Explanation:
Equilibrium position in y direction:
W = Fb (Weight of the block is equal to buoyant force)
m*g = V*p*g
V under water = A*h
hence,
m = A*h*p
Using Newton 2nd Law
![-m*\frac{d^2y}{dt^2} = Fb - W\\\\-m*\frac{d^2y}{dt^2} = p*g*(h+y)*A - A*h*p*g\\\\-A*h*p*\frac{d^2y}{dt^2} = y *p*A*g\\\\\frac{d^2y}{dt^2} + \frac{g}{h} * y =0](https://tex.z-dn.net/?f=-m%2A%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20Fb%20-%20W%5C%5C%5C%5C-m%2A%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20p%2Ag%2A%28h%2By%29%2AA%20-%20A%2Ah%2Ap%2Ag%5C%5C%5C%5C-A%2Ah%2Ap%2A%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%3D%20y%20%2Ap%2AA%2Ag%5C%5C%5C%5C%5Cfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%20%2B%20%5Cfrac%7Bg%7D%7Bh%7D%20%2A%20y%20%3D0)
Hence, T time period
T = 2*pi*sqrt ( h / g )
Answer:
m = 63 grams
Explanation:
ω = 10 cycles/s(2π radians/cycle) = 20π rad/s
ω = √(k/m)
m = k/ω² = 250/(20π)² = 0.06332... kg
Answer:
The polar coordinate of
is
.
Explanation:
Given a point in rectangular form, that is
, its polar form is defined by:
(1)
Where:
- Norm, measured in meters.
- Direction, measured in sexagesimal degrees.
The norm of the point is determined by Pythagorean Theorem:
(2)
And direction is calculated by following trigonometric relation:
(3)
If we know that
and
, then the components of coordinates in polar form is:
![r = \sqrt{(-3.50\,m)^{2}+(-2.50\,m)^{2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28-3.50%5C%2Cm%29%5E%7B2%7D%2B%28-2.50%5C%2Cm%29%5E%7B2%7D%7D)
![r \approx 4.301\,m](https://tex.z-dn.net/?f=r%20%5Capprox%204.301%5C%2Cm)
Since
and
, direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula:
![\theta = 180^{\circ}+\tan^{-1} \left(\frac{-2.50\,m}{-3.50\,m} \right)](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20180%5E%7B%5Ccirc%7D%2B%5Ctan%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B-2.50%5C%2Cm%7D%7B-3.50%5C%2Cm%7D%20%5Cright%29)
![\theta \approx 215.538^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%20215.538%5E%7B%5Ccirc%7D)
The polar coordinate of
is
.
Answer:
3/7 ω
Explanation:
Initial momentum = final momentum
I(-ω) + (2I)(3ω) + (4I)(-ω/2) = (I + 2I + 4I) ωnet
-Iω + 6Iω - 2Iω = 7I ωnet
3Iω = 7I ωnet
ωnet = 3/7 ω
The final angular velocity will be 3/7 ω counterclockwise.