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ss7ja [257]
3 years ago
9

When a spacecraft travels away from Earth, the gravitational force acting on it

Physics
2 answers:
S_A_V [24]3 years ago
6 0
The correct answer is decreases

The further away you are the weaker it would be. That's why at one point you stop being in the field and ti doesn't pull you towards it anymore. Proportionally, if you move towards the Earth then it increases. 
Sindrei [870]3 years ago
4 0

Gravitational force on aircraft at some distance from the Earth is given as

F = \frac{Gm_1m_2}{r^2}

here we know that

m_1= mass of Earth

m_2 = mass of aircraft

r = distance between center of earth and aircraft

now as the aircraft is flying away from the surface of Earth so here the distance between them is increasing with the motion of aircraft

So as it moves away the force between them will decrease

So here we can say that

When a spacecraft travels away from Earth, the gravitational force acting on it  

<u>decreases</u>

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  • Magnitude: 12.1 N.
  • Direction: 17.0° to the 8 N force.
<h3>Explanation</h3>

Refer to the diagram attached (created with GeoGebra). Consider the 5 N force in two directions: parallel to the 8 N force and normal to the 8 N force.

  • \displaystyle F_{\text{1, Parallel}} = F_1 \cdot \cos{45^\textdegree} = \dfrac{5\sqrt{2}}{2}\;\text{N}.
  • \displaystyle F_{\text{1, Normal}} = F_1 \cdot \sin{45^\textdegree} = \dfrac{5\sqrt{2}}{2}\;\text{N}.

The sum of forces on each direction will be the resultant force on that direction:

  • Resultant force parallel to the 8 N force: (8 + \dfrac{5\sqrt{2}}{2})\;\text{N}.
  • Resultant force normal to the 8 N force: \dfrac{5\sqrt{2}}{2}\;\text{N}.

Apply the Pythagorean Theorem to find the magnitude of the resultant force.

\displaystyle \Sigma F = \sqrt{{(8 + \dfrac{5\sqrt{2}}{2})}^2 + {(\dfrac{5\sqrt{2}}{2})}^2} = 12.1\;\text{N} (3 sig. fig.).

The size of the angle between the resultant force and the 8 N force can be found from the tangent value of the angle. Tangent of the angle:

\displaystyle \dfrac{\Sigma F_\text{Normal}}{\Sigma F_\text{Parallel}} = \dfrac{8 + \dfrac{5\sqrt{2}}{2}}{\dfrac{5\sqrt{2}}{2}} \approx 0.306491.

Find the size of the angle using inverse tangent:

\displaystyle \arctan{ \dfrac{\Sigma F_\text{Normal}}{\Sigma F_\text{Parallel}}} = \arctan{0.306491} = 17.0\textdegree.

In other words, the resultant force is 17.0° relative to the 8 N force.

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