By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. If the mass of th
1 answer:
Answer:
The astronaut's acceleration is 155.1 times the vehicle's acceleration
Explanation:
These effects due to Newton's third law of action and reaction. Since the forces are equal but in the opposite direction and each acting on a different body. We distance that the Force is F let's calculate the acceleration of the vehicle and the astronaut
Astronaut
F = a₁
Vehicle
F = a₁
F = 555.1 a₂
Let's match the equation
a₁ = 155.1
a₂
a₁ = 155.1 a₂
a₁ / a₂ = 155.1
The astronaut's acceleration is 155.1 times the vehicle's acceleration
We see that even when the acceleration of the vehicle is small, there is a very high multiplicative factor.
One method to improve this situation is that the vehicles fear some small retro-rocket vehicles to reduce their acceleration. This would have a very favorable impact on the astronaut's mission.
Another method would be for the astronaut himself to have the retro-rocket and control his acceleration.
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The translational equilibrium condition allows finding that the response for cable length with a maximum tension is
L = 2.56 m
Newton's second law says that the force is proportional to the mass and the acceleration of the body, in the special case that the acceleration is zero, the relationship is called the translational equilibrium condition.
∑ F = 0
Where the bold indicates vectors, F is the force and the sum is for all external forces.
The reference systems are coordinate systems with respect to which the decomposition of the vectors is carried out and the measurements are made, in this case we will use a system with the horizontal x axis and the vertical y axis.
In the attachment we can see a free body diagram of the system, let's write the equilibrium condition for each axis.
x-axis
Tₓ -Tₓ = 0
y-axis
2 - W = 0
Let's use trigonometry to decompose the tension, we can see from the graph and the adjoint that each string is half the length, let's call the angle θ
cos θ =
sin θ =
Tₓ = T cos θ
= T sin θ
We substitute
2 T sin θ = W (1)
The text indicates that the length of the block is 2 m, so the distance to the midpoint is
x = 1 m
Let's use the Pythagoras' Theorem
H² = CA² + CO²
CO =
CA = x
CO =
Where CO is the opposite leg, CA is the adjacent leg and H is the hypotenuse indicating H = L / 2,
Let's write the trigonometry functions
sin θ =
Let's substitute
sin θ =
Let's subtitute in the equation 1
2 T ( \frac{2 \sqrt{\frac{L^2}{4} -1 } }{L} ) = W
Let's solve by squaring
They indicate that the maximum tension of the cable is T = 700N and the weight is worth W = 700N, we substitute the values
L = 2.31 m
In conclusion using the translational equilibrium condition we can find that the response for cable length with maximum tension is
L = 2.31 m
Learn more about translational equilibrium here:
