Question

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. 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 3.60 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.
a. What is the mass of the canister?
b. How much kinetic energy is "lost" in this collision, and what happens to that energy?

Answer 1

Answer:

78.4 kg

225.792 J

Explanation:

$m_1$ = Mass of person = 78.4 kg

$m_2$ = Mass of canister = 0.005 kg

$u_1$ = Initial Velocity of person = 0 m/s

$u_2$ = Initial Velocity of canister = 3.6 m/s

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

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

In this system the linear momentum is conserved

$m_2u_2=m_2v_2+m_1v_1\\\Rightarrow m_2=\frac{m_1v_1}{u_2-v_2}\\\Rightarrow m_2=\frac{78.4\times 2.4}{3.6-1.2}\\\Rightarrow\\\Rightarrow m_2=78.4\ kg$

The mass of the canister is 78.4 kg

Kinetic energy is given by

$K={\tfrac {1}{2}}m_{1}u_{1}^{2}+{\tfrac {1}{2}}m_{2}u_{2}^{2}-\left({\tfrac {1}{2}}m_{1}v_{1}^{2}+{\tfrac {1}{2}}m_{2}v_{2}^{2}\right)\\\Rightarrow K={\tfrac {1}{2}}78.4\times 0^{2}+{\tfrac {1}{2}}78.4\times 3.6^{2}-{\tfrac {1}{2}}78.4\times 2.4^{2}-{\tfrac {1}{2}}78.4\times 1.2^{2}\\\Rightarrow K=225.792\ J$

The energy lost in the collision is 225.792 J