The acceleration of the crate after it begins to move is 0.5 m/s²
We'll begin by calculating the the frictional force
Mass (m) = 50 Kg
Coefficient of kinetic friction (μ) = 0.15
Acceleration due to gravity (g) = 10 m/s²
Normal reaction (N) = mg = 50 × 10 = 500 N
<h3>Frictional force (Fբ) =?</h3>
Fբ = μN
Fբ = 0.15 × 500
<h3>Fբ = 75 N</h3>
- Next, we shall determine the net force acting on the crate
Frictional force (Fբ) = 75 N
Force (F) = 100 N
<h3>Net force (Fₙ) =?</h3>
Fₙ = F – Fբ
Fₙ = 100 – 75
<h3>Fₙ = 25 N</h3>
- Finally, we shall determine the acceleration of the crate
Mass (m) = 50 Kg
Net force (Fₙ) = 25 N
<h3>Acceleration (a) =?</h3>
a = Fₙ / m
a = 25 / 50
<h3>a = 0.5 m/s²</h3>
Therefore, the acceleration of the crate is 0.5 m/s²
Learn more on friction: brainly.com/question/364384
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Answer:
a
The x- and y-components of the total force exerted is
![F_{31 +32} = (8.64i - 5.52 j) *10^{-5}](https://tex.z-dn.net/?f=F_%7B31%20%2B32%7D%20%3D%20%20%288.64i%20-%205.52%20j%29%20%2A10%5E%7B-5%7D)
b
The magnitude of the force is
![|F_{31 +32}| = 10.25 *10^{-5} N](https://tex.z-dn.net/?f=%7CF_%7B31%20%2B32%7D%7C%20%3D%2010.25%20%2A10%5E%7B-5%7D%20N)
The direction of the force is
Clockwise from x-axis
Explanation:
From the question we are told that
The magnitude of the first charge is ![q_1 = +5.00nC = 5.00*10^{-9}C](https://tex.z-dn.net/?f=q_1%20%3D%20%2B5.00nC%20%3D%205.00%2A10%5E%7B-9%7DC)
The magnitude of the second charge is ![q_2 = -2.00nC = -2.00*10^{-9}C](https://tex.z-dn.net/?f=q_2%20%3D%20-2.00nC%20%3D%20-2.00%2A10%5E%7B-9%7DC)
The position of the second charge from the first one is ![d_{12} = 4.00i \ cm = \frac{4.00i}{100} = 4.00i *10^{-2} m](https://tex.z-dn.net/?f=d_%7B12%7D%20%3D%204.00i%20%5C%20%20cm%20%3D%20%5Cfrac%7B4.00i%7D%7B100%7D%20%3D%204.00i%20%2A10%5E%7B-2%7D%20m)
The magnitude of the third charge is ![q_3 = +6.00nC = 6.00*10^{-9}C](https://tex.z-dn.net/?f=q_3%20%3D%20%2B6.00nC%20%3D%206.00%2A10%5E%7B-9%7DC)
The position of the third charge from the first one is ![\= d_{31} = (4i + 3j) cm = \frac{ (4i + 3j)}{100} = (4i + 3j) *10^{-2}m](https://tex.z-dn.net/?f=%5C%3D%20d_%7B31%7D%20%3D%20%284i%20%2B%203j%29%20cm%20%3D%20%5Cfrac%7B%20%284i%20%2B%203j%29%7D%7B100%7D%20%3D%20%20%284i%20%2B%203j%29%20%2A10%5E%7B-2%7Dm)
![|d_{31}| =(\sqrt{4 ^2 + 3^2}) *10^{-2} m](https://tex.z-dn.net/?f=%7Cd_%7B31%7D%7C%20%3D%28%5Csqrt%7B4%20%5E2%20%2B%203%5E2%7D%29%20%2A10%5E%7B-2%7D%20m)
![|d_{31}| =5 *10^{-2} m](https://tex.z-dn.net/?f=%7Cd_%7B31%7D%7C%20%3D5%20%2A10%5E%7B-2%7D%20m)
The position of the third charge from the second one is
![\= d_{32} = 3j cm = 3j *10^{-2}m](https://tex.z-dn.net/?f=%5C%3D%20d_%7B32%7D%20%3D%203j%20cm%20%3D%203j%20%2A10%5E%7B-2%7Dm)
![|d_{32}| =(\sqrt{ 3^2}) *10^{-2} m](https://tex.z-dn.net/?f=%7Cd_%7B32%7D%7C%20%3D%28%5Csqrt%7B%203%5E2%7D%29%20%2A10%5E%7B-2%7D%20m)
![|d_{32}| =3 *10^{-2} m](https://tex.z-dn.net/?f=%7Cd_%7B32%7D%7C%20%3D3%20%2A10%5E%7B-2%7D%20m)
The force acting on the third charge due to the first and second charge is mathematically represented as
