Why might a major volcanic eruption lead to cooler global temperatures? Explain your answer.
1 answer:
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Answer:
The magnitude of the resultant decreases from A+B to A-B
Explanation:
The magnitude of the resultant of two vectors is given by
where
A is the magnitude of the first vector
B is the magnitude of the second vector
is the angle between the directions of the two vectors
In the formula, A and B are constant, so the behaviour depends only on the function . The value of
are:
- 1 (maximum) when the angle is 0, so the magnitude of the resultant in this case is
- then it decreases, until it becomes 0 when the angle is 90 degrees, where the magnitude of the resultant is
- then it becomes negative, and continues to decrease, until it reaches a value of -1 when the angle is 180 degrees, and the magnitude of the resultant is
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
. So we can write
that we can solve to find an expression for v:
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
And the total energy of the system is
Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
while the mass is moving at speed v, and therefore the kinetic energy is
And the total energy is
For the law of conservation of energy, the total energy must be conserved, therefore
that we can solve to find an expression for v: