Question

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

Answer 1

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.