Physics, 16.03.2020 20:53, israel8471

A nickel alloy rod having an elastic modulus of 200 GPa and an original diameter of 10 mm experiences only elastic deformation when a tensile load of 80000 N is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is 0.25 mm.

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answered: aksambo4707

50 mm

Explanation:

$200 GPa = 200\times10^9 Pa$

10 mm in diameter = 5 mm in radius or 0.005 m

So the cross-section area of the rod is

$A = \pi r^2 = \pi 0.005^2 = 0.00008 m^2$

The stress on the rod is the ratio of force and cross-section area

$\sigma = F / A = 80000 / 0.00008 = 10^9 Pa$

So the maximum strain when this stress is applied is

$\epsilon = \sigma / E = 10^9/(200\times10^9 Pa) = 1/200 = 0.005$

If the maximum allowable deformation is 0.25 mm, then the maximum original length is

$\epsilon = \Delta L / L$

$L = \Delta L / \epsilon = 0.25 / 0.005 = 50 mm$

answered: bellrivera3434

$l_{o}=0.05m$

Explanation:

Given data

Diameter d=10 mm

Force F=80000 N

Elongation Δl=0.25 mm

Elastic E=200 GPa

We want the length l₀ before deformation.The modulus of elasticity is property of material and could be calculated by Hooks Law which is expresses a relationship between the stress and strain for elastic deformation as:

E=σ/ε

Where ε is strain resulted from applied force and represent as:

ε=Δl/l₀

l₀=Δl/ε.......(i)

As the stress σ the force per unit area so we can find its value first

σ=F/A

σ=(80000N)/π*r²

σ=(80000N)/π*(5×10⁻³m)²

σ=1018591636 Pa

By using the expressing ε from eq(i)

l₀=Δl/ε

l₀=(Δl×E)/σ

Substitute the given values

l₀=(Δl×E)/σ

$=\frac{0.25*10^{-3}m(200*10^{9}Pa)}{1018591636Pa}\\ =0.05m\\l_{o}=0.05m$

answered: Guest

Lx bxh

answered: Guest

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.

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A nickel alloy rod having an elastic modulus of 200 GPa and an original diameter of 10 mm experience...