An atom is chemically stable when it’s outer_____ is completely filled with _____.
1 answer:
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1) 12 cm
2) 3 N
Explanation:
1)
The relationship between force and elongation in a spring is given by Hooke's law:
where
F is the force applied
k is the spring constant
x is the elongation
For the spring in this problem, at the beginning we have:
So the spring constant is
Later, the force is tripled, so the new force is
Therefore, the new elongation is
2)
In this second problem, we know that the elongation of the spring now is
From part a), we know that the spring constant is
Therefore, we can use the following equation to find the force:
And substituting k and x, we find:
So, the force to produce an elongation of 6 cm must be 3 N.
a. 4.52 m/s south
Velocity is a vector, whose magnitude is defined as the ratio between the displacement of the object and the time taken for the displacement to occur:
where
d is the displacement
t is the time
Velocity is a vector, so it also has a direction, which corresponds to that of the displacement.
For the ball in this problem,
d = 9.5 m south
t = 2.1 s
Substituting, we find:
and the directiion is the same as the displacement (south).
b. 4.52 m/s north
For this part, we must keep in mind that the speed is the magnitude of the velocity; however, speed is a scalar, so it does not have a direction.
Here we are told that the tennis ball travels at constant speed, so on its way back from Liam to Katie the ball's velocity is still the same as before, therefore
However, this time the direction is opposite to before, since the ball is travelling in the opposite direction.
Therefore, the ball's velocity when Liam returns Katie's service is
4.52 m/s north
To minimize the material usage we have to have the volume requested with the minimum surface area.
The volume is:
And the surface is:
From the first equation we get:
I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:
To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.
Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).
Now we plug in the first equation into the other and we get:
Now we can calculate y:
And finaly we calculate z:
And finaly let's check our result:
The volume is:
And the surface is:
From the first equation we get:
I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:
To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.
Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).
Now we plug in the first equation into the other and we get:
Now we can calculate y:
And finaly we calculate z:
And finaly let's check our result: