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1 answer:
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The equation of state for an ideal gas is
where p is the gas pressure, V the volume, n the number of moles, R the gas constant and T the temperature.
The equation of state for the initial condition of the gas is
(1)
While the same equation for the final condition is
(2)
We know that in the final condition, half of the mass of the gas is escaped. This means that the final volume of the gas is half of the initial volume, and also that the final number of moles is half the initial number of moles, so we can write:
If we substitute these relationship inside (1), and we divide (1) by (2), we get
And since the initial temperature of the gas is
, we can find the final temperature of the gas:
where p is the gas pressure, V the volume, n the number of moles, R the gas constant and T the temperature.
The equation of state for the initial condition of the gas is
While the same equation for the final condition is
We know that in the final condition, half of the mass of the gas is escaped. This means that the final volume of the gas is half of the initial volume, and also that the final number of moles is half the initial number of moles, so we can write:
If we substitute these relationship inside (1), and we divide (1) by (2), we get
And since the initial temperature of the gas is
Answer:
i) No, the spring scale does not read a different value
ii) The torque will read a different value, it will reduce
iii) The spring scale does not need to be measured at the center of mass location.
Explanation:
The torque caused by the gyroscope can be given by the relation,
r × f
The torque measured by the gyroscope varies directly with the distance, r.
A decrease in the distance r will also cause a decrease in the value of the torque measured. When the distance, r is reduced from 7.5 inches to 5 inches, the torque caused by the gyroscope's weight also reduces.
The weight of the gyroscope remains constant despite the reduction in the distance because the weight of the gyroscope is not a function of the distance from the gyroscope. Therefore, the spring scale will not read a different value.
Yes, the spring scale does not need to be measured from the center of mass location because the weight does not depend on the location of measurement. The reading of the sprig scale remains constant.