steps.
81*(Rem - Rep)² = Rep²
81*Rep² - 162*Rem*Rep + 81*Rem² = Rep²
80*Rep² - 162*Rem*Rep + 81*Rem² = 0
We use the quadratic formula to solve for Rep:
Rep = (81/80)*Rem ± (9/80)*Rem
Rep = (9/8)*Rem and (9/10)*Rem
Obviously, point P cannot be 9/8 of the way to the moon because it'll be
beyond the moon. Therefore, the logical answer would be 9/10 the way
to the moon or B.
Edit: The great thing about this idealized 2-body problem, James, is
that it is disguised as a problem where you need to know a lot of values
but in reality, a lot of them cancel out once you do the math. Funny
thing is, I never saw this problem in physics during Freshman year. I
saw it orbital mechanics in my junior year in Aerospace Engineering. </span>
sylent_reality
· 8 years ago
Answer:
Option b
Explanation:
Metamorphism is the process where the variation of the geological texture resulting from the different arrangement of the minerals or the variation of minerals in protoliths, i.e., pre- existing rocks take place such that there occurs no change in state of the protolith, i.e., it does not melt into magma.
The change takes place as a result of the presence of chemically active fluids, heat and pressure.
There is a reaction between the chemically active fluid and the rock through which it passes and promotes the movement of the dissolved ions of silicate and promotes the growth of the mineral grains.
P = mv
p = 3.5 × 5
p = 17.5 kg .m/s
Hope this helps!
Answer:
a)
b)
Explanation:
Given that
v(t) = 5 t i + t² j - 2 t³ k
We know that acceleration a is given as
Therefore the acceleration function a will be
The acceleration at t = 2 s
a= 5 i + 2 x 2 j - 6 x 2² k m/s²
a=5 i + 4 j -24 k m/s²
The magnitude of the acceleration will be
a= 24.83 m/s²
The direction of the acceleration a is given as
a)
b)
