In a closed system, _____ energy is equal to potential energy plus kinetic energy.

A charge q1 = +5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -2.00 nC is placed on the positive

Ivahew [28]

Answer:

a

The x- and y-components of the total force exerted is

$F_{31 +32} = (8.64i - 5.52 j) *10^{-5}$

b

The magnitude of the force is

$|F_{31 +32}| = 10.25 *10^{-5} N$

The direction of the force is

$\theta =327.43 ^o$ Clockwise from x-axis

Explanation:

From the question we are told that

The magnitude of the first charge is $q_1 = +5.00nC = 5.00*10^{-9}C$

The magnitude of the second charge is $q_2 = -2.00nC = -2.00*10^{-9}C$

The position of the second charge from the first one is $d_{12} = 4.00i \ cm = \frac{4.00i}{100} = 4.00i *10^{-2} m$

The magnitude of the third charge is $q_3 = +6.00nC = 6.00*10^{-9}C$

The position of the third charge from the first one is $\= d_{31} = (4i + 3j) cm = \frac{ (4i + 3j)}{100} = (4i + 3j) *10^{-2}m$

$|d_{31}| =(\sqrt{4 ^2 + 3^2}) *10^{-2} m$

$|d_{31}| =5 *10^{-2} m$

The position of the third charge from the second one is

$\= d_{32} = 3j cm = 3j *10^{-2}m$

$|d_{32}| =(\sqrt{ 3^2}) *10^{-2} m$

$|d_{32}| =3 *10^{-2} m$

The force acting on the third charge due to the first and second charge is mathematically represented as

$F_{31 +32} = \frac{kq_3 q_1}{|d_{31}| ^3} *\= d_{31} + \frac{kq_3 q_2}{|d_{32}| ^3} *\= d_{32}$

Substituting values

$F_{31 +32} = \frac{9 *10^9 * 6 *10^{-9} * 5*10^{-9} }{(5*10^{-2}) ^3} * (4i + 3j ) *10^{-2} \\ \ + \ \ \ \ \ \ \ \ \ \frac{9 *10^9 * 6 *10^{-9} * -2*10^{-9} }{(5*10^{-2}) ^3} * (4i + 3j ) *10^{-2}$

$F_{31 +32} = 2.16 *10^{-5} (4i + 3j) - 12*10^{-5} j$

$F_{31 +32} = (8.64i - 5.52 j) *10^{-5}$

The magnitude of $F_{31 +32}$ is mathematically evaluated as

$|F_{31 +32}| = \sqrt{(8.64^2 + 5.52 ^2) } *10^{-5}$

$|F_{31 +32}| = 10.25 *10^{-5} N$

The direction is obtained as

$tan \theta = \frac{-5.52 *10^{-5}}{8.64 *10^{-5}}$

$\theta = tan ^{-1} [-0.63889]$

$\theta = - 32.57 ^o$

$\theta = 360 - 32.57$

$\theta =327.43 ^o$

5 0

3 years ago

You attach a 2.90 kg mass to a horizontal spring that is fixed at one end. You pull the mass until the spring is stretched by 0.

Murljashka [212]

Answer:

Explanation:

The spring is stretched by .5 m and then released that means its amplitude of oscillation A is 0.5 m .

A = 0.5 m

After the release at one extreme point , the mass comes to rest again at another extreme point after half the time period ie

T / 2 = .3 s

T = 0.6 s

Angular velocity

ω = $\frac{2\times \pi}{T}$

ω = $\frac{2\times \pi}{0.6}$

ω = 10.45

Maximum velocity = ω A

ω and A are angular velocity and amplitude of oscillation.

Maximum velocity = 10.45 x .5

= 5.23 m /s

7 0

3 years ago

Why must we be careful when measuring current with a DMM?

Lemur [1.5K]

Answer:

DMM should be placed in the series combination with the circuit.

Explanation:

DMM is the digital multi meter. It can measure the voltage, current and resistance at a time.

While measuring the current with the DMM you must be ensure that the DMM should be connected with the circuit in series combination. So that it will give the resultant current accurately.

While measuring the voltage the observer should check the open probes.

4 0

3 years ago

In which situation can you be at rest and moving at then same time

anyanavicka [17]

If you are stationary, but in/on a moving vehicle/object you can be at rest and moving at then same time.

<u>Explanation</u>:

A particle, when viewed from a given frame of reference, cannot be both at rest and in motion. However, in one frame of reference, a particle can be in motion whereas in another frame of reference the particle is in motion.

For example, if you are seated in a plane, the plane is stationary in that reference frame and the Earth moves under it, but in the reference frame of the Earth, the plane is moving concerning the Earth. When you are standing still on Earth, in your frame of reference, the Earth is stationary, and the Sun and stars move around the Earth.

However, in the frame of reference of the center of our solar system, the Earth orbits the Sun and the Sun are perturb slightly by the rest of the planets, but the rest of the galaxy orbits our solar system. Of course, in rest from our Galaxy, our solar system orbits a giant black hole at its center.

4 0

3 years ago

Determine which the following are defined Whenever they occur denctes multivariable function and denotes vector field both of wh

tresset_1 [31]

Yes, all of the above are defined whenever they occur and denote multivariable functions and vector fields which are twice continuously differentiable on a common domain.

What is vector field?
A vector field is the assignment of the a vector to each point inside a subset of space in the fields of vector calculus and physics. For example, a vector field inside the plane could be visualised as a group of arrows, each attached to the a point in the plane and each with a specific magnitude and direction. Vector fields are frequently used to simulate various physical phenomena, such as the strength and motion of a force as it shifts through one point to the next or the speed and trajectory of a fluid moving through space.

The first expression, V . (F . Vf), denotes a multivariable function which is the dot product of a vector V and the composition of a function F with a vector field Vf.

The second expression, V . (V x Vf), denotes a multivariable function which is the dot product of a vector V and the cross product of a vector V and a vector field Vf.

The third expression, V x (V . F), denotes a vector field which is the cross product of a vector V and the dot product of a vector V and a function F.

The fourth expression, V x (V x f), denotes a vector field which is the cross product of a vector V and the cross product of a vector V and a function f.

The fifth expression, V x (V x F), denotes a vector field which is the cross product of a vector V and the cross product of a vector V and a function F.

The sixth expression, V . (V x F), denotes a multivariable function which is the dot product of a vector V and the cross product of a vector V and a function F.

To learn more about vector field
brainly.com/question/24332269
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6 0

1 year ago