Question

If the ultimate shear strength of steel is taken to be 3.00 109 Pa, what force is required to punch through a steel plate 1.60 cm thick? Assume the superhero's fist has cross-sectional area of 1.20 102 cm2 and is approximately circular. Qualitatively, what would happen to the superhero on delivery of the punch? What physical law applies?

Answer 1

Answer:

Explanation:

Given

Ultimate shear strength $\tau =3\times 10^9\ Pa$

thickness of steel Plate $t=1.60\ cm$

Cross-sectional $A=1.20\times 10^2\ cm^2$

suppose d is the diameter of cross-section

$\frac{\pi }{4}d^2=1.20\times 10^2$

$d=12.359\ cm$

Shear area of circular cross-section

$A_s=\pi dt$

$A_s=\pi \times 12.359\times 1.6$

$A_s=62.13\ cm^2$

Shear Force $F_s=A_s\times \tau$

$F_s=62.13\times 10^2\times 3000$

$F_s=18.639\ MN$