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# Answers to Properties of Matter Questions

Q.
A
volume of 8 liters of gas has a pressure of 50 kPa and a temp
of 27^{o}C.a) If the pressure were increased to 300 kPa without changing he temperature what would be the resulting volume? V P T If the temperature is constant, then pressure is inversely proportional to the volume ( Boyle's Law) that is P a 1/V or PV = constant P P 50 x 10 V b)
If the temperature was raised to 627 If the pressure is kept constant, then volume is directly proportional to temperature (Charle's Law) that is V a T or V/T = constant V 8 / 300 = V V c)
What would be the resulting volume if the temperature was
raised to 627 P Now T (50 x 10 V |

Q. A cord is 5.71e+1 meters long and 1.56 mm in diameter. When it supports a 1.41 kg load it stretches 3.50 cm. What is the Young's modulus of the cord's material?

A.

length l = 5.71 x 10 m = 57.1 m

d = 1.56 mm = 1.56 x 10^{-3} m

r = 0.78 x 10^{-3}m

m = 1.41 kg

Increase in length ?l = 3.5 x 10^{-2}
m

Area of cross section A = p (0.78 x 10 ^{-3})^{2}
m^{2}

=1.91 x 10^{-6} m^{2}

Young's modulus Y = (F/A)/(?l/l) = stress / strain = F l /A ?l

where F=mg=1.41 x 9.8 = 13.82

Y = (13.82 x
57.1)/(1.91 x 10^{-6} x 3.5 x ^{-2}) = 11.8 x 10^{9}
N/m^{2}

Can Archimedes principle be used to measure the density of a solid object? Can it be applied to the problem of measuring the density of a fluid? Write an equation that will handle these two problems.