We have here what is known as parallel combination of resistors.
Using the relation:
![\frac{1}{ r_{eff} } = \frac{1}{ r_{1} } + \frac{1}{ r_{2} } + \frac{1}{ r_{3} }.. . + \frac{1}{ r_{n} } \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20r_%7Beff%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B%20r_%7B1%7D%20%7D%20%2B%20%5Cfrac%7B1%7D%7B%20r_%7B2%7D%20%7D%20%2B%20%5Cfrac%7B1%7D%7B%20r_%7B3%7D%20%7D..%20.%20%2B%20%5Cfrac%7B1%7D%7B%20r_%7Bn%7D%20%7D%20%5C%5C%20)
And then we can turn take the inverse to get the effective resistance.
Where r is the magnitude of the resistance offered by each resistor.
In this case we have,
(every term has an mho in the end)
![\frac{1}{10000} + \frac{1}{2000} + \frac{1}{1000} \\ \\ = \frac{1}{1000} ( \frac{1}{10} + \frac{1}{2} + \frac{1}{1} ) \\ \\ = \frac{1}{1000} ( \frac{31}{20}) \\ \\ = \frac{31}{20000}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B10000%7D%20%2B%20%5Cfrac%7B1%7D%7B2000%7D%20%2B%20%5Cfrac%7B1%7D%7B1000%7D%20%5C%5C%20%5C%5C%20%3D%20%5Cfrac%7B1%7D%7B1000%7D%20%28%20%5Cfrac%7B1%7D%7B10%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B1%7D%20%29%20%5C%5C%20%5C%5C%20%3D%20%5Cfrac%7B1%7D%7B1000%7D%20%28%20%5Cfrac%7B31%7D%7B20%7D%29%20%5C%5C%20%5C%5C%20%3D%20%5Cfrac%7B31%7D%7B20000%7D%20)
To ger effective resistance take the inverse:
we get,
![\frac{20000}{31} \: ohm \\ = 645 .16 \: ohm](https://tex.z-dn.net/?f=%20%5Cfrac%7B20000%7D%7B31%7D%20%5C%3A%20ohm%20%5C%5C%20%3D%20645%20.16%20%5C%3A%20ohm)
The potential difference is of 9V.
So the current flowing using ohm's law,
V = IR
will be, 0.0139 Amperes.
For the majority of instruments f = n f0 where f is the resonating frequency, n is any whole number and f0 is the fundamental.
<span>This applies to trumpets, violins, flutes and a broad range. </span>
<span>In such a </span>case<span> the first harmonic would be at n=1 and the second harmonic would be at n=2 </span>
<span>which gives a frequency of 84 Hz</span>
Answer:
3331.5 kg
Explanation:
Given:
Spring constant of the spring (k) = 24200 N/m
Frequency of oscillation (f) = 0.429 Hz
Let the mass be 'm' kg.
Now, we know that, a spring-mass system undergoes Simple Harmonic Motion (SHM). The frequency of oscillation of SHM is given as:
![f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
Rewrite the above equation in terms of 'm'. This gives,
![2\pi f=\sqrt{\frac{k}{m}}\\\\Squaring\ both\ sides,\ we\ get:\\\\(2\pi f)^2=\frac{k}{m}\\\\m=\frac{k}{4\pi^2 f^2}](https://tex.z-dn.net/?f=2%5Cpi%20f%3D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D%5C%5C%5C%5CSquaring%5C%20both%5C%20sides%2C%5C%20we%5C%20get%3A%5C%5C%5C%5C%282%5Cpi%20f%29%5E2%3D%5Cfrac%7Bk%7D%7Bm%7D%5C%5C%5C%5Cm%3D%5Cfrac%7Bk%7D%7B4%5Cpi%5E2%20f%5E2%7D)
Now, plug in the given values and solve for 'm'. This gives,
![m=\frac{24200\ N/m}{4\pi^2\times (0.429\ Hz)^2 }\\\\m=\frac{24200\ N/m}{4\pi^2\times 0.184\ Hz^2}\\\\m\approx3331.5\ kg](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B24200%5C%20N%2Fm%7D%7B4%5Cpi%5E2%5Ctimes%20%280.429%5C%20Hz%29%5E2%20%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B24200%5C%20N%2Fm%7D%7B4%5Cpi%5E2%5Ctimes%200.184%5C%20Hz%5E2%7D%5C%5C%5C%5Cm%5Capprox3331.5%5C%20kg)
Therefore, the mass of the truck is 3331.5 kg.
