Answer:
![\vec{F}_{21}=-5.63\times 10^{-11}N\\\\\vec{F}_{21}=\\](https://tex.z-dn.net/?f=%5Cvec%7BF%7D_%7B21%7D%3D-5.63%5Ctimes%2010%5E%7B-11%7DN%5C%5C%5C%5C%5Cvec%7BF%7D_%7B21%7D%3D%3C-4.30%5Ctimes%2010%5E%7B-11%7DN%5C%2C%2C%5C%2C-3.62%5Ctimes%2010%5E%7B-11%7DN%3E%5C%5C)
Explanation:
Given that
![Q_1 = -2e\, C\\\\Q_2=-3e\,C\\\\x= 3.8 \times 10^{-9}\,m\\\\y= 3.2 \times 10^{-9}\,m\\\\r=\sqrt{x^2+y^2}\\\\r= 4.96\times 10^{-9} m\\](https://tex.z-dn.net/?f=Q_1%20%3D%20-2e%5C%2C%20C%5C%5C%5C%5CQ_2%3D-3e%5C%2CC%5C%5C%5C%5Cx%3D%203.8%20%5Ctimes%2010%5E%7B-9%7D%5C%2Cm%5C%5C%5C%5Cy%3D%203.2%20%5Ctimes%2010%5E%7B-9%7D%5C%2Cm%5C%5C%5C%5Cr%3D%5Csqrt%7Bx%5E2%2By%5E2%7D%5C%5C%5C%5Cr%3D%204.96%5Ctimes%2010%5E%7B-9%7D%20m%5C%5C)
As both charges are negative so there exist force of repulsion in direction as shown in figure.
![F_{12}=\frac{kQ_1Q_2}{r^2}\\\\F_{12}= \frac{(9\times 10^9)(6)(1.602\times 10^{-19})^2}{(4.96\times 10^{-9})^2}\\\\F_{12}=5.63\times 10^{-11}N](https://tex.z-dn.net/?f=F_%7B12%7D%3D%5Cfrac%7BkQ_1Q_2%7D%7Br%5E2%7D%5C%5C%5C%5CF_%7B12%7D%3D%20%5Cfrac%7B%289%5Ctimes%2010%5E9%29%286%29%281.602%5Ctimes%2010%5E%7B-19%7D%29%5E2%7D%7B%284.96%5Ctimes%2010%5E%7B-9%7D%29%5E2%7D%5C%5C%5C%5CF_%7B12%7D%3D5.63%5Ctimes%2010%5E%7B-11%7DN)
Angle at which force F12 is acting is
![\theta=tan^{-1}\frac{3.2}{3.8}\\\\\theta=tan^{-1}\frac{y}{x}\\\\\theta= 40.1^o](https://tex.z-dn.net/?f=%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7B3.2%7D%7B3.8%7D%5C%5C%5C%5C%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D%5C%5C%5C%5C%5Ctheta%3D%2040.1%5Eo)
![F_{x}=F_{12}cos\theta\\\\F_{x}=(5.63\times 10^{-11})cos(40.1)\\\\F_{x}=4.306\times 10^{-11}N\\\\F_{y}=F_{12}sin\theta\\\\F_{y}=(5.63\times 10^{-11})sin(40.1)\\\\F_{y}=3.62\times 10^{-11}N\\\\](https://tex.z-dn.net/?f=F_%7Bx%7D%3DF_%7B12%7Dcos%5Ctheta%5C%5C%5C%5CF_%7Bx%7D%3D%285.63%5Ctimes%2010%5E%7B-11%7D%29cos%2840.1%29%5C%5C%5C%5CF_%7Bx%7D%3D4.306%5Ctimes%2010%5E%7B-11%7DN%5C%5C%5C%5CF_%7By%7D%3DF_%7B12%7Dsin%5Ctheta%5C%5C%5C%5CF_%7By%7D%3D%285.63%5Ctimes%2010%5E%7B-11%7D%29sin%2840.1%29%5C%5C%5C%5CF_%7By%7D%3D3.62%5Ctimes%2010%5E%7B-11%7DN%5C%5C%5C%5C)
