Work needed: 720 J
Explanation:
The work needed to stretch a spring is equal to the elastic potential energy stored in the spring when it is stretched, which is given by
where
k is the spring constant
x is the stretching of the spring from the equilibrium position
In this problem, we have
E = 90 J (work done to stretch the spring)
x = 0.2 m (stretching)
Therefore, the spring constant is
Now we can find what is the work done to stretch the spring by an additional 0.4 m, that means to a total displacement of
x = 0.2 + 0.4 = 0.6 m
Substituting,
Therefore, the additional work needed is
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Answer:
(b) Yes, the earth gains momentum but the change in momentum of the earth is much lesser compared to that of everyone in the air. The resistance to motion (inertia of the earth), which is a function of its mass is so great that the earth's acceleration is small in the given time frame.
Explanation:
From Newton's second law which can be stated mathematically as
F = m(v-u)/t = ma.
By Newton's law of gravitation, there is a force between the earth and everyone in the air. This force is responsible for the change in momentum of everyone in the air and this force gives them an acceleration equal to g = 9.80m/s². By Newton's law of gravitation and Newton's third law of motion, this force is also equal to the force exerted by everyone on the earth.
For this to be true,
F = M (everyone) ×a (everyone) = M(earth) × a (earth).
And
a (earth) = {M (everyone) ×a (everyone) }/M (earth)
Then
a (earth) must be lesser than a (everyone) since M(earth) >> M(everyone).
a = change in momentum/ time
Therefore the earth will have a much lesser change in momentum which is the reason we won't notice the earth's movement.
Thank you for reading.
kinetic energy is given as
KE = (0.5) m v²
given that : v = speed of the bottle in each case = 4 m/s
when m = 0.125 kg
KE = (0.5) m v² = (0.5) (0.125) (4)² = 1 J
when m = 0.250 kg
KE = (0.5) m v² = (0.5) (0.250) (4)² = 2 J
when m = 0.375 kg
KE = (0.5) m v² = (0.5) (0.375) (4)² = 3 J
when m = 0.0.500 kg
KE = (0.5) m v² = (0.5) (0.500) (4)² = 4 J
Answer:
1/4 λ film
Explanation:
Let L = total path length then L = 2 t where t is film thickness
There will be a 180 deg phase change at the air-film interface but no
phase change at the film-air interface
L = n * wavelength / 2 where n = 1, 3, 5, 7 etc
(the total path L must be an odd number of 1/2 wavelengths)
Or t = n * wavelength / 4 (the film must be an odd number
of 1/4 wavelengths thick)
1/4 λ film satisfies this condition
Note: Find the missing diagram in the attachment section.
