Answer:
The force constant is ![k =1.316 *10^{7} \ N/m](https://tex.z-dn.net/?f=k%20%3D1.316%20%2A10%5E%7B7%7D%20%5C%20%20N%2Fm)
The energy stored in the spring is ![E = 1.68 *10^{7} \ J](https://tex.z-dn.net/?f=E%20%3D%20%201.68%20%2A10%5E%7B7%7D%20%5C%20J)
Explanation:
From the question we are told that
The mass of the object is ![M = 4.8*10^{5} \ kg](https://tex.z-dn.net/?f=M%20%20%3D%204.8%2A10%5E%7B5%7D%20%5C%20kg)
The period is ![T = 1.2 \ s](https://tex.z-dn.net/?f=T%20%20%3D%201.2%20%5C%20s)
The period of the spring oscillation is mathematically represented as
![T =2 \pi \sqrt{ \frac{M}{k}}](https://tex.z-dn.net/?f=T%20%20%3D2%20%5Cpi%20%5Csqrt%7B%20%5Cfrac%7BM%7D%7Bk%7D%7D)
where k is the force constant
So making k the subject
![k = \frac{4 \pi ^2 M }{T^2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B4%20%5Cpi%20%5E2%20M%20%7D%7BT%5E2%7D)
substituting values
![k = \frac{4 (3.142) ^2 (4.8 *10^{5}) }{(1.2)^2}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B4%20%283.142%29%20%5E2%20%284.8%20%2A10%5E%7B5%7D%29%20%7D%7B%281.2%29%5E2%7D)
![k =1.316 *10^{7} \ N/m](https://tex.z-dn.net/?f=k%20%3D1.316%20%2A10%5E%7B7%7D%20%5C%20%20N%2Fm)
The energy stored in the spring is mathematically represented as
![E = \frac{1}{2} k x^2](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20k%20x%5E2)
Where x is the spring displacement which is given as
![x = 1.6 \ m](https://tex.z-dn.net/?f=x%20%3D%20%201.6%20%5C%20m)
substituting values
![E = \frac{1}{2} (1.316 *10^{7}) (1.6)^2](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%281.316%20%2A10%5E%7B7%7D%29%20%281.6%29%5E2)
![E = 1.68 *10^{7} \ J](https://tex.z-dn.net/?f=E%20%3D%20%201.68%20%2A10%5E%7B7%7D%20%5C%20J)
Answer:
The force is ![F = 3920 \ N](https://tex.z-dn.net/?f=F%20%3D%203920%20%5C%20N)
Explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The weight of the gate is ![G = 100\ kg](https://tex.z-dn.net/?f=G%20%20%3D%20%20100%5C%20%20kg)
The vertical component of F is ![F_y = F\ sin \theta](https://tex.z-dn.net/?f=F_y%20%3D%20%20F%5C%20sin%20%20%5Ctheta)
From the diagram , taking moment about the pivot we have
![W_g * 2 - F_y * 1 = 0](https://tex.z-dn.net/?f=W_g%20%20%2A%202%20-%20F_y%20%20%2A%201%20%3D%20%200)
Where
is the weight of the gate evaluated as
![W_g = m_g * g = 100 * 9.8 = 980 \ N](https://tex.z-dn.net/?f=W_g%20%20%3D%20%20m_g%20%2A%20g%20%3D%20%20100%20%2A%209.8%20%3D%20%20980%20%5C%20N)
=> ![980 * 2 - Fsin(30) * 1 = 0](https://tex.z-dn.net/?f=980%20%2A%202%20-%20Fsin%2830%29%20%20%2A%201%20%3D%20%200)
=> ![F = \frac{1960}{sin(30)}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B1960%7D%7Bsin%2830%29%7D)
=> ![F = 3920 \ N](https://tex.z-dn.net/?f=F%20%3D%203920%20%5C%20N)
It is number 3. Because microwaves are the lowest of the sepectum then visible light the the highest of them all is Gamma Ray's. Hope this helps!!
Answer:
Explanation:
The equivalent resistance for three resistors connected in parallel is given as
(1/R)=(1/R₁)+(1/R₂)+(1/R₃)
now we.need to.insert the value of 3 resistances but only 2 are given in the question.