Consider a 150-w incandescent lamp. the filament of the lamp is 5-cm long and has a diameter of 0.5 mm. the diameter of the glass bulb of the lamp is 8 cm. determine the heat flux, in w/m2, (a) on the surface of the filament and (b) on the surface of the glass bulb, and (c) calculate how much it will cost per year to keep that lamp on for eight hours a day every day if the unit cost of electricity is $0.08/kwh.

(a).the heat trasfer surface area and heat flux on the surface of filament are Area of Surface= µDL=3.14(0.05cm)(5cm)= 0.785 cm square qs=Q/Area of surface= 150W/0.785= 191W/cmsq.=1.91x10³x10³W/Msq (b). the heat surface on the surface of heat bulb Area of surface = 3.14xD²= 3.14(8CM)²= 201.1cm² qs=Q/Area of surface=150w/201.1cm²=0.75 w/cm²= 7500w/m² the amount and cost of electrical energy consumed during one period is Electrical Consumption=QΛt=(0.15 KW)(365X8h/yr)=438 k Wh/yr Annual cost= 438 kWh/yr)($.08/kWh)= $ 35.04 /yr

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s