Error in Young's modulus from a wire
Y = 4 M g L/(π d² l). Y is the modulus, M the load, g the acceleration due to gravity, L the length of the wire, d its diameter and l the extension.
Error in a formula
Maximum error in Y
4.8%
- M0.5%0.5%
- g0.1%0.1%
- L0.2%0.2%
- d22 × 1%2%
- l2%2%
- Totaladd them4.8%
Product, quotient or power: the percentage errors add, each counted |power| times.
4.8% maximum error in Y
ΔY/Y × 100 = ΔM/M × 100 + Δg/g × 100 + ΔL/L × 100 + 2 × Δd/d × 100 + Δl/l × 100
Product, quotient or power: the percentage errors add, each counted |power| times. The diameter is squared and is usually the hardest to measure, so it often decides the total.
Other formulas
Measured the same thing several times? Use repeated readings, or find the least count of your instrument.
Error in Young's modulus from a wire: quick answers
What is the formula for the error in Young's modulus from a wire?
Y is the modulus, M the load, g the acceleration due to gravity, L the length of the wire, d its diameter and l the extension. With Y = 4 M g L/(π d² l), the maximum error is given by ΔY/Y × 100 = ΔM/M × 100 + Δg/g × 100 + ΔL/L × 100 + 2 × Δd/d × 100 + Δl/l × 100. Product, quotient or power: the percentage errors add, each counted |power| times.
How do I work out the error with real numbers?
Take M with 0.5% error and g with 0.1% error and L with 0.2% error and d with 1% error and l with 2% error. The maximum percentage error in Y is 0.5% + 0.1% + 0.2% + 2 × 1% + 2% = 4.8%.
Why are the errors added and never subtracted?
The error shown is the largest possible one. In the worst case every measurement is off in the direction that pushes the result the same way, so the errors pile up. They are added even when the quantity is divided or subtracted.