Question

If a force of 160 ± 6 N is applied to an area of 24 ± 3 cm², determine the pressure and the uncertainty in its calculation?​

Answer 1

Step-by-step explanation:

The pressure is calculated by dividing the force by the area:

P = F / A = 160 N / 24 cm² = 6.67 N/cm²

The uncertainty in the calculation of pressure can be determined by propagating the uncertainties in the force and area measurements. According to the formula for uncertainty propagation, the fractional uncertainty in the pressure calculation is:

ΔP / P = √((ΔF / F)^2 + (ΔA / A)^2)

Plugging in the values:

ΔP / P = √((6 N / 160 N)^2 + (3 cm² / 24 cm²)^2)

ΔP / P = √(0.0375) = 0.195

So the fractional uncertainty in the pressure calculation is 0.195 or 19.5%.

To find the absolute uncertainty in the pressure, multiply the fractional uncertainty by the pressure:

ΔP = P * ΔP / P = 6.67 N/cm² * 0.195 = 1.29 N/cm²

So, the pressure is 6.67 ± 1.29 N/cm².