Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
As Rene Descartes - french mathematician of Cartesian graphs - said "Cogito ergo sum". I think, therefore I am.
This can be adapted to I think therefore I am, I think ... as a "geeky joke".
Answer:
Explanation:
This problem is approached using Coulomb's law of electrostatic attraction which states that the force F of attraction or repulsion between two point charges, 
and 
is directly proportional to the product of the charges and inversely proportional to the square of their distance of separation R.
where k is the electrostatic constant.
We can make k the subject of formula as follows;
Since k is a constant, equation (2) implies that the ratio of the product of the of the force and the distance between two charges to the product of charges is a constant. Hence if we alter the charges or their distance of separation and take the same ratio as stated in equation(2) we will get the same result, which is k.
According to the problem, one of the two identical charges was altered from 
to 
and their distance of separation from 
to 
, this also made the force between them to change from 
to 
. Therefore as stated by equation (2), we can write the following;
Therefore;
From equation (4) we now make the new force the subject of formula as follows;
then cancels out from both side of the equation, hence we obtain the following;
From equation (4) we can now write the following;
This could also be expressed as follows;
1. Changing from solid to a liquid is called melting / fusion and happen
at the melting/ fusion point.
Reason: melting point is a temperature at which a solid melt and converts into liquid by providing heat.
2. Changing from liquid to gas is called evaporation/boiling and happens at the evaporation/boiling point.
Reason. Evaporation is a process in which molecules from surface of liquid convert into gas.
3. Changing from a gas to a liquid is called condensation and happens at the condensation point.
Reason : In condensation process gas particles converts into liquid droplets.
4. Changing from liquid to a solid is called freezing and happens at the freezing point.
Reason : Freezing is a process that convert liquid into soilid state by decreasing temperature of that specific liquid,
Sand. You can identify tiny sugar crystals.
