Year 12s: what will be the first way you research your future options? >>

Particles moving in a plane - defining whether acceleration is contant or variable

Hello all,

Just a mechanics question (I guess at Sixth Form level). As part of my revision, I am classifying what techniques are used for motion of particle(s), where individual motions for the system are not all in the same straight line, for example when two snooker balls are moving (either oblique or perpendicualr) and determining when/if they collide.

Now the particles can be moving in straight or curved paths.

Here is my question: by definition a particle moving in a plane is acted only by forces in line with the plane. So by some physics proof (which I am sturggling with hence asking!), if particles in a plane follow a curved path can the particle's acceleration (as a vector) be variable OR constant?

In parabolic motion of projectile, acceleration due to gravity is contant, and obviously a curved path is followed then. In an example in my text book, acceleration (vector) = function of time, ie variable. They then plot a displacment graph of the particle, and it has a curved path.

So I would be grateful if somone is able to clarify this for me.
:confused:

Thank you!

Reply 1

ghostwalker

Original post by Choochoo_baloo

...

If the path of the particle is curved, then the acceleration could be constant or variable; you can't tell from that information alone.

Reply 2

atsruser

Original post by Choochoo_baloo

. So by some physics proof (which I am sturggling with hence asking!), if particles in a plane follow a curved path can the particle's acceleration (as a vector) be variable OR constant?

1. Consider a planet orbiting a star, moving in a circular orbit. Then its path is curved, and its acceleration is constant, directed towards the star.

2. Consider a firework tied via a rope to circular post. The rope rotates freely about the post so the firework moves in a (horizontal) circle. When the firework is lit, then it has a tangential acceleration which increases as its mass decreases. It moves in a curved path, however, just as in the case of the planet.

[edit: I've just noticed that you stressed "as a vector", in which case these examples may not satisfy you, as neither vector is constant; I've described varying magnitudes]

(edited 10 years ago)

Reply 3

atsruser

[QUOTE=Choochoo_baloo;43460754
Here is my question: by definition a particle moving in a plane is acted only by forces in line with the plane. So by some physics proof (which I am sturggling with hence asking!), if particles in a plane follow a curved path can the particle's acceleration (as a vector) be variable OR constant?

In parabolic motion of projectile, acceleration due to gravity is contant, and obviously a curved path is followed then. In an example in my text book, acceleration (vector) = function of time, ie variable. They then plot a displacment graph of the particle, and it has a curved path.

In the example of projectile motion, the acceleration vector is truly constant, in both magnitude and direction, with

a=g

, the accln due to gravity. Why do you think that the acceleration is variable?

Reply 4

Choochoo_baloo

Original post by atsruser

In the example of projectile motion, the acceleration vector is truly constant, in both magnitude and direction, with

a=g

, the accln due to gravity. Why do you think that the acceleration is variable?

No I do not think that acceleration in case of projectile motion is variable (as a vector). It is constant as you say.

Having re-read my post i realised that I wasn't very clear in the next sentence. The next sentence about acceleration as a function of time was of a completely different situation - a question involving i and j vectors. Nothing to do with projectile motion!!