![F_{31 +32} = \frac{kq_3 q_1}{|d_{31}| ^3} *\= d_{31} + \frac{kq_3 q_2}{|d_{32}| ^3} *\= d_{32}](https://tex.z-dn.net/?f=F_%7B31%20%2B32%7D%20%3D%20%5Cfrac%7Bkq_3%20q_1%7D%7B%7Cd_%7B31%7D%7C%20%5E3%7D%20%2A%5C%3D%20d_%7B31%7D%20%2B%20%5Cfrac%7Bkq_3%20q_2%7D%7B%7Cd_%7B32%7D%7C%20%5E3%7D%20%2A%5C%3D%20d_%7B32%7D)
Substituting values
![F_{31 +32} = \frac{9 *10^9 * 6 *10^{-9} * 5*10^{-9} }{(5*10^{-2}) ^3} * (4i + 3j ) *10^{-2} \\ \ + \ \ \ \ \ \ \ \ \ \frac{9 *10^9 * 6 *10^{-9} * -2*10^{-9} }{(5*10^{-2}) ^3} * (4i + 3j ) *10^{-2}](https://tex.z-dn.net/?f=F_%7B31%20%2B32%7D%20%3D%20%5Cfrac%7B9%20%2A10%5E9%20%2A%206%20%2A10%5E%7B-9%7D%20%2A%205%2A10%5E%7B-9%7D%20%7D%7B%285%2A10%5E%7B-2%7D%29%20%5E3%7D%20%20%2A%20%284i%20%2B%203j%20%29%20%2A10%5E%7B-2%7D%20%20%5C%5C%20%5C%20%2B%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%20%5Cfrac%7B9%20%2A10%5E9%20%2A%206%20%2A10%5E%7B-9%7D%20%2A%20-2%2A10%5E%7B-9%7D%20%7D%7B%285%2A10%5E%7B-2%7D%29%20%5E3%7D%20%20%2A%20%284i%20%2B%203j%20%29%20%2A10%5E%7B-2%7D)
![F_{31 +32} = 2.16 *10^{-5} (4i + 3j) - 12*10^{-5} j](https://tex.z-dn.net/?f=F_%7B31%20%2B32%7D%20%3D%202.16%20%2A10%5E%7B-5%7D%20%284i%20%2B%203j%29%20%20-%2012%2A10%5E%7B-5%7D%20j)
![F_{31 +32} = (8.64i - 5.52 j) *10^{-5}](https://tex.z-dn.net/?f=F_%7B31%20%2B32%7D%20%3D%20%20%288.64i%20-%205.52%20j%29%20%2A10%5E%7B-5%7D)
The magnitude of
is mathematically evaluated as
![|F_{31 +32}| = 10.25 *10^{-5} N](https://tex.z-dn.net/?f=%7CF_%7B31%20%2B32%7D%7C%20%3D%2010.25%20%2A10%5E%7B-5%7D%20N)
The direction is obtained as
![tan \theta = \frac{-5.52 *10^{-5}}{8.64 *10^{-5}}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7B-5.52%20%2A10%5E%7B-5%7D%7D%7B8.64%20%2A10%5E%7B-5%7D%7D)
![\theta = tan ^{-1} [-0.63889]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%20%5E%7B-1%7D%20%5B-0.63889%5D)
![\theta = - 32.57 ^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20-%2032.57%20%5Eo)
![\theta = 360 - 32.57](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20360%20-%2032.57)
![\theta =327.43 ^o](https://tex.z-dn.net/?f=%5Ctheta%20%3D327.43%20%5Eo)
Answer:
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Part 1
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Part 2
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Explanation:
Given that
Diameter,d=1 μm
Length ,l=2 μm
As we know that volume of cylinder given as
![V=\pi r^2l](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2l)
![V=\pi \times 0.5^2\times 2 \ \mu m^3](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Ctimes%200.5%5E2%5Ctimes%202%20%5C%20%5Cmu%20m%5E3)
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Surface area,A
A=π d l
![A=\pi \times 1 \times 2\ \mu m^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Ctimes%201%20%5Ctimes%202%5C%20%5Cmu%20m%5E2)
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)
Part 1
![V=1.57 \ \mu m^3](https://tex.z-dn.net/?f=V%3D1.57%20%5C%20%5Cmu%20m%5E3)
Part 2
![A=6.28\ \mu m^2](https://tex.z-dn.net/?f=A%3D6.28%5C%20%5Cmu%20m%5E2)