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Vladimir79 [104]
3 years ago
11

A vertical spring with stiffness k originally is at rest with no mass attached. Then, a mass M is attached, and the spring rocks

back and forth until it is at rest at a new equilibrium position. What is this position in terms of g, M, and k?
Physics
1 answer:
Alina [70]3 years ago
8 0

Answer:

The position of the spring in terms of g, m & k is x = \frac{m g}{k}

Explanation:

Stiffness of the spring = k

Mass = m

When a mass m is attached with the spring then spring stretched. in that case the force exerted on the spring is equal to weight of the mass attached.

⇒ Force exerted on the spring F = k x

⇒ m g = k x

⇒ x = \frac{m g}{k}

This is the position of the spring in terms of g, m & k.

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A mixture is not a pure substance
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A person hears the echo of his own voice from a distant hill after 2 seconds. How far away is the person from the hill, if the s
olga nikolaevna [1]

Answer: 330 m

Explanation:

The speed of sound V is defined as the distance traveled by the sound wave d in a especific time t:  

V=\frac{d}{t}  

Where:  

V=330 m/s is the speed of sound  

t=\frac{2 s}{2}=1 s is half the time the sound wave travels since the person speaks, the sound wave hits the hill and then returns to the person again  as an echo

d is the distance between the person and the hill

So, we have to find d:

d=Vt

d=(330 m/s)(1 s)

Finally:

d=330 m

4 0
2 years ago
An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.50 mm. A 25
torisob [31]

Answer:

The electric field is 16666.66 V/m.

The surface charge density is 1.474\times10^{-7}\ C/m^2

The capacitance is 4.484\times10^{-12}\ F

The charge on each plate is 112.1\times10^{-12}\ C

Explanation:

Given that,

Area =7.70 cm²

Distance = 1.50 mm

Potential difference = 25.0 V

Suppose  we find the electric field between the plates, the surface charge density, the capacitance and the charge on each plates.

We need to calculate the electric field

Using formula of electric field

E=\dfrac{V}{d}

Put the value into the formula

E=\dfrac{25.0}{1.50\times10^{-3}}

E=16666.66\ V/m

We need to calculate the charge density

Using formula of charge density

\sigma=E\times\epsilon_{0}

Put the value into the formula

\sigma=16666.66\times8.85\times10^{-12}

\sigma=1.474\times10^{-7}\ C/m^2

We need to calculate the capacitance

Using formula of capacitance

C=\dfrac{\epsilon_{0}A}{d}

Put the value into the formula

C=\dfrac{8.85\times10^{-12}\times7.60\times10^{-4}}{1.50\times10^{-3}}

C=4.484\times10^{-12}\ F

We need to calculate the charge

Using formula of charge

q=CV

Put the value into the formula

q=4.484\times10^{-12}\times25.0

q=112.1\times10^{-12}\ C

Hence, The electric field is 16666.66 V/m.

The surface charge density is 1.474\times10^{-7}\ C/m^2

The capacitance is 4.484\times10^{-12}\ F

The charge on each plate is 112.1\times10^{-12}\ C

8 0
3 years ago
Calculate the self-inductance (in mH) of a 45.0 cm long, 10.0 cm diameter solenoid having 1000 loops. mH (b) How much energy (in
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Answer:

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(b) The energy stored, E = 4.84 J

(c) the time, t = 0.154 s

Explanation:

(a) Self inductance is calculated as;

L = \frac{N^2 \mu_0 A}{l}

where;

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μ is the permeability of free space = 4π x 10⁻⁷ H/m

l is the length of the inductor, = 45 cm = 0.45 m

A is the area of the inductor (given diameter = 10 cm = 0.1 m)

A = \pi r^2 = \frac{\pi d^2}{4} = \frac{\pi \times (0.1)^2}{4} = 0.00786 \ m^2

L = \frac{(1000)^2 \times (4\pi \times 10^{-7}) \times (0.00786)}{0.45} \\\\L = 0.02195 \ H\\\\L = 21.95 \ mH

(b) The energy stored in the inductor when 21 A current ;

E = \frac{1}{2}LI^2\\\\E = \frac{1}{2} \times (0.02195) \times (21) ^2\\\\E = 4.84 \ J

(c) time it can be turned off if the induced emf cannot exceed 3.0 V;

emf = L \frac{\Delta I}{\Delta t} \\\\t = \frac{LI}{emf} \\\\t = \frac{0.02195 \times 21}{3} \\\\t = 0.154 \ s

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