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Old Jan 6th 2012, 10:24 PM   #1
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What is the trajectory of a moving object with a force applied to it?

What is the trajectory of an object moving at constant velocity with a constant force applied to it?

I can think of two scenarios which determine the trajectory:
1) The direction of the applied constant force is in the direction of the object's velocity. The trajectory is linear and the object is accelerating in that direction. (Decelerating if the force is applied in the direction opposite of the direction of the object's velocity.)
2) The direction of the applied constant force is in any arbitrary direction except the direction of the velocity and the direction opposite of the direction of velocity. For any direction, the trajectory is circular. If the force is perpendicular to the velocity, the object will undergo uniform circular motion. If the force is not perpendicular, the object will undergo non-uniform circular motion (the object will accelerate on its circular path).

Is this right?


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I was told that the hypothetical situation I described in 2) describes curvilinear motion.

I know that for an object undergoing non-uniform circular motion, there are two components of acceleration: one component that keeps the object in a circular motion and one component that causes the object to accelerate on its circular trajectory. The two acceleration component comprise an acceleration vector that is not perpendicular to the velocity of the object and not in the direction of the velocity or opposite that direction.

Curvilinear motion describes the non-uniform circular motion (defined above) doesn't it? Any arbitrary constant-value acceleration vector can be resolved into two components, one of which will always be perpendicular to the direction of velocity which is responsible for an object following a circular trajectory. Therefore, shouldn't all curvilinear motion have a circular trajectory?

Last edited by elusive1324; Jan 6th 2012 at 10:43 PM.
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Old Jan 9th 2012, 04:53 AM   #2
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I'm not sure what you meant by the first few lines, because if I understood well, the object will no more be moving at constant speed...

But whatever, I'm short on time and I will tell you that no, it won't be circular motion, but a 'spiral' motion.
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