Classical Mechanics Answers

A steel tension bar 8-mm thick and 50-mm wide with an initial single-edge crack of 10-mm long is subjected to a uniaxial stress s = 140 MPa.

 i Determine the stress intensity factor K_I. If K_IC = 60 MPa , is the crack stable?

 ii. Determine the critical crack size, and

 iii. Determine the critical load.

[Take Y=1]

Determine the total charge entering a terminal between t = 1 and t = 2 s and t = 2 s if the current passing the terminal is I = (3t² -t) A.

Suppose now that the momentum of the ball also has a y-component before it collides elastically with the wall. After the collision the x-component of the ball’s momentum changes but its y-component does not. If the momentum of the ball before the collision is ~p = px ˆi + py ˆj, what is its momentum after the collision. 

If m_1,m₂ and m₃ be the masses of three particles v_12, v₂₃ and v₁₃ be their relative velocities, prove that the total kinetic energy (E) of the system about the centre of mass is given by

m₁m₂v²₁₂₊ m₂m₃v²₂₃₊ m₁m₃v²₁₃ / m₁+ m₂ + m₃

Radius of capillary is 2mm. A liquid of weight 6.28 x 10^-4N may remain in the capillary, then the surface tension of liquid will be?

A ball moving along the x -axis bounces elastically off a horizonal wall that runs in along y-axis. The magnitude of the momentum of the ball is the same before and after the collision. Explain how we can conclude that the ball-wall system is closed but not isolated. 

*Conservative force and its potential energy function Consider the components of a position dependent force F(r): Fx = ayz + bx + c Fy = axz + bz Fz = axy + by. (a) Show that this force is conservative. (b) Find its corresponding potential energy function, V (r)