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4 years ago

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Sir Dudley the Dextrous is loading cannons on top of the castle's tallest towers in preparation for an expected attack. He slips

, and a cannonball of mass 14.0 kg 14.0 kg rolls to the edge of the tower, which has a perfectly horizontal surface, and falls to the ground below. It takes the cannonball 3.15 s 3.15 s to fall to the ground, and air resistance is negligible. How much work is done by gravity on the falling cannonball?

1 answer:

JulsSmile [24]4 years ago

4 0

Answer:

6667.9 J

Explanation:

We are given that

Mass of cannon.m=14 kg

Time,t=3.15 s

Initial velocity,u=0

We have to find the work done by gravity on the falling cannon ball.

$g=9.8 m/s^2$

$h=ut+\frac{1}{2}gt^2$

Substitute the values

$h=0+\frac{1}{2}\times 9.8\times (3.15)^2=48.6 m$

Work done,W=mgh

Using the formula

$W=14\times 9.8\times 48.6=6667.9 J$

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Explanation:

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Consider a series LRC-circuit in which C-120.0 uF. When driven at a frequency w = 200.0 rad s-1 the com ples impedance is given

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(II). The inductance of the circuit is 0.1583 Henry.

(b). The resonant angular frequency is 229.4 rad/s.

Explanation:

Given that,

Capacitor = 120.0 μC

Frequency = 200.0 rad/s

Impedance = 100.0 -10j

(I). We need to calculate the $X_{C}$

$X_{C}=\dfrac{1}{C\times\omega}$

Put the value into the formula

$X_{C}=\dfrac{1}{120\times10^{-6}\times200}$

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(II). We know that,

Formula of impedance is

$Z=\sqrt{R^2+X_{L}^2+X_{C}^2}$ ...(I)

Given equation of impedance is

$Z=(100-10j)$ ...(II)

On Comparing of equation (I) and (II)

$R = 100$

$X_{L}-X_{C}=-10$

Now, put the value of $X_{C}$

$X_{L=41.66-10$

$X_{L}=31.66\ \Omega$

We need to calculate the inductance

Using formula of inductance

$X_{L}=\omega\times L$

Put the value into the formula

$L=\dfrac{X_{L}}{\omega}$

$L=\dfrac{31.66}{200}$

$L=0.1583\ Henry$

(b). We need to calculate the resonant angular frequency

Using formula of the resonant angular frequency

$angular\ frequency =\dfrac{1}{\sqrt{L\times C}}$

$angular\ frequency =\dfrac{1}{\sqrt{0.1583\times120\times10^{-6}}}$

$angular\ frequency =229.4\ rad/s$

Hence, (a). (i). The reactants are $X_{L} =31.66\ \Omega$ .

(II). The inductance of the circuit is 0.1583 Henry.

(b). The resonant angular frequency is 229.4 rad/s.

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