![\vec{F}_{12}=\vec{F}_{x}+\vec{F}_y\\\\\vec{F}_{12}=4.30\times 10^{-11}\,\hat{i} + 3.62\times 10^{-11}\,\hat{j}\\\\\vec{F}_{12}=](https://tex.z-dn.net/?f=%5Cvec%7BF%7D_%7B12%7D%3D%5Cvec%7BF%7D_%7Bx%7D%2B%5Cvec%7BF%7D_y%5C%5C%5C%5C%5Cvec%7BF%7D_%7B12%7D%3D4.30%5Ctimes%2010%5E%7B-11%7D%5C%2C%5Chat%7Bi%7D%20%2B%203.62%5Ctimes%2010%5E%7B-11%7D%5C%2C%5Chat%7Bj%7D%5C%5C%5C%5C%5Cvec%7BF%7D_%7B12%7D%3D%3C4.30%5Ctimes%2010%5E%7B-11%7DN%5C%2C%2C%5C%2C3.62%5Ctimes%2010%5E%7B-11%7DN%3E)
Force exerted on charge -2e is equal in magnitude to F12 but is in opposite direction
![F_{21}=-5.63\times 10^{-11}N](https://tex.z-dn.net/?f=F_%7B21%7D%3D-5.63%5Ctimes%2010%5E%7B-11%7DN)
![\vec{F}_{21}=](https://tex.z-dn.net/?f=%5Cvec%7BF%7D_%7B21%7D%3D%3C-4.30%5Ctimes%2010%5E%7B-11%7DN%5C%2C%2C%5C%2C-3.62%5Ctimes%2010%5E%7B-11%7DN%3E)
Answer:
4.763 × 10⁶ N/C
Explanation:
Let E₁ be the electric field due to the 4.0 μC charge and E₂ be the electric field due to the -6.0 μC charge. At the third corner, E₁ points in the negative x direction and E₂ acts at an angle of 60 to the negative x - direction.
Resolving E₂ into horizontal and vertical components, we have
E₂cos60 as horizontal component and E₂sin60 as vertical component. E₁ has only horizontal component.
Summing the horizontal components we have
E₃ = -E₁ + (-E₂cos60) = -kq₁/r²- kq₂cos60/r²
= -k/r²(q₁ + q₂cos60)
= -k/r²(4 μC + (-6.0 μC)(1/2))
= -k/r²(4 μC - 3.0 μC)
= -k/r²(1 μC)
= -9 × 10⁹ Nm²/C²(1.0 × 10⁻⁶)/(0.10 m)²
= -9 × 10⁵ N/C
Summing the vertical components, we have
E₄ = 0 + (-E₂sin60)
= -E₂sin60
= -kq₂sin60/r²
= -k(-6.0 μC)(0.8660)/(0.10 m)²
= -9 × 10⁹ Nm²/C²(-6.0 × 10⁻⁶)(0.8660)/(0.10 m)²
= 46.77 × 10⁵ N/C
The magnitude of the resultant electric field, E is thus
E = √(E₃² + E₄²) = √[(-9 × 10⁵ N/C)² + (46.77 10⁵ N/C)²) = (√226843.29) × 10⁴
= 476.28 × 10⁴ N/C
= 4.7628 × 10⁶ N/C
≅ 4.763 × 10⁶ N/C
Answer:
work=f(costheta)
Explanation:
work is done when a force acts on a body and displaces it on the direction of force
Answer:
Initial velocity = 10 m/s
θ = 60°
This is the case of projectile motion
So the horizontal component of velocity 10 m/s = 10 cosθ
u = 10 cosθ
u = 10 cos 60°
u=5 m/s
x= 5 m
So in the horizontal direction
x = u .t
5 = 5 .t
t = 1 sec The vertical component of velocity 10 m/s = 10 sinθ
Vo= 10 sinθ
Vo= 10 sin 60°
Vo = 8.66 m/s
h=3.75 m
So height of robot = 3.75 - 0.75 m
height of robot =3 m
Answer:
No, it's not there.
Explanation:
For a machine to be 100% efficient, it has to be with an output which is equal to its input. But machines have an out put less than an input, hence efficiency below 100%.