A Federation starship ( 2.10×106 kg ) uses its tractor beam to pull a shuttlecraft ( 2.10×104 kg ) aboard from a distance of 18.0 km away. The tractor beam exerts a constant force of 4.0×104N on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

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Asked Oct 27, 2019
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A Federation starship ( 2.10×106 kg ) uses its tractor beam to pull a shuttlecraft ( 2.10×104 kg ) aboard from a distance of 18.0 km away. The tractor beam exerts a constant force of 4.0×104N on the shuttlecraft. Both spacecraft are initially at rest.

 

How far does the starship move as it pulls the shuttlecraft aboard?

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Expert Answer

Step 1

Given information:

Mass of the shuttle craft (ms) = 2.10 × 104 kg

Mass of the Federation ship (mf) = 2.10 × 106 kg

Force excreted by the tractor beam (F) = 4 × 104 N

Distance between the two ships (s) = 18 km

Step 2

As the tractor beam excretes a force “F” on shuttle craft it causes a reaction force of the same magnitude on the Federation ship, hence both ships are accelerated due the force “F” but in the opposite direction. The magnitude of this acceleration is given by:

Let the acceleration of the shuttle craft be "ag"
4 X 104
F
1.90 m/s2
2.10 x 104
ms
Let the acceleration of the federation ship be "a?
4x 104
-0.019 m/s2
af
2.10 x 106
mf
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Let the acceleration of the shuttle craft be "ag" 4 X 104 F 1.90 m/s2 2.10 x 104 ms Let the acceleration of the federation ship be "a? 4x 104 -0.019 m/s2 af 2.10 x 106 mf

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Step 3

Given that the space crafts are 18 km away from each other and are initially at rest i.e. (u = 0) for both the ships. If they started coming towards each other then let the point at which they meet be measured as “x km” from initial point of federation ship. It is obvious that this poi...

For shuttle craft:
18 x uTa,T2
Substitute the corresponding values we get:
2(18 x
Equation (1)
т?
as
For Federation ship:
x uTaT2
Substitute the corresponding values we get:
2(x)
т2
. Equation (2)
as
help_outline

Image Transcriptionclose

For shuttle craft: 18 x uTa,T2 Substitute the corresponding values we get: 2(18 x Equation (1) т? as For Federation ship: x uTaT2 Substitute the corresponding values we get: 2(x) т2 . Equation (2) as

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Newtons Laws of Motion

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