A _______ is used to electrically replace the injector in the circuit and flash if the injector circuit is working correctly.

Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total di

S_A_V [24]

Answer:

1keff=1k1+1k2

see further explanation

Explanation:for clarification

Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination. Also, each spring must exert the same force. Do you see why?

From Hooke's law , we know that the force exerted on an elastic object is directly proportional to the extension provided that the elastic limit is not exceeded.

Now the spring is in series combination

F $\alpha$ e

F=ke

k=f/e.........*

where k is the force constant or the constant of proportionality

k=f/e

$f_{eff} =f_{1} +f_{2}$ ............................1

also for effective force constant

divide all through by extension

1) Total force is

Ft=F1+F2

Ft=k1e1+k2e2

F = k(e1+e2) 2)

Since force on the 2 springs is the same, so

k1e1=k2e2

e1=F/k1 and e2=F/k2,

and e1+e2=F/keq

Substituting e1 and e2, you get

1/keq=1/k1+1/k2

Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination.

4 0

3 years ago

An object will remain at rest or maintain constant, straight-line motion unless acted on by a force that is ___________________.

vivado [14]

An object will remain at rest of maintain constant straight-line motion unless acted on by a force that is c. unbalanced

8 0

3 years ago

Why are newtons second and third law important to everyday life?

Rzqust [24]

Because it always happens everyday, everytime, everyseconds...
Like typing on a keyboard, pushing a table. And if you're an engineer, you must able to measure it...
Bad english...

6 0

3 years ago

Astronomers can now report that active star formation was going on at a time when the universe was only 20% as old as it is toda

disa [49]

Answer:

First, as you may know, the light travels at a given velocity.

In vaccum, this velocity is c = 3x10^8 m/s.

And we know that:

distance = velocity*time

Now, if some object (like a star ) is really far away, the light that comes from that star may take years to reach the Earth.

This means that the images that the astronomers see today, actually happened years and years ago (So the night sky is like a picture of the "past" of the universe)

Also, for example, if an astronomer sees some particular thing, he can apply a model (a "simplification" of some phenomena that is used to simplify it an explain it) and with the model, the scientist can infer the information of the given thing some time before it was seen.

8 0

3 years ago

A solenoidal coil with 25 turns of wire is wound tightly aroundanother coil with 300 turns. The inner solenoid is 25.0 cm long a

Aneli [31]

Answer:

(a). The average magnetic flux through each turn of the inner solenoid is $5.68\times10^{-8}\ Wb$

(b). The mutual inductance of the two solenoids is $1.183\times10^{-5}\ H$

(c). The emf induced in the outer solenoid by the changing current in the inner solenoid is -0.0207 V.

Explanation:

Given that,

Number of turns of coil = 25

Number of turns of another coil = 300

Length = 25.0 cm

Diameter = 2.00 cm

Current = 0.120 A

Rate $\dfrac{di_{2}}{dt}=1.75\times10^{3}\ A/s$

(a). We need to calculate the magnetic field due to inner solenoid

Using formula of magnetic field

$B=\mu_{0}(\dfrac{N_{2}}{l})I$

Put the value into the formula

$B=4\pi\times10^{-7}\times(\dfrac{300}{0.25})\times0.120$

$B=1.81\times10^{-4}\ T$

We need to calculate the average magnetic flux through each turn of the inner solenoid

Using formula of magnetic flux

$\phi=B\cdot A$

Put the value into the formula

$\phi=1.81\times10^{-4}\times\pi\times (1.00\times10^{-2})^2$

$\phi=5.68\times10^{-8}\ Wb$

The average magnetic flux through each turn of the inner solenoid is $5.68\times10^{-8}\ Wb$

(b). We need to calculate the mutual inductance of the two solenoids

Using formula of mutual inductance

$M=\dfrac{N_{1}\phi}{i_{1}}$

Put the value into the formula

$M=\dfrac{25\times5.68\times10^{-8}}{0.120}$

$M=0.00001183\ H$

$M=1.183\times10^{-5}\ H$

The mutual inductance of the two solenoids is $1.183\times10^{-5}\ H$

(c). We need to calculate the emf induced in the outer solenoid by the changing current in the inner solenoid

Using formula of emf

$\epsilon=-M\dfrac{di_{2}}{dt}$

Put the value into the formula

$\epsilon=-1.183\times10^{-5}\times1.75\times10^{3}$

$\epsilon=-0.0207\ V$

The emf induced in the outer solenoid by the changing current in the inner solenoid is -0.0207 V.

Hence, (a). The average magnetic flux through each turn of the inner solenoid is $5.68\times10^{-8}\ Wb$

(b). The mutual inductance of the two solenoids is $1.183\times10^{-5}\ H$

(c). The emf induced in the outer solenoid by the changing current in the inner solenoid is -0.0207 V.

5 0

3 years ago