Answer:
See solution with all the conditions considered. A gaseous mixture of A and B for which species A is chemically consumed at the catalytic surface.
The total pore reaction rate is stated below and it can be inferred by applying the bellow analogy.
A. Impulse is simply the product of Force and time.
Therefore,
I = F * t --->
1
where I is impulse, F is force, t is time
However another formula for solving impulse is:
I = m vf – m vi --->
2
where m is mass, vf is final velocity and vi is initial
velocity
Therefore using equation 2 to solve for impulse I:
I = 2000kg (0) – 2000kg (77 m/s)
I = -154,000 kg m/s
B. By conservation of momentum, we also know that Impulse
is conserved. That means that increasing the time by a factor of 3 would still
result in an impuse of -154,000 kg m/s. So,
I = F’ * (3 t) = -154,000 kg m/s
Since t is multiplied by 3, therefore this only means
that Force is decreased by a factor of 3 to keep the impulse constant,
therefore:
(F/3) (3t) = -154,000 kg m/s
Summary of Answers:
A. I = -154,000 kg m/s
B. Force is decreased by factor of 3
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Answer:
a) w = 2.52 10⁷ rad / s, b) K / K₀ = 1.19 10⁴
Explanation:
a) We can solve this exercise using the conservation of angular momentum.
Initial instant. Before collapse
L₀ = I₀ w₀
Final moment. After the collapse
L_f = I w
angular momentum is conserved
L₀ = L_f
I₀ w₀ = I w (1)
The moment of inertia of a sphere is
I = 2/5 m r²
we take from the table the mass and diameter of the star
m = 1,991 10³⁰ kg
r₀ = 6.96 10⁸ m
r = 6.37 10⁶ m
to find the angular velocity let's use
w = L / T
where the length of a circle is
L = 2π r
T = 24 days (24 h / 1 day) (3600 s / 1h) = 2.0710⁶ s
we substitute
w = 2π r / T
wo = 2π 6.96 10⁸ / 2.07 10⁶
wo = 2.1126 10³ rad / s
we substitute in equation 1
w =
w = 2/5 mr₀² / 2/5 m r² w₀
w = (
) ² wo
w = (6.96 10⁸ / 6.37 10⁶) ² 2.1126 10³
w = 2.52 10⁷ rad / s
b) the kinetic energy ratio
K = ½ m w²
K₀ = ½ m w₀²
K = ½ m w²
K / K₀ = (w / wo) ²
K / K₀ = 2.52 10⁷ / 2.1126 10³
K / K₀ = 1.19 10⁴
Answer:
For the aceleration we have:
Vf = Vo + a * t
Clearing "a":
a = (Vf - Vo) / t
Replacing and resolving:
a = (34 m/s - 0 m/s) / 21 s
a = 34 m/s / 21 s
a = 1,61 m/s^2
The aceleration of the vehicle is<u> 1,61 meters per second squared</u>