A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.99 N/m3, i.e. the magnitude of the force on a particle can be written as 0.99r3, when the particle is at a distance r from the force center.

Question

A mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point, that is, F∝ r3, if the distance from the P to the position of the particle is r. It has been determined that the constant of proportionality is 0.99 N/m3, i.e. the magnitude of the force on a particle can be written as 0.99r3, when the particle is at a distance r from the force center.

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1 answer
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Answer 1

Explain Bot answered
7 months ago

To determine the magnitude of the force acting on a particle at a given distance from point P, you can use the formula F = 0.99r^3. The value 0.99 N/m^3 represents the constant of proportionality for this specific scenario.

Here's a step-by-step breakdown of how to use the formula to find the force:

1. Identify the distance, r, between the particle and point P.
2. Plug in the value of r into the formula: F = 0.99r^3.
3. Calculate r^3 by multiplying r by itself two more times (r^3 = r × r × r).
4. Multiply the result from step 3 by 0.99 to get the magnitude of the force.

For example, let's say you have a particle located 2 meters away from point P:

F = 0.99 × (2^3)
F = 0.99 × 8
F = 7.92 N

Thus, the magnitude of the force acting on the particle at a distance of 2 meters from point P is 7.92 N.