SAT Physics and A-Level Physics

[monoceros]

Hi, I am currently studying the Cambridge A-Level and I will also be taking the SAT Physics sometime end of this year. I am not too sure which category these belong to, so hopefully they fit in the K-12 level alright. I currently have two questions which have been bothering me past two days, and I stumbled across this community so I thought I'd try asking for help.

I'll start with the "easy" one, a SAT question which I don't quite get:

Two objects move toward each other, collide, and separate. If there was no net external force acting on the objects, but some kinetic energy was lost, then
(A) the collision was elastic and total linear momentum was conserved.
(B) the collision was elastic and total linear momentum was not conserved.
(C) the collision was not elastic and total linear momentum was conserved.
(D) the collision was not elastic and total linear momentum was not conserved.
(E) None of the above.

The given answer to this question is (C). As I understand, in a collision where two objects separate, is an elastic collision rather than an inelastic one? Anyone care to explain why is this so?

As for the next question, a written A-Level Physics one:

A stone of mass m is attached to a string of length r, which will break if the tension in it exceeds Tmax. The stone is whirled in a vertical circle.

(a) draw diagrams showing the forces acting on the stoe when it is (i) at the top, (ii) at the bottom, of the circle.

The angular speed is increased very slowly.

(b) For what position of the stone, relative to the axis of the rotation, is the string most likely to break?

(c) What will be the angular speed when this occurs?

Okay, I have no problems drawing the diagrams for (a), where I have T (tension of the string), W (weight of the stone), N (normal force), and Fc (centripetal force) labeled correctly, I hope.

The problem comes to part (b). I can't actually see where do I start. Here's what I tried figuring out from: that in order for the string to break, the net force must be greater than the tension of the string? Where do I go from here?

As for (c), I think I'd know how to solve this one as I get part (b).

Any help would be appreciated. Thanks in advance.

 

[Päällikkö]

The given answer to this question is (C). As I understand, in a collision where two objects separate, is an elastic collision rather than an inelastic one? Anyone care to explain why is this so?

If I'm not totally wrong on this, it's not elastic as kinetic energy is not conserved.
I hate terminology, especially in a foreign language :).

As for the next question, a written A-Level Physics one:

A stone of mass m is attached to a string of length r, which will break if the tension in it exceeds Tmax. The stone is whirled in a vertical circle.

(a) draw diagrams showing the forces acting on the stoe when it is (i) at the top, (ii) at the bottom, of the circle.

The angular speed is increased very slowly.

(b) For what position of the stone, relative to the axis of the rotation, is the string most likely to break?

The problem comes to part (b). I can't actually see where do I start. Here's what I tried figuring out from: that in order for the string to break, the net force must be greater than the tension of the string? Where do I go from here?

As for (c), I think I'd know how to solve this one as I get part (b).

You drew the diagrams. Which of these situations exert the greater force on the string? Which situation calls for higher string tension?


I hope I was of any help :).

 

[Knavish]

The first one explicitly states that KE was lost--this automatically means the collision was inelastic. Just because the two objects separate doesn't mean the collision was elastic; this can also happen in inelastic collisions (but of course with KE being lost, and in the extreme situation the objects being stuck together). Linear momentum is always conserved

 

[OlderDan]

Two objects move toward each other, collide, and separate. If there was no net external force acting on the objects, but some kinetic energy was lost.

As I understand, in a collision where two objects separate, is an elastic collision rather than an inelastic one? Anyone care to explain why is this so?

"Elastic" and "inelastic" are terms that are usually used to represent the ends of the spectrum of possibilities. If the problem makes no qualifying statement you should interpret ineleastic to mean that the objects stick together after the collision, and elastic to mean there is NO loss of energy. In most cases, some mechanical energy is converted into other forms, primarily heat, during a collision. If the energy lost is less than the maximum (sticking together) the objects will separate.

A ball bouncing on the floor is an example of a partial loss of energy. On each bounce the ball bounces to a lower height because some energy is lost in every collision. The ratio of the relative velocities after and before a collision is called the "coefficient of restitution." When no energy is lost, the coefficient is 1.