Answer:
19.5°
Explanation:
The energy of the mass must be conserved. The energy is given by:
1) ![E=\frac{1}{2}mv^2+mgh](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2%2Bmgh)
where m is the mass, v is the velocity and h is the hight of the mass.
Let the height at the lowest point of the be h=0, the energy of the mass will be:
2) ![E=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=E%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
The energy when the mass comes to a stop will be:
3) ![E=mgh](https://tex.z-dn.net/?f=E%3Dmgh)
Setting equations 2 and 3 equal and solving for height h will give:
4) ![h=\frac{v^2}{2g}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7Bv%5E2%7D%7B2g%7D)
The angle ∅ of the string with the vertical with the mass at the highest point will be given by:
5) ![cos\phi=\frac{l-h}{l}](https://tex.z-dn.net/?f=cos%5Cphi%3D%5Cfrac%7Bl-h%7D%7Bl%7D)
where l is the lenght of the string.
Combining equations 4 and 5 and solving for ∅:
6) ![\phi={cos}^{-1}(\frac{l-h}{l})={cos}^{-1}(1-\frac{h}{l})={cos}^{-1}(1-\frac{v^2}{2gl})](https://tex.z-dn.net/?f=%5Cphi%3D%7Bcos%7D%5E%7B-1%7D%28%5Cfrac%7Bl-h%7D%7Bl%7D%29%3D%7Bcos%7D%5E%7B-1%7D%281-%5Cfrac%7Bh%7D%7Bl%7D%29%3D%7Bcos%7D%5E%7B-1%7D%281-%5Cfrac%7Bv%5E2%7D%7B2gl%7D%29)
Answer:
![q=7.965*10^-^6C](https://tex.z-dn.net/?f=q%3D7.965%2A10%5E-%5E6C)
Explanation:
From the question we are told that
Altitude of ![d_1 390m](https://tex.z-dn.net/?f=d_1%20390m)
Magnitude![M_1=60.0 N/C](https://tex.z-dn.net/?f=M_1%3D60.0%20N%2FC)
Altitude of ![d_2=240 m](https://tex.z-dn.net/?f=d_2%3D240%20m)
Magnitude is ![M_2= 100 N/C](https://tex.z-dn.net/?f=M_2%3D%20100%20N%2FC)
Distance of cube ![d_c=150 m](https://tex.z-dn.net/?f=d_c%3D150%20m)
Generally the flux
is mathematical given as
![\phi=60(150)^2cos180+100(150)^2*cos0](https://tex.z-dn.net/?f=%5Cphi%3D60%28150%29%5E2cos180%2B100%28150%29%5E2%2Acos0)
![\phi=-9*10^5](https://tex.z-dn.net/?f=%5Cphi%3D-9%2A10%5E5)
Generally Quantity of charge q is mathematically given as
![q=\varepsilon _0 *\phi](https://tex.z-dn.net/?f=q%3D%5Cvarepsilon%20_0%20%2A%5Cphi)
![q=8.85*10^-^1^2 *9*10^5](https://tex.z-dn.net/?f=q%3D8.85%2A10%5E-%5E1%5E2%20%2A9%2A10%5E5)
![q=7.965*10^-^6C](https://tex.z-dn.net/?f=q%3D7.965%2A10%5E-%5E6C)
Answer:
The total amount of CO₂ produced will be = 20680 kg/year
The reduction in the amount of CO₂ emissions by that household per year = 3102 kg/year
Explanation:
Given:
Power used by household = 14000 kWh
Fuel oil used = 3400 L
CO₂ produced of fuel oil = 3.2 kg/L
CO₂ produced of electricity = 0.70 kg/kWh
Now, the total amount of CO₂ produced will be = (14000 kWh × 0.70 kg/kWh) + (3400 L × 3.2 kg/L)
⇒ The total amount of CO₂ produced will be = 9800 + 10880 = 20680 kg/year
Now,
if the usage of electricity and fuel oil is reduced by 15%, the reduction in the amount of the CO₂ emission will be = 0.15 × 20680 kg/year = 3102 kg/year