Answer:
The vertical distance is ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
Explanation:
From the question we are told that
The mass of the cylinder is m
The kinetic frictional force is f
Generally from the work energy theorem
![E = P + W_f](https://tex.z-dn.net/?f=E%20%20%3D%20%20P%20%2B%20%20W_f)
Here E the the energy of the spring which is increasing and this is mathematically represented as
![E = \frac{1}{2} * k * d^2](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%5E2)
Here k is the spring constant
P is the potential energy of the cylinder which is mathematically represented as
![P = mgd](https://tex.z-dn.net/?f=P%20%20%3D%20mgd)
And
is the workdone by friction which is mathematically represented as
![W_f = f * d](https://tex.z-dn.net/?f=W_f%20%20%3D%20%20f%20%2A%20%20d)
So
![\frac{1}{2} * k * d^2 = mgd + f * d](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%5E2%20%3D%20%20mgd%20%2B%20%20f%20%2A%20%20d%20)
=> ![\frac{1}{2} * k * d^2 = d[mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%5E2%20%3D%20%20d%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![\frac{1}{2} * k * d = [mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%20%3D%20%20%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
Answer:
![3.3\times 10^8\ btu/yr=11\ kW](https://tex.z-dn.net/?f=3.3%5Ctimes%2010%5E8%5C%20btu%2Fyr%3D11%5C%20kW)
Explanation:
Btu of British thermal unit is a unit of heat. The relation between btu/year and watts is given by :
![1\ btu/yr=3.343\times 10^{-5}\ W\\\\3.3\times 10^8\ btu/yr=3.343\times 10^{-5}\times 3.3\times 10^8\ W\\\\3.3\times 10^8\ btu/yr=11031.9\ W\\\\3.3\times 10^8\ btu/yr=11\ kW](https://tex.z-dn.net/?f=1%5C%20btu%2Fyr%3D3.343%5Ctimes%2010%5E%7B-5%7D%5C%20W%5C%5C%5C%5C3.3%5Ctimes%2010%5E8%5C%20btu%2Fyr%3D3.343%5Ctimes%2010%5E%7B-5%7D%5Ctimes%203.3%5Ctimes%2010%5E8%5C%20W%5C%5C%5C%5C3.3%5Ctimes%2010%5E8%5C%20btu%2Fyr%3D11031.9%5C%20W%5C%5C%5C%5C3.3%5Ctimes%2010%5E8%5C%20btu%2Fyr%3D11%5C%20kW)
So,
is equal to 11 kW. Hence, the correct option is (d).
Answer:
Option B
Explanation:
Speed of a wave is denoted by:
v=fλ
where f is the frequency which is unchanged 15Hz and λ is the new wavelength which is 28m
v=fλ
![v=15(28)\\v=420m/s](https://tex.z-dn.net/?f=v%3D15%2828%29%5C%5Cv%3D420m%2Fs)
Answer:
A physical change involves a change in physical properties. Examples of physical properties include melting, transition to a gas, change of strength, change of durability, changes to crystal form, textural change, shape, size, color, volume and density.