If the specific surface energy for magnesium oxide is 1.0 J/m2 and its modulus of elasticity is (225 GPa), compute the critical stress required for the propagation of an internal crack of length 0.3 mm.

The critical stress required for the propagation of an initial crack               =  21.84 M pa

Explanation:

Given data

Modulus of elasticity E = 225 ×

Specific surface energy for magnesium oxide is = 1

Crack length (a) = 0.3 mm = 0.0003 m

Critical stress is given by = -------- (1)

⇒ 2 E = 2 × 225 × × 1 = 450 ×

⇒ a = 3.14 × 0.0003 = 0.000942  

⇒ Put these values in equation 1 we get

⇒ =

⇒ = 4.77 ×

⇒ = 2.184 ×

⇒ =  21.84

⇒ =  21.84 M pa

This is the critical stress required for the propagation of an initial crack.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.