Where are the following awnsers?
Answer:
a)![v=13.2171\,m.s^{-1}](https://tex.z-dn.net/?f=v%3D13.2171%5C%2Cm.s%5E%7B-1%7D)
b)![H=8.9605\,m](https://tex.z-dn.net/?f=H%3D8.9605%5C%2Cm)
Explanation:
Given:
mass of bullet, ![m=4.97\times 10^{-3}\,kg](https://tex.z-dn.net/?f=m%3D4.97%5Ctimes%2010%5E%7B-3%7D%5C%2Ckg)
compression of the spring, ![\Delta x=0.0476\,m](https://tex.z-dn.net/?f=%5CDelta%20x%3D0.0476%5C%2Cm)
force required for the given compression, ![F=9.12 \,N](https://tex.z-dn.net/?f=F%3D9.12%20%5C%2CN)
(a)
We know
![F=m.a](https://tex.z-dn.net/?f=F%3Dm.a)
where:
a= acceleration
![9.12=4.97\times 10^{-3}\times a](https://tex.z-dn.net/?f=9.12%3D4.97%5Ctimes%2010%5E%7B-3%7D%5Ctimes%20a)
![a\approx 1835\,m.s^{-2}\\](https://tex.z-dn.net/?f=a%5Capprox%201835%5C%2Cm.s%5E%7B-2%7D%5C%5C)
we have:
initial velocity,![u=0\,m.s^{-1}](https://tex.z-dn.net/?f=u%3D0%5C%2Cm.s%5E%7B-1%7D)
Using the eq. of motion:
![v^2=u^2+2a.\Delta x](https://tex.z-dn.net/?f=v%5E2%3Du%5E2%2B2a.%5CDelta%20x)
where:
v= final velocity after the separation of spring with the bullet.
![v^2= 0^2+2\times 1835\times 0.0476](https://tex.z-dn.net/?f=v%5E2%3D%200%5E2%2B2%5Ctimes%201835%5Ctimes%200.0476)
![v=13.2171\,m.s^{-1}](https://tex.z-dn.net/?f=v%3D13.2171%5C%2Cm.s%5E%7B-1%7D)
(b)
Now, in vertical direction we take the above velocity as the initial velocity "u"
so,
![u=13.2171\,m.s^{-1}](https://tex.z-dn.net/?f=u%3D13.2171%5C%2Cm.s%5E%7B-1%7D)
∵At maximum height the final velocity will be zero
![v=0\,m.s^{-1}](https://tex.z-dn.net/?f=v%3D0%5C%2Cm.s%5E%7B-1%7D)
Using the equation of motion:
![v^2=u^2-2g.h](https://tex.z-dn.net/?f=v%5E2%3Du%5E2-2g.h)
where:
h= height
g= acceleration due to gravity
![0^2=13.2171^2-2\times 9.8\times h](https://tex.z-dn.net/?f=0%5E2%3D13.2171%5E2-2%5Ctimes%209.8%5Ctimes%20h)
![h=8.9129\,m](https://tex.z-dn.net/?f=h%3D8.9129%5C%2Cm)
is the height from the release position of the spring.
So, the height from the latched position be:
![H=h+\Delta x](https://tex.z-dn.net/?f=H%3Dh%2B%5CDelta%20x)
![H=8.9129+0.0476](https://tex.z-dn.net/?f=H%3D8.9129%2B0.0476)
![H=8.9605\,m](https://tex.z-dn.net/?f=H%3D8.9605%5C%2Cm)
Answer:
Black Hole
Explanation:
A black hole is a very dense and massive stellar object, which has a field of gravity so large that not even light can escape it.
Since it does not emit light, <u>we cannot see them directly</u>, hence the name of black hole.
So in this case,<u> if the object has a mass of 8 solar masses that is enough to form a black hole</u>, and <u>also cannot be seen</u>, all of this indicates that the object we are talking about is a black hole.
It should be mentioned that although these objects do not emit light, because it cannot escape due to the immense force of gravity, black holes can be detected by a type of radiation emitted on their event horizon due to quantum effects called Hawking radiation .
The Netherlands controlled Indonesia for centuries!
Let's calculate the average acceleration. It is the rate of changing speeds. Hence, we need to calculate the difference of speeds. 10-6=4 m/s. The rate is now
![\frac{4m/s}{2s} =2m/s^2](https://tex.z-dn.net/?f=%20%5Cfrac%7B4m%2Fs%7D%7B2s%7D%20%3D2m%2Fs%5E2)
.
In general, the formula for the mean acceleration between two times 1 and 2 is given by:
![\frac{u_2-u_1}{T}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bu_2-u_1%7D%7BT%7D%20)
where v1 and v2 are the speeds at the respective points and T is the time interval between them.