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| sage: g = 9.8*units.length.meter/(units.time.second^2); | |
| ....: h = 10*units.length.meter; | |
| ....: cw = 4.1868*units.energy.joule/(units.temperature.celsius*units.mass.gram);t = g*h/cw | |
| sage: t | |
| 23.4068978694946*celsius*gram*meter^2/(joule*second^2) | |
| sage: tt = t/(units.temperature.celsius) | |
| sage: tt.convert() | |
| 0.0234068978694946 |
problem 1.4
sage: density_water = 1.0units.mass.gram/(units.length.centimeter)^3
sage: eqn = atm(1.0units.length.centimeter)^2 == tdensity_water*(1.0units.length.centimeter)^2
sage: sol = solve(eqn, t)
sage: sol[0].rhs()
atmospherecentimeter^3/gram
sage: _.convert()
4053/40meter^2/second^2
sage: _1.0
101.325000000000meter^2/second^2
sage: eqn = atm(1.0units.length.centimeter)^2 == density_watert*(1.0units.length.centimeter)^2(9.8u
....: nits.length.meter/units.time.second^2)
sage: sol = solve(eqn, t)
sage: sol[0].rhs()
5/49atmospherecentimeter^3second^2/(grammeter)
sage: _.convert()
579/56meter
sage: _1.0
10.3392857142857meter
Problem 1.9
sage: density_water = 1.0units.mass.gram/(units.length.centimeter)^3
sage: eqn = atm(1.0units.length.centimeter)^2 == tdensity_water*(1.0units.length.centimeter)^2
sage: sol = solve(eqn, t)
sage: sol[0].rhs()
atmospherecentimeter^3/gram
sage: _.convert()
4053/40meter^2/second^2
sage: _1.0
101.325000000000meter^2/second^2
sage: eqn = atm(1.0units.length.centimeter)^2 == density_watert*(1.0units.length.centimeter)^2(9.8u
....: nits.length.meter/units.time.second^2)
sage: sol = solve(eqn, t)
sage: sol[0].rhs()
5/49atmospherecentimeter^3second^2/(grammeter)
sage: _.convert()
579/56meter
sage: _1.0
10.3392857142857meter
problem 1.10
sage: m = 400units.mass.gram
sage: v = 120units.length.meter/(units.time.second)^2
sage: v = 120units.length.meter/(units.time.second)
sage: v = 120units.length.kilometer/(units.time.hour)
sage: energy_per_one_pitch = m/2v^2
sage: energy_per_one_pitch.convert()
2000/9kilogrammeter^2/second^2
sage: energy_per_one_pitch.convert(units.energy.joule)
2000/9joule
sage: one_humberger = 270units.energy.calorie
sage: t = var('t')
sage: eqn = one_humberger == tenergy_per_one_pitch
sage: s = solve(eqn, t)
sage: s[0].rhs()
3/32000caloriehour^2/(gramkilometer^2)
sage: .convert()
2543481/500000
sage: n()
5.08696200000000
sage: eqn = tone_humberger == 200energy_per_one_pitch
sage: s = solve(eqn, t)
sage: s[0].rhs()
6400000/3gramkilometer^2/(caloriehour^2)
sage: .convert()
100000000/2543481
sage: n()
39.3161969757195
sage: energy_per_one_pitch1.0
2.88000000000000e6gramkilometer^2/hour^2
sage: _.convert(units.energy.joule)
222.222222222222joule
sage: one_humberger.convert(units.energy.joule)
282609/250joule
sage: _1.0
1130.43600000000joule
sage: one_humberger = 270units.energy.calorie1000
sage: eqn = tone_humberger == 200energy_per_one_pitch
sage: s = solve(eqn,t)
sage: s
[t == 6400/3gramkilometer^2/(caloriehour^2)]
sage: s[0].rhs()
6400/3gramkilometer^2/(caloriehour^2)
sage: _1.0
2133.33333333333gramkilometer^2/(calorie*hour^2)
sage: _.convert()
0.0393161969757195
problem 1.11
sage: torque = 200units.force.newtonunits.length.meter
sage: rpm = 2pi4000/(units.time.minute)
sage: power = torquerpm
sage: power.convert(units.power.horsepower)
(4000000000000000000/111854980737340533pi)horsepower
sage: n((4000000000000000000/111854980737340533pi))
112.345203865957
sage: power.convert(units.power.watt)
(80000/3*pi)watt
sage: n((80000/3pi))
83775.8040957278
question 1.3 (p.24)
sage: density_hg = 13.6units.mass.gram/(units.length.centimeter)^3
sage: atm = 1.0units.pressure.atmosphere
sage: t = var('t')
sage: eqn = atm*(1.0units.length.centimeter)^2 == tdensity_hg*(1.0units.length.centimeter)^2
sage: eqn
1.00000000000000atmospherecentimeter^2 == 13.6000000000000gramt/centimeter
sage: sol = solve(eqn, t)
sage: sol[0].rhs()
5/68atmospherecentimeter^3/gram
sage: _.convert()
4053/544meter^2/second^2
sage: _1.0
7.45036764705882meter^2/second^2
sage: eqn = atm*(1.0units.length.centimeter)^2 == density_hgt*(1.0units.length.centimeter)^2(9.8unit
....: s.length.meter/units.time.second^2)
sage: sol = solve(eqn,t)
sage: s = sol[0].rhs()
sage: s
25/3332atmospherecentimeter^3second^2/(grammeter)
sage: s1.0
0.00750300120048019atmospherecentimeter^3second^2/(grammeter)
sage: convert(s)
NameError Traceback (most recent call last)
/usr/lib/python3/dist-packages/sage/all_cmdline.py in
----> 1 convert(s)
NameError: name 'convert' is not defined
sage: s
25/3332atmospherecentimeter^3second^2/(grammeter)
sage: s.convert()
2895/3808*meter
sage: _1.0
0.760241596638655meter