Explanation:
Given that,
Radius of the disk, r = 0.25 m
Mass, m = 45.2 kg
Length of the ramp, l = 5.4 m
Angle made by the ramp with horizontal, ![\theta=17^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D17%5E%7B%5Ccirc%7D)
Solution,
As the disk starts from rest from the top of the ramp, the potential energy is equal to the sum of translational kinetic energy and the rotational kinetic energy or by using the law of conservation of energy as :
(a) ![mgh=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2](https://tex.z-dn.net/?f=mgh%3D%5Cdfrac%7B1%7D%7B2%7Dmv%5E2%2B%5Cdfrac%7B1%7D%7B2%7DI%5Comega%5E2)
h is the height of the ramp
![sin\theta=\dfrac{h}{5.4}](https://tex.z-dn.net/?f=sin%5Ctheta%3D%5Cdfrac%7Bh%7D%7B5.4%7D)
![h=sin(17)\times 5.4=1.57\ m](https://tex.z-dn.net/?f=h%3Dsin%2817%29%5Ctimes%205.4%3D1.57%5C%20m)
v is the speed of the disk's center
I is the moment of inertia of the disk,
![I=\dfrac{1}{2}mr^2](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7B1%7D%7B2%7Dmr%5E2)
![\omega=\dfrac{v}{r}](https://tex.z-dn.net/?f=%5Comega%3D%5Cdfrac%7Bv%7D%7Br%7D)
![mgh=\dfrac{1}{2}mv^2+\dfrac{1}{2}\dfrac{1}{2}mr^2\times (\dfrac{v}{r})^2](https://tex.z-dn.net/?f=mgh%3D%5Cdfrac%7B1%7D%7B2%7Dmv%5E2%2B%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B1%7D%7B2%7Dmr%5E2%5Ctimes%20%28%5Cdfrac%7Bv%7D%7Br%7D%29%5E2)
![gh=\dfrac{1}{2}v^2+\dfrac{1}{4}v^2](https://tex.z-dn.net/?f=gh%3D%5Cdfrac%7B1%7D%7B2%7Dv%5E2%2B%5Cdfrac%7B1%7D%7B4%7Dv%5E2)
![gh=\dfrac{3}{4}v^2](https://tex.z-dn.net/?f=gh%3D%5Cdfrac%7B3%7D%7B4%7Dv%5E2)
![9.8\times 1.57=\dfrac{3}{4}v^2](https://tex.z-dn.net/?f=9.8%5Ctimes%201.57%3D%5Cdfrac%7B3%7D%7B4%7Dv%5E2)
v = 4.52 m/s
(b) At the bottom of the ramp, the angular speed of the disk is given by :
![\omega=\dfrac{v}{r}](https://tex.z-dn.net/?f=%5Comega%3D%5Cdfrac%7Bv%7D%7Br%7D)
![\omega=\dfrac{4.52}{0.25}](https://tex.z-dn.net/?f=%5Comega%3D%5Cdfrac%7B4.52%7D%7B0.25%7D)
![\omega=18.08\ rad/s](https://tex.z-dn.net/?f=%5Comega%3D18.08%5C%20rad%2Fs)
Hence, this is the required solution.
Answer:
its a negative work, not a negative force
Explanation:
I took the quiz first i put negative force i got it wrong
then when i put negative work it was right
Hope it help:)♥︎ plz mark me as brainliest