Answer:
Explanation:
Let fuel is released at the rate of dm / dt where m is mass of the fuel
thrust created on rocket
= d ( mv ) / dt
= v dm / dt
this is equal to force created on the rocket
= 220 dv / dt
so applying newton's law
v dm / dt = 220 dv / dt
v dm = 220 dv
dv / v = dm / 220
integrating on both sides
∫ dv / v = ∫ dm / 220
lnv = ( m₂ - m₁ ) / 220
ln4000 - ln 2500 = ( m₂ - m₁ ) / 220
( m₂ - m₁ ) = 220 x ( ln4000 - ln 2500 )
( m₂ - m₁ ) = 220 x ( 8.29 - 7.82 )
= 103.4 kg .
Answer:
Explanation:
firstly we have to find the frequency and then the angular frequency.
The frequency will be:
The angular frequency is:
ω
ω
ω
Now we can apply simple pendulum relationship
ω
make g the subject of the formula
Answer:
a) W = 180.87 J
, b) ΔU = -180.87 J
, c) ΔU = -180.87 J
Explanation:
a) Work is defined as
W = F .ds
Where bold indicates vectors, we can write the scalar product
W = F s cos θ
Where the angle is between force and displacement.
The force of gravity is the weight of the body, which is directed downwards and the displacement thickens the tip of the cliff at the bottom, so that it is directed downwards, therefore the angle is zero degrees
W = y
W = m g y
For this problem we must fix a reference system, from the statement it is established that the system is placed at the base of the cliff, so that final height is zero and the initial height (y₀ = 7.69m)
W = 2.40 9.8 (7.69-0)
W = 180.87 J
b) The potential energy is
U = mg y
The change in potential energy,
ΔU = - U₀
ΔU = mg (- y₀)
ΔU = 2.4 9.8 (0 -7.69)
ΔU = -180.87 J
c) in this case we change the reference system to the height of the cliffs, for this configuration
y₀ = 0
= -7.69 m
ΔU = 2.4 9.8 (-7.69 -0)
ΔU = -180.87 J
Answer:
2649600 Joules
Explanation:
Efficiency = 40%
m = Mass of air = 92000 kg
v = Velocity of wind = 12 m/s
Kinetic energy is given by
The kinetic energy of the wind is 6624000 Joules
The wind turbine extracts 40% of the kinetic energy of the wind
The energy extracted by the turbine every second is 2649600 Joules
The jet streams are narrow bands of fast moving air. They travel from the west coast towards the east coast over the United States, and so an aircraft flying from New York to Los Angeles would be flying into the jet stream rather than with it. This would cause the following:
- The flight would use more fuel, as the aircraft must push its way against the force of the jet stream
- The flight would also take longer, as thrust is needed to push against the jet stream as well as to push the aircraft forwards.