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3 years ago

What is the relationship between the spring constant and the period in a mass hanging on a spring oscillation and why?

Physics

2 answers:

anygoal [31]3 years ago

3 0

Explanation:

Period of a mass on a spring is:

T = 2π√(m/k)

T is inversely proportional with the square root of k. So as the spring constant increases, the period decreases.

liubo4ka [24]3 years ago

3 0

Answer:

$T\propto \dfrac{1 }{\sqrt{k}} \text{ and } k \propto \dfrac{1}{T^{2}}$

Explanation:

The period T is inversely proportional to the square root of the spring constant, and

The spring constant is inversely proportional to the square of the period.

It all comes from Hooke's Law.

We usually get the equation for the period, but we can easily rearrange it to get an equation for the spring constant.

$\begin{array}{rcl}T &= &\mathbf{2\pi \sqrt{\dfrac{m}{k}}}\\\\T^{2} &=& 4 \pi^{2} \dfrac{m}{k}\\kT^{2}& =& 4 \pi^{2}m\\k &=& \mathbf{\dfrac{4 \pi^{2}m}{T^{2}}}\end{array}$

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Question 4 of 10 A student measures the time it takes for two reactions to be completed. Reaction A is completed in 39 seconds,

Delicious77 [7]

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2 years ago

Sometimes a person cannot clearly see objects close up or far away. To correct this type of vision, bifocals are often used. The

Alexxx [7]

Answer:

The power of top half of the lens is 0.55 Diopters.

Explanation:

Since, the person can see an object at a distance between 34 cm and 180 cm away from his eyes. Therefore, 180 cm must be the focal length of the upper part of lens, as the top half of the lens is used to see the distant objects.

The general formula for power of a lens is:

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Therefore, for the top half of the lens:

Power = 1/1.8 m

<u>Power = 0.55 Diopters</u>

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2 years ago

A 2 eV electron encounters a barrier 5.0 eV high and width a. What is the probability b) 0.5 that it will tunnel through the bar

denis23 [38]

Answer:

The tunnel probability for 0.5 nm and 1.00 nm are $5.45\times10^{-4}$ and $7.74\times10^{-8}$ respectively.

Explanation:

Given that,

Energy E = 2 eV

Barrier V₀= 5.0 eV

Width = 1.00 nm

We need to calculate the value of $\beta$

Using formula of $\beta$

$\beta=\sqrt{\dfrac{2m}{\dfrac{h}{2\pi}}(v_{0}-E)}$

Put the value into the formula

$\beta = \sqrt{\dfrac{2\times9.1\times10^{-31}}{(1.055\times10^{-34})^2}(5.0-2)\times1.6\times10^{-19}}$

$\beta=8.86\times10^{9}$

(a). We need to calculate the tunnel probability for width 0.5 nm

Using formula of tunnel barrier

$T=\dfrac{16E(V_{0}-E)}{V_{0}^2}e^{-2\beta a}$

Put the value into the formula

$T=\dfrac{16\times 2(5.0-2.0)}{5.0^2}e^{-2\times8.86\times10^{9}\times0.5\times10^{-9}}$

$T=5.45\times10^{-4}$

(b). We need to calculate the tunnel probability for width 1.00 nm

$T=\dfrac{16\times 2(5.0-2.0)}{5.0^2}e^{-2\times8.86\times10^{9}\times1.00\times10^{-9}}$

$T=7.74\times10^{-8}$

Hence, The tunnel probability for 0.5 nm and 1.00 nm are $5.45\times10^{-4}$ and $7.74\times10^{-8}$ respectively.

6 0

3 years ago

In the lab, you submerge 100 g of 40°C nails in 200 g of 20°C water. (The specific heat of iron is 0.12 cal/g # °C.) Equate the

Deffense [45]

Answer:

Final temperature of the mixture becomes

$T = 21.13^oC$

Explanation:

Here we know that heat given by the nail is equal to the heat absorbed by water

So here we know that heat to change the temperature is given as

$Q = ms\Delta T$

so by equating the heat we have

$m_{iron}s_{iron}\Delta T = m_{water}s_{water}\Delta T$

now we have

$100 (0.12) (40 - T) = 200 (1) (T - 20)$

$4.8 - 0.12 T = 2T - 40$

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2 years ago

What is the speed between reflected ray and the incident ray

Korvikt [17]

Answer:

The speed is the same as long as the reflection is regular.

Explanation:

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Since speed of light depends on the angle of the light ray it makes with the reflecting surface, the speed is the same

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3 years ago