A 10kg mass sits inside a cylinder of cross-sectional area 0.05m² and is attached to one end by a spring with unstretched length 0.2m and spring constant k=5000N/m. The mass acts as a piston separating the spring side (which has no gas, so P=0) from the other side (also 0.2m when the spring is unstretched), filled with gas that has pressure Po= 10kPa when the spring is unstretched. Po 0.2m T=300 Mmm a) Defining X to be the distance between the left wall of the cylinder and the mass, what equilibrium value of X if the system is at 300K? b) What is the frequency f for small horizontal oscillations about this equilibrium position assuming the oscillations are slow enough that the air remains at a constant temperatur Hint: see the tips on the first page for finding k in a general system
A 10kg mass sits inside a cylinder of cross-sectional area 0.05m² and is attached to one end by a spring with unstretched length 0.2m and spring constant k=5000N/m. The mass acts as a piston separating the spring side (which has no gas, so P=0) from the other side (also 0.2m when the spring is unstretched), filled with gas that has pressure Po= 10kPa when the spring is unstretched. Po 0.2m T=300 Mmm a) Defining X to be the distance between the left wall of the cylinder and the mass, what equilibrium value of X if the system is at 300K? b) What is the frequency f for small horizontal oscillations about this equilibrium position assuming the oscillations are slow enough that the air remains at a constant temperatur Hint: see the tips on the first page for finding k in a general system
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Transcribed Image Text:Question 2 (from an old exam):
A 10kg mass sits inside a cylinder of cross-sectional area 0.05m²
and is attached to one end by a spring with unstretched length
0.2m and spring constant k=5000N/m. The mass acts as a piston
separating the spring side (which has no gas, so P=0) from the
other side (also 0.2m when the spring is unstretched), filled with
gas that has pressure Po = 10kPa when the spring is unstretched.
a) Defining X to be the distance between the left wall of the cylinder and the mass, what is the
equilibrium value of X if the system is at 300K?
Po
0.2m
T= 300K
Mum
P=0
0.2m
b) What is the frequency f for small horizontal oscillations about this equilibrium position,
assuming the oscillations are slow enough that the air remains at a constant temperature?
Hint: see the tips on the first page for finding k in a general system
·area
0.05m²
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