(-6C₆) / x⁷ newton; it is an attractive force.
<h3>Further explanation
</h3>
Given:
The potential energy of a pair of hydrogen atoms separated by a large distance x is given by , where C₆ is a positive constant.
Question:
- What is the force that one atom exerts on the other?
- Is this force attractive or repulsive?
The Process:
Let us rewrite the potential energy of the pair of the hydrogen atom:
The component of a conservative force in a particular direction, equals the negative of the derivative of the corresponding potential energy, properly concerning a displacement in that direction.
For one-dimensional motion, say along the x-axis, the relationship between force and potential energy is as follows:
Let us determine the force.
Thus, we get:
From the data problem above, we know that C₆ is a positive constant. Hence, Fₓ is positive when x is negative and vice versa. Thus Fₓ is always directed toward the origin. Besides, a negative sign means that an attractive force occurs.
In essence, the directions are toward the origin, since this is the potential energy for a restoring force.
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Notes:
We know that the difference of potential energy from point 1 to point 2 as the negative of the work done:
The work done by the given force as the particle moves from coordinate x to (x + d
x) in one dimension is
Therefore, for motion along a straight line, a conservative force is the negative derivative of its associated potential energy function, i.e.,
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Conservative force
: force that does work independent of path.
<h3>Learn more
</h3>
- The derivatives of the composite function brainly.com/question/6013189
- About vector components brainly.com/question/1600633
- What is the approximate potential energy (PE) due to the gravity of the mass with respect to the ground? brainly.com/question/39225