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A 100 mH inductor whose windings have a resistance of 6.0 Ω is connected across a 12 Vbattery having an internal resistance of 3

Alexus [3.1K]

Answer:

The store energy in the inductor is 0.088 J

Explanation:

Given that,

Inductor = 100 mH

Resistance = 6.0 Ω

Voltage = 12 V

Internal resistance = 3.0 Ω

We need to calculate the current

Using ohm's law

$V = IR$

$I=\dfrac{V}{R+r}$

Put the value into the formula

$I=\dfrac{12}{6.0+3.0}$

$I=1.33\ A$

We need to calculate the store energy in the inductor

$U=\dfrac{1}{2}LI^2$

$U=\dfrac{1}{2}\times100\times10^{-3}\times(1.33)^2$

$U=0.088\ J$

Hence, The store energy in the inductor is 0.088 J

7 0

3 years ago

A uniform thin wire is bent into a quarter-circle of radius a = 20.0 cm, and placed in the first quadrant. Determine the coordin

Mashcka [7]

Answer:

$r_{cm}=[12.73,12.73]cm$

Explanation:

The general equation to calculate the center of mass is:

$r_{cm}=1/M*\int\limits {r} \, dm$

Any differential of mass can be calculated as:

$dm = \lambda*a*d\theta$ Where "a" is the radius of the circle and λ is the linear density of the wire.

The linear density is given by:

$\lambda=M/L=M/(a*\pi/2)=\frac{2M}{a\pi}$

So, the differential of mass is:

$dm = \frac{2M}{a\pi}*a*d\theta$

$dm = \frac{2M}{\pi}*d\theta$

Now we proceed to calculate X and Y coordinates of the center of mass separately:

$X_{cm}=1/M*\int\limits^{\pi/2}_0 {a*cos\theta*2M/\pi} \, d\theta$

$Y_{cm}=1/M*\int\limits^{\pi/2}_0 {a*sin\theta*2M/\pi} \, d\theta$

Solving both integrals, we get:

$X_{cm}=2*a/\pi=12.73cm$

$Y_{cm}=2*a/\pi=12.73cm$

Therefore, the position of the center of mass is:

$r_{cm}=[12.73,12.73]cm$

5 0

3 years ago

A cannon is fired horizontally at 243 m/s off of a 62 meter tall, shear vertical cliff. How far in meters from the base of the c

Alekssandra [29.7K]

Answer:

865.08 m

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 243 m/s

Height (h) of the cliff = 62 m

Horizontal distance (s) =?

Next, we shall determine the time taken for the cannon to get to the ground. This can be obtained as follow:

Height (h) of the cliff = 62 m

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) =?

h = ½gt²

62 = ½ × 9.8 × t²

62 = 4.9 × t²

Divide both side by 4.9

t² = 62/4.9

Take the square root of both side.

t = √(62/4.9)

t = 3.56 s

Finally, we shall determine the horizontal distance travelled by the cannon ball as shown below:

Initial velocity (u) = 243 m/s

Time (t) = 3.56 s

Horizontal distance (s) =?

s = ut

s = 243 × 3.56 s

s = 865.08 m

Thus, the cannon ball will impact the ground 865.08 m from the base of the cliff.

6 0

3 years ago

Is jewelry gold a compound or mixture?

USPshnik [31]

I think it’s a mixture.

7 0

3 years ago

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An astronaut drops a hammer from 2.0 meters above the surface of the moon. if the acceleration due to gravity on the moon is 1.6

aivan3 [116]

Answer:

1.57 s

Explanation:

Since the motion of the hammer is a uniformly accelerated motion, the distance covered by the hammer in a time t is

$S=\frac{1}{2}at^2$

Where, in this case

S = 2.0 m is the distance covered

a = 1.62 m/s^2 is the acceleration due to gravity

t is the time taken

Re-arranging the equation, we can find the time the hammer takes:

$t=\sqrt{\frac{2S}{a}}=\sqrt{\frac{2(2.0 m)}{1.62 m/s^2}}=1.57 s$

8 0

3 years ago

Read 2 more answers