Answer:
Hey, bro here is the explanation....
Explanation:
Hope it helps...
Answer:
1)
is<u> positive.</u>
<u></u>
2) ![\rm q_2=4.56\times 10^{-10}\ C.](https://tex.z-dn.net/?f=%5Crm%20q_2%3D4.56%5Ctimes%2010%5E%7B-10%7D%5C%20C.)
Explanation:
<h2><u>
Part 1:</u></h2>
<u></u>
The charged rod is held above the balloon and the weight of the balloon acts in downwards direction. To balance the weight of the balloon, the force on the balloon due to the rod must be directed along the upwards direction, which is only possible when the rod exerts an attractive force on the balloon and the electrostatic force on the balloon due to the rod is attractive when the polarities of the charge on the two are different.
Thus, In order for this to occur, the polarity of charge on the rod must be positive, i.e.,
is <u>positive.</u>
<u></u>
<h2><u>
Part 2:</u></h2>
<u></u>
<u>Given:</u>
- Mass of the balloon, m = 0.00275 kg.
- Charge on the balloon,
![\rm q_1 = -3.50\times 10^{-8}\ C.](https://tex.z-dn.net/?f=%5Crm%20q_1%20%3D%20-3.50%5Ctimes%2010%5E%7B-8%7D%5C%20C.)
- Distance between the rod and the balloon, d = 0.0640 m.
- Acceleration due to gravity,
![\rm g = 9.81\ m/s^2.](https://tex.z-dn.net/?f=%5Crm%20g%20%3D%209.81%5C%20m%2Fs%5E2.)
In order to balloon to be float in air, the weight of the balloom must be balanced with the electrostatic force on the balloon due to rod.
Weight of the balloon, ![\rm W = mg = 0.00275\times 9.81=2.70\times 10^{-2}\ N.](https://tex.z-dn.net/?f=%5Crm%20W%20%3D%20mg%20%3D%200.00275%5Ctimes%209.81%3D2.70%5Ctimes%2010%5E%7B-2%7D%5C%20N.)
The magnitude of the electrostatic force on the balloon due to the rod is given by
![\rm F_e = \dfrac{1}{4\pi \epsilon_o}\dfrac{|q_1||q_2|}{d^2}.](https://tex.z-dn.net/?f=%5Crm%20F_e%20%3D%20%5Cdfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon_o%7D%5Cdfrac%7B%7Cq_1%7C%7Cq_2%7C%7D%7Bd%5E2%7D.)
is the Coulomb's constant.
For the elecric force and the weight to be balanced,
![\rm F_e = W\\\dfrac{1}{4\pi \epsilon_o}\dfrac{|q_1||q_2|}{d^2}=W\\8.99\times 10^9\times \dfrac{3.50\times10^{-8}\times |q_2| }{0.0640^2}=2.70\times 10^{-2}\\|q_2| = \dfrac{2.70\times 10^{-2}\times 0.00640^2}{8.99\times 10^9\times 2.70\times 10^{-7}}=4.56\times 10^{-10}\ C.](https://tex.z-dn.net/?f=%5Crm%20F_e%20%3D%20W%5C%5C%5Cdfrac%7B1%7D%7B4%5Cpi%20%5Cepsilon_o%7D%5Cdfrac%7B%7Cq_1%7C%7Cq_2%7C%7D%7Bd%5E2%7D%3DW%5C%5C8.99%5Ctimes%2010%5E9%5Ctimes%20%5Cdfrac%7B3.50%5Ctimes10%5E%7B-8%7D%5Ctimes%20%7Cq_2%7C%20%7D%7B0.0640%5E2%7D%3D2.70%5Ctimes%2010%5E%7B-2%7D%5C%5C%7Cq_2%7C%20%3D%20%5Cdfrac%7B2.70%5Ctimes%2010%5E%7B-2%7D%5Ctimes%200.00640%5E2%7D%7B8.99%5Ctimes%2010%5E9%5Ctimes%202.70%5Ctimes%2010%5E%7B-7%7D%7D%3D4.56%5Ctimes%2010%5E%7B-10%7D%5C%20C.)
Answer:
![\theta = n\pi/2, {\rm where~n~is~an~integer.}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20n%5Cpi%2F2%2C%20%7B%5Crm%20where~n~is~an~integer.%7D)
Explanation:
We should first find the velocity and acceleration functions. The velocity function is the derivative of the position function with respect to time, and the acceleration function is the derivative of the velocity function with respect to time.
![\vec{v}(t) = \frac{d\vec{r}(t)}{dt} = (2)\^i + (\sqrt{7})\^j + (6t)\^k](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%28t%29%20%3D%20%5Cfrac%7Bd%5Cvec%7Br%7D%28t%29%7D%7Bdt%7D%20%3D%20%282%29%5C%5Ei%20%2B%20%28%5Csqrt%7B7%7D%29%5C%5Ej%20%2B%20%286t%29%5C%5Ek)
Similarly,
![\vec{a}(t) = \frac{d\vec{v}(t)}{dt} = (6)\^k](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%28t%29%20%3D%20%5Cfrac%7Bd%5Cvec%7Bv%7D%28t%29%7D%7Bdt%7D%20%3D%20%286%29%5C%5Ek)
Now, the angle between velocity and acceleration vectors can be found.
The angle between any two vectors can be found by scalar product of them:
![\vec{A}.\vec{B} = |\vec{A}|.|\vec{B}|.\cos(\theta)](https://tex.z-dn.net/?f=%5Cvec%7BA%7D.%5Cvec%7BB%7D%20%3D%20%7C%5Cvec%7BA%7D%7C.%7C%5Cvec%7BB%7D%7C.%5Ccos%28%5Ctheta%29)
So,
![\vec{v}(t).\vec{a}(t) = |\vec{v}(t)|.|\vec{a}(t)|.\cos(\theta)\\36t = \sqrt{4 + 7 + 36t^2}.6.\cos(\theta)](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%28t%29.%5Cvec%7Ba%7D%28t%29%20%3D%20%7C%5Cvec%7Bv%7D%28t%29%7C.%7C%5Cvec%7Ba%7D%28t%29%7C.%5Ccos%28%5Ctheta%29%5C%5C36t%20%3D%20%5Csqrt%7B4%20%2B%207%20%2B%2036t%5E2%7D.6.%5Ccos%28%5Ctheta%29)
At time t = 0, this equation becomes
![0 = 6\sqrt{11}\cos(\theta)\\\cos(\theta) = 0\\\theta = n\pi/2, {\rm where~n~is~an~integer.}](https://tex.z-dn.net/?f=0%20%3D%206%5Csqrt%7B11%7D%5Ccos%28%5Ctheta%29%5C%5C%5Ccos%28%5Ctheta%29%20%3D%200%5C%5C%5Ctheta%20%3D%20n%5Cpi%2F2%2C%20%7B%5Crm%20where~n~is~an~integer.%7D)
There are two atoms of potassium bonded to one atom of sulfur.
Answer:3,600 Newtons
Explanation:
The net force acting on the car is
3×10^3squared
Newtons.
Force is defined as the product of the mass of the body and its aaceleration,⇒F=ma
Substituting the above given values we get,F=(1500kg) (2.0m /s^2 squared)=3000 N=3×10^3 squared N.
N=newtons