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3 years ago

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An astronaut in space cannot use a conventional means, such as a scale or balance, to determine the mass of an object. But she d

oes have devices to measure distance and time accurately. She knows her own mass is 78.4 kg, but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.50 m/s, she pushes against it, which slows it down to 1.20 m/s (but does not reverse it) and gives her a speed of 2.40 m/s. What is the mass of this canister

1 answer:

Flura [38]3 years ago

7 0

Answer:

81.81 kg

Explanation:

$m_1$ = Mass of person = 78.4 kg

$m_2$ = Mass of canister

$u_1$ = Initial velocity of person = 0

$u_2$ = Initial velocity of canister = 3.5 m/s

$v_1$ = Final velocity of person = 2.4 m/s

$v_2$ = Final velocity of canister = 1.2 m/s

The momentum balance in the system is given by

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow 78.4\times 0+m_2\times 3.5=78.4\times 2.4+m_2\times 1.2\\\Rightarrow m_2=\dfrac{78.4\times 2.4}{3.5-1.2}\\\Rightarrow m_2=81.81\ \text{kg}$

Mass of the canister is 81.81 kg.

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$f = -\left(\frac{W}{g} \right)\cdot \left(\frac{v-v_{o}}{t}\right)$ (Eq. 1b)

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$W$ - Weight, measured in newtons.

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$v$ - Final speed, measured in meters per second.

$t$ - Time, measured in seconds.

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