Answer:
Mass = 18.0 kg
Explanation:
From Hooke's law,
F = ke
where: F is the force, k is the spring constant and e is the extension.
But, F = mg
So that,
mg = ke
On the Earth, let the gravitational force be 10 m/
.
3.0 x 10 = k x 5.0
30 = 5k
⇒ k =
................ 1
On the Moon, the gravitational force is
of that on the Earth.
m x
= k x 5.0
= 5k
⇒ k =
............. 2
Equating 1 and 2, we have;
= ![\frac{10m}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B10m%7D%7B30%7D)
m = ![\frac{900}{50}](https://tex.z-dn.net/?f=%5Cfrac%7B900%7D%7B50%7D)
= 18.0
m = 18.0 kg
The mass required to produce the same extension on the Moon is 18 kg.
If you are under a tree, they kind of act like lightning rods, so stay away from trees, so roll in dat grass. Fun Fact: Lightning comes from the ground more than it comes from the sky, its like when you rub a blanket on your head, some lil' lightnings come from your head while a little come from the blanket, its the same with grass and clouds only, 10000 volts stronger and deadly.
Answer:
a The kinetic energy is ![KE = 0.0543 J](https://tex.z-dn.net/?f=KE%20%3D%200.0543%20J)
b The height of the center of mass above that position is
Explanation:
From the question we are told that
The length of the rod is ![L = 1.4m](https://tex.z-dn.net/?f=L%20%3D%201.4m)
The mass of the rod
The angular speed at the lowest point is ![w = 1.09 \ rad/s](https://tex.z-dn.net/?f=w%20%3D%201.09%20%5C%20rad%2Fs)
Generally moment of inertia of the rod about an axis that passes through its one end is
Substituting values
![I = \frac{(0.140) (1.4)^2}{3}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B%280.140%29%20%281.4%29%5E2%7D%7B3%7D)
![I = 0.0915 \ kg \cdot m^2](https://tex.z-dn.net/?f=I%20%3D%200.0915%20%5C%20kg%20%5Ccdot%20m%5E2)
Generally the kinetic energy rod is mathematically represented as
![KE = \frac{1}{2} Iw^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Iw%5E2)
![KE = \frac{1}{2} (0.0915) (1.09)^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%280.0915%29%20%281.09%29%5E2)
![KE = 0.0543 J](https://tex.z-dn.net/?f=KE%20%3D%200.0543%20J)
From the law of conservation of energy
The kinetic energy of the rod during motion = The potential energy of the rod at the highest point
Therefore
![KE = PE = mgh](https://tex.z-dn.net/?f=KE%20%3D%20PE%20%3D%20mgh)
![0.0543 = mgh](https://tex.z-dn.net/?f=0.0543%20%3D%20mgh)
![h = \frac{0.0543}{9.8 * 0.140}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B0.0543%7D%7B9.8%20%2A%200.140%7D)
1 and A
2 and B
3 and D
4 and C