The distance an object falls from rest through gravity is
D = (1/2) (g) (t²)
Distance = (1/2 acceleration of gravity) x (square of the falling time)
We want to see how the time will be affected
if ' D ' doesn't change but ' g ' does.
So I'm going to start by rearranging the equation
to solve for ' t '. D = (1/2) (g) (t²)
Multiply each side by 2 : 2 D = g t²
Divide each side by ' g ' : 2 D/g = t²
Square root each side: t = √ (2D/g)
Looking at the equation now, we can see what happens to ' t ' when only ' g ' changes:
-- ' g ' is in the denominator; so bigger 'g' ==> shorter 't'
and smaller 'g' ==> longer 't' .--
They don't change by the same factor, because 1/g is inside the square root. So 't' changes the same amount as √1/g does.
Gravity on the surface of the moon is roughly 1/6 the value of gravity on the surface of the Earth.
So we expect ' t ' to increase by √6 = 2.45 times.
It would take the same bottle (2.45 x 4.95) = 12.12 seconds to roll off the same window sill and fall 120 meters down to the surface of the Moon.
To solve this problem, it will be necessary to apply the concepts related to the fundamental resonance frequency in a closed organ pipe.
This is mathematically given as
For fundamental frequency n is 0, then,
When,
v = Velocity of sound
L = Length,
Rearranging to find the velocity,
Therefore the speed of sound in this gas is 416m/s
You don't count trailing zeros. A.29.3
<em><u>One</u></em>
Givens
- delta B = 0.20 T/s
- A = 0.07 m^2
- R = 3.5 ohms
Formula
Φ = ΔB*A
e = Φ
Solution (first part)
e = 0.2 * 0.07
e = 0.014 emf
Solution (second part)
i = e/R
i = 0.014 / 3.5
i = 4 * 10^-3
i = 4 ma
Answer
A
<em><u>Two</u></em>
Givens
N = 200 turns
Φ = 30 degrees
Delta B = 0.45 T/s
phi = 30 degrees
r = 0.06 meters
Formula
e = -N * delta B * A * Cos(phi)
Solution
e = -200 * 0.45 (pi r^2) * Cos(30)
e = - 200 * 0.45 * (3.14 * 0.06^2) * cos(30)
e = 0.881 emf
Answer
A