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A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just
Question
A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. How much work was done by the internal forces that caused the separation
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Physics
3 years
2021-08-25T11:04:38+00:00
2021-08-25T11:04:38+00:00 1 Answers
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Answers ( )
Answer:
W = ½ m v²
Explanation:
In this exercise we must solve it in parts, in a first part we use the conservation of the moment to find the speed after the separation
We define the system formed by the two parts of the rocket, therefore the forces during internal separation and the moment are conserved
initial instant. before separation
p₀ = m v
final attempt. after separation
p₀ = p_{f}
m v = m /2![Rendered by QuickLaTeX.com v_{f}](https://documen.tv/wp-content/ql-cache/quicklatex.com-bda3036763009360ff2e8533e6b29cae_l3.png)
v_{f}= 2 v
this is the speed of the second part of the ship
now we can use the relation of work and energy, which establishes that the work is initial to the variation of the kinetic energy of the body
initial energy
K₀ = ½ m v²
final energy
K_{f} = ¼ m (2v)²
K_{f} = m v²
the expression for work is
W = ΔK = K_{f} – K₀
W = m v² – ½ m v²
W = ½ m v²