4. the bar has cross-sectional area a and modulus of elasticity e. if an axial force f directed toward the right is applied at c: (a) what is the normal stress in the part of the bar to the left of c? [15 pts] (b) what is the resulting displacement of the point c? [15 pts]

a)  ΔL/L = F / (E A),  b)   = L (1 + L F /(EA) )

Explanation:

Let's write the formula for Young's module

     E = P / (ΔL / L)

Let's rewrite the formula, to have the pressure alone

    P = E ΔL / L

The pressure is defined as

    P = F / A

Let's replace

   F / A = E ΔL / L

   F = E A ΔL / L

   ΔL / L = F / (E A)

b) To calculate the elongation we must have the variation of the length, so the length of the bar must be a fact. Let's clear

    ΔL = L [F / EA]

    -L = L (F / EA)

    = L + L (F / EA)

    = L (1 + L (F / EA))

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.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2