To solve the problem it is necessary to take into account the concepts related to frequency depending on the wavelength and the speed of light.
By definition we know that the frequency is equivalent to,
![f=\frac{c}{\lambda}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7Bc%7D%7B%5Clambda%7D)
where,
c= Speed of light
![\lambda = Wavelength](https://tex.z-dn.net/?f=%5Clambda%20%3D%20Wavelength)
While the wavelength is equal to,
![\lambda = \frac{2L}{n}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B2L%7D%7Bn%7D)
Where,
L = Length
n = Number of antinodes/nodes
PART A) For the first part we have that our wavelength is 110MHz, therefore
![\lambda = \frac{c}{f}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7Bc%7D%7Bf%7D)
![\lambda = \frac{3*10^8}{11*10^6}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B3%2A10%5E8%7D%7B11%2A10%5E6%7D)
![\lambda = 1.36m](https://tex.z-dn.net/?f=%5Clambda%20%3D%201.36m)
Therefore the distance between the nodal planes is 1.36m
PART B) For this part we need to find the Length through the number of nodes (8) and the wavelength, that is,
![\lambda'=\frac{2L}{n}](https://tex.z-dn.net/?f=%5Clambda%27%3D%5Cfrac%7B2L%7D%7Bn%7D)
![L = \frac{\lambda n}{2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B%5Clambda%20n%7D%7B2%7D)
![L = \frac{8*2.72}{2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B8%2A2.72%7D%7B2%7D)
![L = 10.90m](https://tex.z-dn.net/?f=L%20%3D%2010.90m)
Therefore the length of the cavity is 10.90m
Answer:
-223.64684 J
Explanation:
F = Force that is applied to the crate = 68 N
s = Displacement of the crate = 3.5 m
= Angle between the force and displacement vector = (180-20)
Work done is given by
![W=Fscos\theta\\\Rightarrow W=68\times 3.5\times cos(180-20)\\\Rightarrow W=-223.64684\ J](https://tex.z-dn.net/?f=W%3DFscos%5Ctheta%5C%5C%5CRightarrow%20W%3D68%5Ctimes%203.5%5Ctimes%20cos%28180-20%29%5C%5C%5CRightarrow%20W%3D-223.64684%5C%20J)
The work that Paige does on the crate is -223.64684 J
Answer:
6. Acceleration = 4.74 m/s^2
7. Centripetal force = 40.5 N
Explanation:
Problem 6.
Recall that the centripetal acceleration is defined as:
, where V is the object's tangential velocity, and r the radius of the circular motion. Therefore, in or case, the centripetal acceleration would be:
![a_c=\frac{v^2}{r}\\a_c=\frac{3.77^2}{3}\,\frac{m}{s^2} \\a_c=4.7376 \frac{m}{s^2}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7Bv%5E2%7D%7Br%7D%5C%5Ca_c%3D%5Cfrac%7B3.77%5E2%7D%7B3%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%5C%5Ca_c%3D4.7376%20%5Cfrac%7Bm%7D%7Bs%5E2%7D)
which we can round to 4.74 m/s^2 (option b in your list)
Problem 7.
Now we need to find not just the centripetal acceleration using the same formula as above, but then the centripetal force.
![a_c=\frac{v^2}{r}\\a_c=\frac{4.5^2}{2.5}\,\frac{m}{s^2} \\a_c=8.1 \frac{m}{s^2}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7Bv%5E2%7D%7Br%7D%5C%5Ca_c%3D%5Cfrac%7B4.5%5E2%7D%7B2.5%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%5C%5Ca_c%3D8.1%20%5Cfrac%7Bm%7D%7Bs%5E2%7D)
Now we calculate the centripetal force by multiplying this acceleration times the mass of the object following the definition of force as mass times acceleration:
Centripetal force = 5.0 kg * 8.1 m/s^2 = 40.5 N
The answers comes in Newtons (N)
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