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saveliy_v [14]
3 years ago
5

A block of mass 0.249 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that th

e spring is compressed by 0.107 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (Round your answer to two decimal places.)
Physics
1 answer:
Brut [27]3 years ago
7 0

Answer:

h = 11.67 m

Explanation:

Mass, m = 0.249 kg

Spring constant, k = 4975 N/m

Compression, x = 0.107 m

Energy stored in the spring,W, is:

W = 0.5kx²

W = 0.5*4975*0.107²

W = 28.48N·m

The potential energy is given by the formula:

PE = mgh

PE = 0.249*9.8*h

PE = 2.4402h

According to energy conservation principle, Potential Energy = spring energy.

That is, PE = W

2.4402h = 28.48

h = 28.48/2.4402

h = 11.67 m

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When you double capacitance and inductance, the new resonance frequency becomes f/2.

  • Resonance frequency:

The resonance frequency of RLC series circuit, is the frequency at which the capacity reactance is equal to inductive reactance.

It can also be defined as the natural frequency of an object where it tends to vibrate at a higher amplitude.

Xc = Xl

which gives the value for resonance frequency:

f = \frac{1}{2\pi \sqrt{LC} }

where;

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When you double capacitance and inductance, the new resonance frequency becomes;

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Learn more about resonance frequency here:

<u>brainly.com/question/13040523</u>

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Aloop of wire of area 71 cm^2 is placed with its plane parallel to a 16 mt magnetic field. the loop is then rotated so that its
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Answer:

Approximately 1.62 × 10⁻⁴ V.

Explanation:

The average EMF in the coil is equal to

\displaystyle \frac{\text{Final Magnetic Flux} - \text{Initial Magnetic Flux}}{2},

Why does this formula work?

By Faraday's Law of Induction, the EMF \epsilon induced in a coil (one loop) is equal to the rate of change in the magnetic flux \Phi through the coil.

\displaystyle \epsilon(t) = \frac{d}{dt}(\Phi(t)).

Finding the average EMF in the coil is similar to finding the average velocity.

\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt.

However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:

\displaystyle \int_0^{t} \epsilon(t)\cdot dt = \int_0^{t} \frac{d}{dt}\Phi(t)\cdot dt = \Phi(t) - \Phi(0).

Hence the equation

\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt = \frac{\Phi(t)- \Phi(0)}{t}.

Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in \Phi(t) won't matter.

Apply this formula to this question. Note that \Phi, the magnetic flux through the coil, can be calculated with the equation

\Phi = B \cdot A \cdot N \; \sin{\theta}.

For this question,

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  • \theta is the angle between the field lines and the coil.
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  • At \rm 0.7\; s, the field lines are perpendicular to the coil, \displaystyle \theta = 90^{\circ}.

Initial flux: \Phi(0)= 0.

Final flux: \Phi(0.7) = \rm 1.1136\times 10^{-4}\; Wb.

Average EMF, which is the same as the average rate of change in flux:

\displaystyle \frac{\Phi(0.7) - \Phi(0)}{0.7} \approx\rm 1.62\times 10^{-4}\; V.

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