Five groups of four vectors are shown below. All magnitudes of individual vectors are equal. Please rank the groups based on the
magnitude of the resultant vectors if the four vectors in each group were added together. Rank the groups of vectors from the greatest resultant magnitude to the smallest resultant magnitude.
Rank the groups of vectors from the greatest resultant magnitude to the smallest resultant magnitude.
Rank the groups of vectors from the greatest resultant magnitude to the smallest resultant magnitude.
1 answer:
With the addition of vectors we can find that the correct answer is:
C) Q> P > R = S > T
The addition of vectors must be done taking into account that they have modulus and direction. The analytical method is one of the easiest methods, the method to do it is:
- Set a Cartesian coordinate system
- Decompose vectors into their components in a Cartesian system
- Perform the algebraic sums on each axis
- Find the resultant vector using the Pythagoras' Theorem to find the modulus and trigonometry to find the direction.
In this exercise indicate that the modulus of all vectors is the same, suppose that the value of the modulus is A.
We fix a Cartesian coordinate system with the horizontal x axis and the vertical y axis, we can see that we do not need to perform any decomposition, so we perform the algebraic sums
Diagram P
x-axis
x = 2A
y-axis
y = 2A
The modulus of the resulting vector can be found with the Pythagorean Theorem
P =
P =
P = 2 √2 A
Diagram Q
x-axis
x = 3A
y-axis
y = A
Resulting
Q =
Q =
Q =
Diagram R
x- axis
x = 0
y-axis
y = 2 A
Resulting
R =
R =
Diagram S
x-axis
x = 2 A
y-axis
y = 0
Resulting
S = 2A
Diagram T
x- axis
x = 0
y-axis
y = 0
Resultant T = 0
We order the diagram from highest to lowest
Q> P> R = S> T
When reviewing the different answers, the correct one is:
C. Q> P> R = S> T
Learn more about adding vectors here:
You might be interested in
1) In the first case, the correct answer is
<span>A.Wavelengths measured would match the actual wavelengths emitted.
In fact, the stars are not moving relative to Earth, so there is no shift in the measured wavelength.
2) In this second case, the correct answer is
</span><span>A.Wavelengths measured would be shorter than the actual wavelengths emitted.
</span>in fact, since the stars in this case are moving towards the Earth, then apparent frequency of their emitted light will be larger than the actual frequency, because of the Doppler effect, according to the formula:
where f0 is the actual frequency, f' the apparent frequency, c the speed of light and vs the velocity of the source (the stars) relative to the obsever (Earth). Vs is negative when the source is moving towards the observer, so the apparent frequency f' is larger than the actual frequency f0. But the wavelength is inversely proportional to the frequency, so the apparent wavelength will be shorter than the actual wavelength.
<span>A.Wavelengths measured would match the actual wavelengths emitted.
In fact, the stars are not moving relative to Earth, so there is no shift in the measured wavelength.
2) In this second case, the correct answer is
</span><span>A.Wavelengths measured would be shorter than the actual wavelengths emitted.
</span>in fact, since the stars in this case are moving towards the Earth, then apparent frequency of their emitted light will be larger than the actual frequency, because of the Doppler effect, according to the formula:
where f0 is the actual frequency, f' the apparent frequency, c the speed of light and vs the velocity of the source (the stars) relative to the obsever (Earth). Vs is negative when the source is moving towards the observer, so the apparent frequency f' is larger than the actual frequency f0. But the wavelength is inversely proportional to the frequency, so the apparent wavelength will be shorter than the actual wavelength.
Answer:
Q = +1.4 pC
Explanation:
- The capacitance of any capacitor, by definition, is as follows:
-
- Applying Gauss'Law and the definition of electric potential, it can be showed that the capacitance of a parallel-plate capacitor can be expressed as follows:
-
- Where εr is the dielectric constant of the material that fills the space between the plates, A is the area of one of the plates, and d, is the separation between them.
- Replacing by the givens in (2) we can find the value of the capacitance C, as follows:
- Replacing the values of C and V in (1), we can solve for Q, as follows:
- As the outer surface is at a higher potential that the inside surface, the charge on it must be positive, and is equal to +1.4 pC.