Problem 1: a low-carbon steel billet is 75 mm long with diameter = 35 mm. it is direct extruded to a diameter = 20 mm using an extrusion die angle = 75˚. the steel’s strength coefficient = 500 mpa, and its strain hardening exponent = 0.25. in the johnson extrusion strain equation, a = 0.8 and b = 1.4. determine (a) true strain in ideal condition (no redundant work); (b) extrusion strain by johnson equation; and (c) l (remaining billet length) when the metal just reaches the exit of the die; and (d) ram pressure and force at l = 70 and l = 10 mm (hints: there is friction).

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.