A hypothetical metal alloy has a grain diameter of 2.4 10-2 mm. After a heat treatment at 575C for 500 min, the grain diameter has increased to 7.3 10-2 mm. Compute the time required for a specimen of this same material (i. e., d0

The time to achieve a grain diameter of 7.3× 10⁻² mm is 477 minutes

Explanation:

We need to first solve for K

Given that:

grain diameter exponent (n) = 2.2

grain diameter (d) = 7.3 × 10⁻² mm = 7.3× 10⁻⁵ m

d₀ =  2.4 × 10⁻² mm =  2.4 × 10⁻⁵ m

t = 500 min

then from k =

= 7.48 × 10⁻¹³ m/min

= = 1.44×10⁻¹²

From K we can determine the time required based on the desired diameter

grain diameter (d) =  7.3 × 10⁻² mm = 7.3× 10⁻⁵ m

so t =  = =503.08 = 504 min approximately.

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.