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3 years ago

What is the physical representation of the area under a force versus extension or compression curve?

1 answer:

5 0

The compression curve would be theoretically given for a system of bodies in which the spring applies the force (Although in the same way the following process can be extrapolated to any system, depending on the type of Force to consider) For a spring mass system, the strength is given by Hooke's law as

$F = Kx$

Where,

K = Spring constant

x = Displacement

If we integrate based on distance we would have

$\int F = \int K x dx$

This integral represents the area under the Force Curve based on each distance segment traveled.

$\int F = K \int xdx$

$\int F = K (\frac{1}{2} x^2)$

$\int F = \frac{1}{2} Kx^2$

This is the same formula that represents the elastic potential energy of a body. Therefore the correct answer is D.

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How is it possible for the same object to have different amounts of gravitational potential energy?

Arlecino [84]

Answer:

In Newtonian mechanics, the gravitational energy possessed by a mass, because of the gravitational field produced by a second mass.

Explanation:

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3 years ago

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3 years ago

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(III) An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the e

Iteru [2.4K]

Answer: 12Mg/h

Explanation:

Let the spring is compressed by a distance x,before the lift stops,then

Mg(h+x)= 1/2 kx^2 ............... 1

Kx - Mg = M ( 5g ) ............ 2

Make x the subject in equation 2

Kx = 5Mg + Mg

Kx = 6Mg

x = 6Mg/k ............ 3

Put equation 3 into 1

Mg ( h + x ) = 1/2 kx^2

Mgh + Mgx = 1/2kx^2

Mgh + Mg × 6Mg/k = 1/2k × ( 6Mg/k )^2

Mgh + Mg× 6Mg/k = 1/2k 36M^2g^2/ k^2

h =18Mg/k - 6Mg/h

K = 12Mg/h

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3 years ago

Read 2 more answers

Explain how the fixed points are used when calibrating a thermometer.

8090 [49]

<u>Answer:</u>

First, the thermometer is dipped into boiling water, and the mercury inside the thermometer rises to a high level, called the boiling point. This level is then marked as 100°C. The thermometer is then dipped into melting ice, which causes the mercury level to fall to a point called the ice point. This point is then marked as 0°C. The length of the thermometer from the 0°C mark to the 100°C point is then divided into 100 equal sections, and the rest of the levels are marked accordingly.

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2 years ago

A rough estimate of the radius of a nucleus is provided by the formula r 5 kA1/3, where k is approximately 1.3 × 10213 cm and A

Sphinxa [80]

Answer:

Density of 127 I = $\rm 1.79\times 10^{14}\ g/cm^3.$

Also, $\rm Density\ of\ ^{127}I=3.63\times 10^{13}\times Density\ of\ the\ solid\ iodine.$

Explanation:

Given, the radius of a nucleus is given as

$\rm r=kA^{1/3}$ .

where,

$\rm k = 1.3\times 10^{-13} cm.$

A is the mass number of the nucleus.

The density of the nucleus is defined as the mass of the nucleus M per unit volume V.

$\rm \rho = \dfrac{M}{V}=\dfrac{M}{\dfrac 43 \pi r^3}=\dfrac{M}{\dfrac 43 \pi (kA^{1/3})^3}=\dfrac{M}{\dfrac 43 \pi k^3A}.$

For the nucleus 127 I,

Mass, M = $\rm 2.1\times 10^{-22}\ g.$

Mass number, A = 127.

Therefore, the density of the 127 I nucleus is given by

$\rm \rho = \dfrac{2.1\times 10^{-22}\ g}{\dfrac 43 \times \pi \times (1.3\times 10^{-13})^3\times 127}=1.79\times 10^{14}\ g/cm^3.$

On comparing with the density of the solid iodine,

$\rm \dfrac{Density\ of\ ^{127}I}{Density\ of\ the\ solid\ iodine}=\dfrac{1.79\times 10^{14}\ g/cm^3}{4.93\ g/cm^3}=3.63\times 10^{13}.\\\\\Rightarrow Density\ of\ ^{127}I=3.63\times 10^{13}\times Density\ of\ the\ solid\ iodine.$

7 0

3 years ago