Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:
- The limitation of the maximum number of electrons in a given energy level can be used to account for the periodic recurrence of properties as the number of electrons increases.
Explanation:
First - Scientists have not yet determined exactly why electrons do not collapse into the nucleus. FALSE: Scientists do know why electrons do not collapse. Since the beginins of quantum mechanics it's known that the energy at small scales is quantized, that means there only can be certain values meaning that the energy do not change continously. In the case of the electron, it can only have certain levels of energy, that means they do not radiate continously as the go arround the atom, instead it is only allowed to have a certain amount of energy in a given state therefore it can not lose energy continously collapsing into the nucleus.
Second - Electrons cannot be located between levels except when they are in the process of moving. FALSE: We can not say that a electron moves between energy levels, it only can exist in any of the levels, but never in between. Also, the electron in any of its possible energy lavels can not be located with complete certainty due to the uncertainty principle.
Fourth - Electrons have any random energy. FALSE: as exposed above the electrons can only have certain cuantized energy levels acordinly to the rules of quantum physics
Fifth - Electrons can be found between energy levels. FALSE: Like said before we can not say that a electron exists between energy levels, it only can exist in any of the allowed levels, but never in between.
Thirth (correct one) : - The limitation of the maximum number of electrons in a given energy level can be used to account for the periodic recurrence of properties as the number of electrons increases. TRUE: the maximum number of electrons allowed in a given energy level directly determines the tipe of bond an atom can made with another (this due to the number of electrons in the higest energy level), so for example the elements in the left of a given row of the periodic table tend to have ionic bonds, but in the other hand the elements on right side tend form more covalent bonds. And this characteristic directly correllate with diferent properties of the elements.
Answer:
Angle of reflection of light is 34 degree
Explanation:
As per law of reflection of light we know that
angle of incidence of light = angle of reflection of light
So here we know that
angle of incidence on the surface of oil is given as

so we know that

so here we can say that reflection angle of light will be same as angle of incidence

Answer:
The force required to move the quarterback with linebacker is <u>1215 N</u>
Explanation:



Using Newton's second law, it is established that F = Ma
Where F is net force acting on the system, a is the acceleration and M is mass of the two object 
Now consider both
as a system, so net force acting on the system is 
Substitute the given values in the above formula,


Force = 1215 N
<u>1215 N </u>is the force required to move the quarterback with linebacker.
Speed = distance / time.
Speed of him leaving the nest:
S = 100 / 20sec
5 m/s.
Catching the snake:
S2 = 50 / 5sec
10 m/s.
Average of 5& 10 = 7.5
7.5 m/s has to be the answer.