Answer:
11.625 Ohm
Explanation:
Let V be the Voltage charge of the loop, as this is constant we know that before the resistor addition the current I is:
V/R1 = 1.9 or V = 1.9R1
After the resistor addition to series R = R1 + 3.1
I = V/R = V/(R1 + 3.1) = 1.5
We can substitute V = 1.9R1
1.9R1 = 1.5R1 + 1.5*3.1
0.4R1 = 4.65
R1 = 4.65/0.4 = 11.625 Ohm
Answer:
The velocity of the man is 0.144 m/s
Explanation:
This is a case of conservation of momentum.
The momentum of the moving ball before it was caught must equal the momentum of the man and the ball after he catches the ball.
Mass of ball = 0.65 kg
Mass of the man = 54 kg
Velocity of the ball = 12.1 m/s
Before collision, momentum of the ball = mass x velocity
= 0.65 x 12.1 = 7.865 kg-m/s
After collision the momentum of the man and ball system is
(0.65 + 54)Vf = 54.65Vf
Where Vf is their final common velocity.
Equating the initial and final momentum,
7.865 = 54.65Vf
Vf = 7.865/54.65 = 0.144 m/s
To find the change in centripetal acceleration, you should first look for the centripetal acceleration at the top of the hill and at the bottom of the hill.
The formula for centripetal acceleration is:
Centripetal Acceleration = v squared divided by r
where:
v = velocity, m/s
r= radium, m
assuming the velocity does not change:
at the top of the hill:
centripetal acceleration = (4.5 m/s^2) divided by 0.25 m
= 81 m/s^2
at the bottom of the hill:
centripetal acceleration = (4.5 m/s^2) divided by 1.25 m
= 16.2 m/s^2
to find the change in centripetal acceleration, take the difference of the two.
change in centripetal acceleration = centripetal acceleration at the top of the hill - centripetal acceleration at the bottom of the hill
= 81 m/s^2 - 16.2 m/s^2
= 64.8 m/s^2 or 65 m/s^2
The magnitude of <em>electrical</em> force on charge
due to the others is 0.102 newtons.
<h3>
How to calculate the electrical force experimented on a particle</h3>
The vector <em>position</em> of each particle respect to origin are described below:
![\vec r_{1} = (-0.500, 0)\,[m]](https://tex.z-dn.net/?f=%5Cvec%20r_%7B1%7D%20%3D%20%28-0.500%2C%200%29%5C%2C%5Bm%5D)
Then, distances of the former two particles particles respect to the latter one are found now:
![\vec r_{13} = (+0.500, +0.500)\,[m]](https://tex.z-dn.net/?f=%5Cvec%20r_%7B13%7D%20%3D%20%28%2B0.500%2C%20%2B0.500%29%5C%2C%5Bm%5D)


![\vec r_{23} = (-0.500, +0.500)\,[m]](https://tex.z-dn.net/?f=%5Cvec%20r_%7B23%7D%20%3D%20%28-0.500%2C%20%2B0.500%29%5C%2C%5Bm%5D)


The resultant force is found by Coulomb's law and principle of superposition:
(1)
Please notice that particles with charges of <em>same</em> sign attract each other and particles with charges of <em>opposite</em> sign repeal each other.
(2)
Where:
- Electrostatic constant, in newton-square meters per square Coulomb.
,
,
- Electric charges, in Coulombs.
,
- Distances between particles, in meters.
,
- Unit vectors, no unit.
If we know that
,
,
,
,
,
,
and
, then the vector force on charge
is:

![\vec R = 0.072\cdot \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right) + 0.072\cdot \left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right)\,[N]](https://tex.z-dn.net/?f=%5Cvec%20R%20%3D%200.072%5Ccdot%20%5Cleft%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%20-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%20%5Cright%29%20%2B%200.072%5Ccdot%20%5Cleft%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%20-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%20%5Cright%29%5C%2C%5BN%5D)
![\vec R = 0.072\cdot \left(0, -\sqrt{2}\right)\,[N]](https://tex.z-dn.net/?f=%5Cvec%20R%20%3D%200.072%5Ccdot%20%5Cleft%280%2C%20-%5Csqrt%7B2%7D%5Cright%29%5C%2C%5BN%5D)
And the magnitude of the <em>electrical</em> force on charge
(
), in newtons, due to the others is found by Pythagorean theorem:

The magnitude of <em>electrical</em> force on charge
due to the others is 0.102 newtons. 
To learn more on Coulomb's law, we kindly invite to check this verified question: brainly.com/question/506926
Answer:
μ = 0.6
Explanation:
F = μN
N = mg
F = μmg
3 N = μ*0.5 kg * 9.8 m/s²
μ = 3/(0.5*9.8) = 0.6