To solve this problem it is necessary to apply the concepts related to optical magnification (is the process of enlarging the apparent size, not physical size, of something.). Specifically the angular magnification of an optical telescope is given by
![M = -\frac{f_o}{f_e}](https://tex.z-dn.net/?f=M%20%3D%20-%5Cfrac%7Bf_o%7D%7Bf_e%7D)
Where,
Focal length of the objective lens in a refractor
Focal length of the eyepiece
Our values are given as
71cm
2.1cm
Replacing we have
![M = -\frac{f_o}{f_e}](https://tex.z-dn.net/?f=M%20%3D%20-%5Cfrac%7Bf_o%7D%7Bf_e%7D)
![M = -\frac{71}{2.1}](https://tex.z-dn.net/?f=M%20%3D%20-%5Cfrac%7B71%7D%7B2.1%7D)
![M = - 33.81](https://tex.z-dn.net/?f=M%20%3D%20-%2033.81)
Therefore the magnification of this astronomical telescope is -33.81
Galaxies are much further apart than stars. This is the reason why they are less likely to collide and the likelihood of galactic collision is much smaller than the likelihood of stellar collision. Example for galaxy collision is the collision of the Milky Way galaxy with Andromeda. It is estimated that the collision will be <span>in about 4.5 billion years. </span>
Answer:
a)
, b) From east to west.
Explanation:
Vectorially, the magnetic force can be calculed by the following formula:
![\vec F_{B} = i\cdot \vec l\, \times \, \vec B](https://tex.z-dn.net/?f=%5Cvec%20F_%7BB%7D%20%3D%20i%5Ccdot%20%5Cvec%20l%5C%2C%20%5Ctimes%20%5C%2C%20%5Cvec%20B)
The cross product is:
![\vec F_{B} = \left|\begin{array}{ccc}i&j&k\\1015000\,A\cdot m&0\,A\cdot m&0\,A\cdot m\\22.471\times 10^{-6}\,T&-61.738\times 10^{-6}\,T&0\,T\end{array}\right|](https://tex.z-dn.net/?f=%5Cvec%20F_%7BB%7D%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1015000%5C%2CA%5Ccdot%20m%260%5C%2CA%5Ccdot%20m%260%5C%2CA%5Ccdot%20m%5C%5C22.471%5Ctimes%2010%5E%7B-6%7D%5C%2CT%26-61.738%5Ctimes%2010%5E%7B-6%7D%5C%2CT%260%5C%2CT%5Cend%7Barray%7D%5Cright%7C)
![\vec F_{B} = - 62.664\,N\cdot k](https://tex.z-dn.net/?f=%5Cvec%20F_%7BB%7D%20%3D%20-%2062.664%5C%2CN%5Ccdot%20k)
a) The magnitude of the magnetic force is:
![||\vec F_{B}||=62.664\,N](https://tex.z-dn.net/?f=%7C%7C%5Cvec%20F_%7BB%7D%7C%7C%3D62.664%5C%2CN)
b) The direction of the magnetic force is:
From east to west.
By
vector addition.
In fact, velocity is a vector, with a magnitude intensity, a direction and a verse, so we can't simply do an algebraic sum of the two (or more velocities).
First we need to decompose each velocity on both x- and y-axis (if we are on a 2D-plane), then we should do the algebraic sum of all the components on the x- axis and of all the components on the y-axis, to find the resultants on x- and y-axis. And finally, the magnitude of the resultant will be given by
![R= \sqrt{(R_x)^2+(R_y)^2}](https://tex.z-dn.net/?f=R%3D%20%5Csqrt%7B%28R_x%29%5E2%2B%28R_y%29%5E2%7D%20)
where Rx and Rx are the resultants on x- and y-axis. The direction of the resultant will be given by
![\tan \alpha = \frac{R_y}{R_x}](https://tex.z-dn.net/?f=%5Ctan%20%5Calpha%20%3D%20%20%5Cfrac%7BR_y%7D%7BR_x%7D%20)
where
![\alpha](https://tex.z-dn.net/?f=%5Calpha)
is its direction with respect to the x-axis.
Answer:
The coefficient of static friction between the ground and the soles of a runner’s shoes is 0.98. What is the maximum speed in which the runner can accelerate without slipping if they have a mass of 73 kg?
Explanation: