What Happens to the Particle on the Inclined Plane After the String Breaks?

[skipthecereal]

Homework Statement

Consider two particles connected by a massless string; 1 with mass of 2kg situated on a smooth (frictionless) inclined plane of 20 degrees, the other of mass 3kg hanging over the side of the plane over a smooth massless pulley attatched to the upermost point of the plane. The system is held at rest and when released experiences an acceleration of 5 ms-2 (sorry don't know how to superscript). After 2 seconds the string connecting the two particles breaks. After the string has snapped what motion (if any) will the particle on the inclined plane experience assuming the particle doesn't reach the pulley? Furthermore state any magnitude of acceleration experienced by the particle after detatchment from the string, if it does indeed accelerate.

Homework Equations

F=ma

The Attempt at a Solution

Im sure this is a very straightforward question, but i am entirely new to any sort of physics, my main endeavour being biology which is of a far less quantitative nature on the whole. Hopefully someone can enlighten me in a reasonably simple way. Thanks.

 

[Doc Al]

To analyze the motion of either particle you must examine the forces that act on that particle, then use the net force to figure out the acceleration (using Newton's 2nd law). It looks like they gave you the acceleration when the particles were connected--they didn't have to, since you were also given enough information to solve for the acceleration.

When the string breaks, what forces act on each mass? What is their resulting accelerations?

 

[skipthecereal]

Thanks. This is exactly what I considered. And on that basis i thought that the particle on the plane would move down the plane, as it no longer experiences a 'pull' by the tension of the string, and only experiences a gravitational pull. Therefore i can use F=ma , with F being the component of the gravitational force perp. to the plane. The anwser given says that the particle continues to move up the plane. Is this correct or an error on the books side?

 

[Doc Al]

And on that basis i thought that the particle on the plane would move down the plane, as it no longer experiences a 'pull' by the tension of the string, and only experiences a gravitational pull. Therefore i can use F=ma , with F being the component of the gravitational force perp. to the plane.

I assume you mean the component of gravity parallel to the plane.

In any case, once the string is cut you correctly deduce that the particle's acceleration is down the incline. But that's not all you need to consider to describe its velocity at any given moment.

The anwser given says that the particle continues to move up the plane. Is this correct or an error on the books side?

The book is correct. At the moment the string breaks, the particle is moving up the plane. Once the string breaks, its acceleration is down the plane so it continues moving up as it slows down. It will slow down, stop, and then slide down the plane.

Make sense?

Compare this to tossing a ball straight up in the air. The only force acting is gravity (ignore air resistance), so the acceleration is always down even when you toss the ball up. Acceleration tells you how the velocity changes, so you know that as time goes on, the change in velocity is always down. Thus the ball first slows down (which can be viewed as a negative or downward change in velocity) then starts going back down, picking up speed as it falls.

 

[skipthecereal]

Thank you! That makes perfect sense; and now it seems so obvious... Thanks again.