A long wire of diameter D= 1 mm is submerged in an oil bath of temperature [infinity] T[infinity]= 15°C. The wire has an electrical resistance per unit length of Re′= 0.01 Ω/m. If a current of I= 96 A flows through the wire and the convection coefficient is h= 500 W/m2·K, what is the steady-state temperature of the wire? From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value? The properties of the wire are rho= 8000 kg/m3, c= 500 J/kg·K, and k= 20 W/m·K.

a) what is the steady-state temperature of the wire?

83.67°C

b) From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value?

8.31s

Explanation:

a) what is the steady-state temperature of the wire?

From the above question we are given the following values:

Oil bath temperature = 15°C.

Diameter of wire = 1mm

Converting to m(meter)

1 mm = 0.001m

The wire has an electrical resistance per unit length of Re′= 0.01 Ω/m. Current of I= 96 A

Convection coefficient is h= 500 W/m²·K,

Temperature in steady state formula =

Temperature + I² × Re' /π × D × h

= 25°C + 96² × 0.01/π × 0.001 × 500

= 25°C + 92.16/1.5707963268

= 25°C + 58.670878232

= 83.670878232°C

≈ 83.67°C

b)From the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°C of the steady-state value?

For question b, we are given the following values

rho= 8000 kg/m3, c= 500 J/kg·K, and k= 20 W/m·K

Formula

= Exp( -4 × h/rho × c × k)

=Exp(- 4 × 500 W/m²·K)/8000 kg/m³ ×

500 J/kg·K × 20 W/m·K

= 8.31s

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.