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Question

Figure: http://session.masteringphysics.com/problemAsset/1001073/9/knight_Figure_14_36.jpg

Astronauts need to be able to measure their weight or mass while on extended missions in space. However, they cannot weight themselves by standing on a bathroom scale, but they can find their mass by measuring the oscillation they make on a large spring. If an astronaut in space attaches one end of a spring to the wall and the other to her belt, and her fellow pulls her away from the wall and lets her go, they could use a sonar ranger or some other measurement device to measure the distance fromt eh wall L(t), shown in the graph below.

a) Use the data to find her mass if the spring constant is 240N/m
b) Find her speed when the spring

Explanation / Answer

from the figure time period=3 seconds

Now, for mass spring oscillation mass time period=2*pi*sqrt(m/k)

or m=k*T^2/(4*pi^2)=240*3^2/(4*pi^2)=54.713kg

b)since at 1.2 m the spring is 0.2 m from equilibrium

therefore speed=2*pi/T*amplitude*sqrt(1-0.2^2/amplitude^2)=2*pi/3*0.4*sqrt(1-0.2^2/0.4^2)=0.7255m/s

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