- #1
IWantToLearn
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i know that bathroom scales measures the normal force, hence the equivalence mass
but if we took Earth rotation into account then the normal force will be less by a value mv2/R
according to this relation
N = mg -mv2/R
Example : a 70 kg man standing on a bathroom scale on the equator , where the radius of the Earth at the equator is R = 6378 km , and the time to complete one rotation is T = 24 hours
[assuming that the gravitational acceleration is constant everywhere on the surface of the Earth and equals to g = 9.8 m/s2]
doing the mass : we found that the normal force (the reading of the scale in Newtons)
equals N = 683.64 N
while the gravitational force must be equal to mg = 686 N , this means that the reading is less than the actual value (2.36 N less)
if we did the same calculations near the north pole where the radius is R = 6,356 km
there will be less by a value (2.35 N less)
both readings are not accurate, i know that all scales are calibrated to indicate the mass
now my questions is :
1- These small deviations from the actual value, are they neglected?
2- If they aren't, and the manufacturers take into account the Earth rotation and where in the Earth you are, is that means that if bought a bathroom scale from london it will not be accurate for me to use it in kenya?
3- what about the change of the value of g itself from place to place on the surface of the earth?
but if we took Earth rotation into account then the normal force will be less by a value mv2/R
according to this relation
N = mg -mv2/R
Example : a 70 kg man standing on a bathroom scale on the equator , where the radius of the Earth at the equator is R = 6378 km , and the time to complete one rotation is T = 24 hours
[assuming that the gravitational acceleration is constant everywhere on the surface of the Earth and equals to g = 9.8 m/s2]
doing the mass : we found that the normal force (the reading of the scale in Newtons)
equals N = 683.64 N
while the gravitational force must be equal to mg = 686 N , this means that the reading is less than the actual value (2.36 N less)
if we did the same calculations near the north pole where the radius is R = 6,356 km
there will be less by a value (2.35 N less)
both readings are not accurate, i know that all scales are calibrated to indicate the mass
now my questions is :
1- These small deviations from the actual value, are they neglected?
2- If they aren't, and the manufacturers take into account the Earth rotation and where in the Earth you are, is that means that if bought a bathroom scale from london it will not be accurate for me to use it in kenya?
3- what about the change of the value of g itself from place to place on the surface of the earth?