Answer:
The force induced on the aircraft is 2.60 N
Solution:
As per the question:
Power transmitted, ![P_{t} = 8 kW = 8000 W](https://tex.z-dn.net/?f=P_%7Bt%7D%20%3D%208%20kW%20%3D%208000%20W)
Now, the force, F is given by:
(1)
where
v = velocity
Now,
For a geo-stationary satellite, the centripetal force,
is provided by the gravitational force,
:
![F_{c} = F_{G}](https://tex.z-dn.net/?f=F_%7Bc%7D%20%3D%20F_%7BG%7D)
![\frac{mv^{2}}{R} = \frac{GM_{e}m{R^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bmv%5E%7B2%7D%7D%7BR%7D%20%3D%20%5Cfrac%7BGM_%7Be%7Dm%7BR%5E%7B2%7D%7D)
Thus from the above, velocity comes out to be:
![v = \sqrt{\frac{GM_{e}}{R}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7BGM_%7Be%7D%7D%7BR%7D%7D)
![v = \sqrt{\frac{6.67\times 10^{- 11}\times 5.979\times 10^{24}}{42166\times 10^{3}}} = 3075.36 m/ s](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B6.67%5Ctimes%2010%5E%7B-%2011%7D%5Ctimes%205.979%5Ctimes%2010%5E%7B24%7D%7D%7B42166%5Ctimes%2010%5E%7B3%7D%7D%7D%20%3D%203075.36%20m%2F%20s)
where
R = ![R_{e} + H](https://tex.z-dn.net/?f=R_%7Be%7D%20%2B%20H)
R = ![\sqrt{GM_{e}(\frac{T}{2\pi})^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7BGM_%7Be%7D%28%5Cfrac%7BT%7D%7B2%5Cpi%7D%29%5E%7B2%7D%7D)
where
G = Gravitational constant
T = Time period of rotation of Earth
R is calculated as 42166 km
Now, from eqn (1):
![8000 = F\times 3075.36](https://tex.z-dn.net/?f=8000%20%3D%20F%5Ctimes%203075.36)
F = 2.60 N
The drawbar or other connections must be strong enough to pull all the weight of the vehicle being towed. The drawbar or other connection may not exceed 15 feet from one vehicle to the other.
Answer:
Option ‘a’ is the cheapest for this house.
Explanation:
Cheapest method of heating must have least cost per kj of energy. So, convert all the energy in the same unit (say kj) and take select the cheapest method to heat the house.
Given:
Three methods are given to heat a particular house are as follows:
Method (a)
Through Gas, this gives energy of amount $1.33/therm.
Method (b)
Through electric resistance, this gives energy of amount $0.12/KWh.
Method (c)
Through oil, this gives energy of amount $2.30/gallon.
Calculation:
Step1
Change therm to kj in method ‘a’ as follows:
![C_{1}=\frac{\$ 1.33}{therm}\times(\frac{1therm}{105500kj})](https://tex.z-dn.net/?f=C_%7B1%7D%3D%5Cfrac%7B%5C%24%201.33%7D%7Btherm%7D%5Ctimes%28%5Cfrac%7B1therm%7D%7B105500kj%7D%29)
$/kj.
Step2
Change kWh to kj in method ‘b’ as follows:
![C_{2}=\frac{\$ 0.12}{kWh}\times(\frac{1 kWh }{3600kj})](https://tex.z-dn.net/?f=C_%7B2%7D%3D%5Cfrac%7B%5C%24%200.12%7D%7BkWh%7D%5Ctimes%28%5Cfrac%7B1%20kWh%20%7D%7B3600kj%7D%29)
$/kj.
Step3
Change kWh to kj in method ‘c’ as follows:
![C_{3}=\frac{\$ 2.30}{gallon}\times(\frac{1 gallon }{138500kj})](https://tex.z-dn.net/?f=C_%7B3%7D%3D%5Cfrac%7B%5C%24%202.30%7D%7Bgallon%7D%5Ctimes%28%5Cfrac%7B1%20gallon%20%7D%7B138500kj%7D%29)
$/kj.
Thus, the method ‘a’ has least cost as compare to method b and c.
So, option ‘a’ is the cheapest for this house.
Answer:
250.7mw
Explanation:
Volume of the reservoir = lwh
Length of reservoir = 10km
Width of reservoir = 1km
Height = 100m
Volume = 10x10³x10³x100
= 10⁹m³
Next we find the volume flow rate
= 0.1/100x10⁹x1/3600
= 277.78m³/s
To get the electrical power output developed by the turbine with 92 percent efficiency
= 0.92x1000x9.81x277.78x100
= 250.7MW
Answer:
A) About
newtons
B) 76.518 newtons
C) 111.834 newtons
Explanation:
A)
, where G is the universal gravitational constant, M 1 and 2 are the masses of both objects in kilograms, and r is the radius in meters. Plugging in the given numbers, you get:
![F_g=\dfrac{(6.67408 \times 10^{-11})(7.8)(11.4)}{(0.8)^2}\approx 9.273 \times 10^{-9}](https://tex.z-dn.net/?f=F_g%3D%5Cdfrac%7B%286.67408%20%5Ctimes%2010%5E%7B-11%7D%29%287.8%29%2811.4%29%7D%7B%280.8%29%5E2%7D%5Capprox%209.273%20%5Ctimes%2010%5E%7B-9%7D)
B) You can find the weight of each object on Earth because you know the approximate acceleration due to gravity is 9.81m/s^2. Multiplying this by the mass of each object, you get a weight for the first particle of 76.518 newtons.
C) You can do a similar thing to the previous particle and find that its weight is 11.4*9.81=111.834 newtons.
Hope this helps!