Section A
Q1.
For the mechanism shown in the figure below, determine the angular velocities of the links AB and OA. Given, QB = 20 mm, AB = 30 mm, OA = 20 mm; O, A and Q are in the same horizontal level : Two 20° involute gears are in mesh with gear ratio 2.5. The number of teeth on pinion is 24. The gears have a module of 6 mm and the addendum is equal to one module. Determine the (i) angle of action of the pinion and (ii) maximum velocity of sliding, if the pitch line velocity is 2 m/s. The state of stress at some point in a body is defined as follows : σ_x = 138 MPa, σ_y = -28 MPa, \tauxy = 35 MPa Determine the number of lattice points per cell in the simple cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) crystal systems. If there is only one atom located at each lattice point, calculate the number of atoms per unit cell. Determine the relationship between the atomic radius (r) and the lattice parameter (a0) in simple cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) structures when one atom is located at each lattice point. A cemented carbide cutting tool used for machining contains 75 percent by weight of tungsten carbide (WC), 15 percent by weight of titanium carbide (TiC), 5 percent by weight of tantalum carbide (TaC) and 5 percent by weight of cobalt (Co). Estimate the density of the composite material. Given : Density of tungsten carbide, \rhoWC = 15.77 gm/cm3
Density of titanium carbide, \rho_{\textTiC} = 4.94 gm/cm3
Density of tantalum carbide, \rhoTaC = 14.5 gm/cm3
Density of cobalt, \rhoCo = 8.90 gm/cm3
(a) For the mechanism shown in the figure below, determine the angular velocities of the links AB and OA. Given, QB = 20 mm, AB = 30 mm, OA = 20 mm; O, A and Q are in the same horizontal level :
(b) Two 20° involute gears are in mesh with gear ratio 2.5. The number of teeth on pinion is 24. The gears have a module of 6 mm and the addendum is equal to one module. Determine the (i) angle of action of the pinion and (ii) maximum velocity of sliding, if the pitch line velocity is 2 m/s.
(c)
The state of stress at some point in a body is defined as follows :
σ_x = 138 MPa, σ_y = -28 MPa, \tauxy = 35 MPa
(i) Draw a view of the element for the given state of stress and mark the above stresses.
(ii) Draw the Mohr circle for the combined stresses, showing the above state of stress and obtain the principal stresses from the same.
(d) (i) Determine the number of lattice points per cell in the simple cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) crystal systems. If there is only one atom located at each lattice point, calculate the number of atoms per unit cell.
(ii) Determine the relationship between the atomic radius (r) and the lattice parameter (a0) in simple cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) structures when one atom is located at each lattice point.
(e)
A cemented carbide cutting tool used for machining contains 75 percent by weight of tungsten carbide (WC), 15 percent by weight of titanium carbide (TiC), 5 percent by weight of tantalum carbide (TaC) and 5 percent by weight of cobalt (Co). Estimate the density of the composite material. Given :
Density of tungsten carbide, \rhoWC = 15.77 gm/cm3
Density of titanium carbide, \rho_{\textTiC} = 4.94 gm/cm3
Density of tantalum carbide, \rhoTaC = 14.5 gm/cm3
Density of cobalt, \rhoCo = 8.90 gm/cm3
