An electrical heater 150 mm long and 5mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of 10W/mK. The temperature of the electrical heater is 70 oC and the temperature of block surface is 40 oC. Estimate the power dissipation of the electrical heater. (in W)

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.

Different types of steels contain different elements that alter the characteristics of the steel. for each of the following elements, explain what the element does when alloyed with steel.

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.