In an old coal factory, a conveyor belt will move at a constant velocity of 20.3m/s and can deliver a maximum power of 15MW. Each wheel in the conveyor belt has a diameter of 2m. However a changing demand has pushed the coal factory to fill their coal hoppers with a different material with a certain constant specific density. These "coal" hoppers have been modified to deliver a constant 18m3s−1 of the new material to the conveyor belt. Assume that the kinetic and static friction are the same and that there is no slippage. What is the maximum density of the material?
Given constants:
- Proton mass, mp=1.67⋅10−27kg
- Neutron mass, mn=1.67⋅10−27kg
- Electron mass, me=9.11⋅10−31kg
- Avogadro's constant, N0=6.02⋅1023mol−1
- Universal gas constant, R=8.31J/(mol⋅K)
- Boltzmann's constant, kB=1.38⋅10−23J/K
- Electron charge magnitude, e=1.60⋅10−19C
- 1 electron volt, 1eV=1.60⋅10−19J
- Speed of light, c=3.00⋅108m/s
- Universal Gravitational constant,
G=6.67⋅10−11(N⋅m2)/kg2
- Solar Mass
M⊙=1.988⋅1030kg
- Acceleration due to gravity, g=9.8m/s2
- 1 unified atomic mass unit,
1u=1.66⋅10−27kg=931MeV/c2
- Planck's constant,
h=6.63⋅10−34J⋅s=4.41⋅10−15eV⋅s
- Permittivity of free space,
ϵ0=8.85⋅10−12C2/(N⋅m2)
- Coulomb's law constant,
k=4πϵ01=8.99⋅109(N⋅m2)/C2
- Permeability of free space,
μ0=4π⋅10−7T⋅m/A
- Magnetic constant,
4πμ0=1⋅10−7(T⋅m)/A
- 1 atmospheric pressure,
1atm=1.01⋅105N/m2=1.01⋅105Pa
- Wien's displacement constant, b=2.9. 10−3m⋅K
- Stefan-Boltzmann constant,
σ=5.67⋅10−8W/m2/K4