Answer:
Explanation:
Resonant frequency is 240
4π² x 240² = 1 / LC
230400π² = 1 / LC
Let the required frequency = n
inductive reactance = 2 πn L
capacitative reactance = 1 / 2 π n C
inductive reactance / capacitative reactance
= 4π² x n ² x LC = 5.68
4π² x n ² = 1 / LC x 5.68
= 230400π² x 5.68
4n ²= 230400 x 5.68
n ²= 57600 x 5.68
n ² = 327168
n = 572 approx
Answer:
2. B
3. A
4. C
5. B
6. A
Explanation:
2. Sound waves use vibrating molecules to move. With this being said, sound waves would travel best through dense materials, and would travel worst in empty materials, like space. Using this information, you can infer that B would be the answer because water is denser than air and water is the densest material on that list.
3. The speed of the wave is equal to the frequency times the wavelength. Since it has a wavelength of 100 meter and 20 Hertz, the speed would 2000 m/s
4. Like noted in question 2, sound waves travel best in dense materials. Rock is the densest material in that last.
5. By looking at the chart, you can see that the speed increases by 4 m/s when the temperature increases by 10. Using simple division, you could determine that the speed would go up by 2 m/s since the jump between 15 degrees and 20 degrees is 5, which is half of 10, making the speed half of 4.
6. The speed would decrease because, like stated above, sound travels best through dense materials. Since rock is denser than air, the speed would decrease as it leaves.
Answer:
![T=9.42Nm](https://tex.z-dn.net/?f=T%3D9.42Nm)
Explanation:
From the question we are told that:
Radius ![r= 0.5 m](https://tex.z-dn.net/?f=r%3D%200.5%20m)
Current ![I= 3.0 A](https://tex.z-dn.net/?f=I%3D%203.0%20A)
Normal vector ![n=\frac{(2i - j +2k)}{3}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B%282i%20-%20j%20%2B2k%29%7D%7B3%7D)
Magnetic field ![B= (2i-6j) T](https://tex.z-dn.net/?f=B%3D%20%282i-6j%29%20T)
Generally the equation for Area is mathematically given by
![A=\pi r^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
![A=3.1415 *0.5^2](https://tex.z-dn.net/?f=A%3D3.1415%20%2A0.5%5E2)
![A=0.7853 m^2](https://tex.z-dn.net/?f=A%3D0.7853%20m%5E2)
Generally the equation for Torque is mathematically given by
![T=A(i'*B)](https://tex.z-dn.net/?f=T%3DA%28i%27%2AB%29)
Where
![i'*B= \begin{bmatrix}2&-1&2\\2&-6&0\end{bmatrix}](https://tex.z-dn.net/?f=i%27%2AB%3D%20%5Cbegin%7Bbmatrix%7D2%26-1%262%5C%5C2%26-6%260%5Cend%7Bbmatrix%7D)
![X\ component\ of\ i'*B= [(-1 * 0)-(2*-6)]](https://tex.z-dn.net/?f=X%5C%20component%5C%20of%5C%20i%27%2AB%3D%20%5B%28-1%20%2A%200%29-%282%2A-6%29%5D)
![X\ component\ of\ i'*B=12](https://tex.z-dn.net/?f=X%5C%20component%5C%20of%5C%20i%27%2AB%3D12)
Therefore
![T=0.7853*12](https://tex.z-dn.net/?f=T%3D0.7853%2A12)
![T=9.42Nm](https://tex.z-dn.net/?f=T%3D9.42Nm)
Answer:
a)801KJoules
b)The woman must climb stairs for an equivalent of 1.57km
Number of stairs=7850 stairs
Explanation:
a)We use the conversion between Joules and Kcal:
4184Joules=1Kcal
540Kcal*(1484Joules/1Kcal)=801KJoules
b)The physical Work must be equal to the food energy
![W_{physical}=E_{food}\\ mgh=E_{food}\\h=E_{food}/(mg)=801KJoules/(52Kg*9.81m/s^{2})=1.57Km\\](https://tex.z-dn.net/?f=W_%7Bphysical%7D%3DE_%7Bfood%7D%5C%5C%20mgh%3DE_%7Bfood%7D%5C%5Ch%3DE_%7Bfood%7D%2F%28mg%29%3D801KJoules%2F%2852Kg%2A9.81m%2Fs%5E%7B2%7D%29%3D1.57Km%5C%5C)
The woman must climb stairs for an equivalent of 1.57Km
For example if an stair measure 20cm=0.2m
Number of stairs=1.57km/0.2m=7850 stairs
Answer:
They have each lost the same amount of potential energy. (The lost potential energy is converted to kinetic energy.)