Physics question

[WULRICH]

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I came across this question in one my Physics books.
1) when a stone is swinging on the thread and the string suddenly breaks
Momentum and Energy conserved
Energy only conserved
momentum only
Neither both conserved

Other random facts that i am a bit confused

2)As the surface of the contact area increases what happens to force of friction

3) Is acceleration of the pendulum, the same direction as velocity?

 

[amikhchi]

I don't claim to be a physics expert, so maybe someone else can correct me if I'm wrong:

assuming that either the string is massless or when it breaks it somehow detaches from the stone, I would suspect that since the mass doesn't change and the velocity is constant (rather the magnitude of it) then, 1/2 mv^2, along with mv should also remain constant so both momentum and kinetic energy should be conserved

Force of friction is proportional to the coefficient of static friction, and the normal force, not the contact area. If you compare 2 objects of equal density and equal volume, just different *shape* giving one more contact area than the other, the normal force will still be MG (assuming it's on a flat table)

3. This one seems a bit tricky, the only acceleration acting on the pendulum is gravity, which is pointed down, but in any case the *restoring* component of the gravitational force will be pointing inwards towards equilibrium (mg * sin theta). However if you are moving away from equilibrium (i.e. swinging to the right after passing mid-point), your V and A are opposite, if you are moving toward equilibrium (i.e. after reaching the right and stopping to come back towards the mid-point) they are going in the same direction.

 

[WULRICH]

I don't claim to be a physics expert, so maybe someone else can correct me if I'm wrong:

assuming that either the string is massless or when it breaks it somehow detaches from the stone, I would suspect that since the mass doesn't change and the velocity is constant (rather the magnitude of it) then, 1/2 mv^2, along with mv should also remain constant so both momentum and kinetic energy should be conserved

Force of friction is proportional to the coefficient of static friction, and the normal force, not the contact area. If you compare 2 objects of equal density and equal volume, just different *shape* giving one more contact area than the other, the normal force will still be MG (assuming it's on a flat table)

3. This one seems a bit tricky, the only acceleration acting on the pendulum is gravity, which is pointed down, but in any case the *restoring* component of the gravitational force will be pointing inwards towards equilibrium (mg * sin theta). However if you are moving away from equilibrium (i.e. swinging to the right after passing mid-point), your V and A are opposite, if you are moving toward equilibrium (i.e. after reaching the right and stopping to come back towards the mid-point) they are going in the same direction.

Thanks a lot, can someone else also clarify these answers please

 

[amikhchi]

As for #2, i should say force of friction is proportional to the coefficient of friction (not specifically static) and the normal force, becuase it could be static or kinetic friction. In any case I think learning what the coefficient of friction is dependent upon is outside of the scope of the MCAT, but i believe it has to do with the interaction between the molecules fo the surfaces, not their actual contact area though, again i'm not sure of that and I think it's OOS of the MCAT

 

[zayka]

Just to clarify, I haven't started studying yet but regarding your #2, kinda confused what you're saying, but friction is related to the coeficient of friction and the normal force. As you may or may not remember from the Magic School Bus, coefficient of friction, conceptually at least, has to do with how the two surfaces like to stay together, if they attract each otehr

For the pendulum, draw a vector diagram - the acceleration always changes: you have the force of gravity and the tension of string and maybe air resistance.

 

[rocketbooster]

I came across this question in one my Physics books.
1) when a stone is swinging on the thread and the string suddenly breaks
Momentum and Energy conserved
Energy only conserved
momentum only
Neither both conserved

Other random facts that i am a bit confused

2)As the surface of the contact area increases what happens to force of friction

3) Is acceleration of the pendulum, the same direction as velocity?

1) i'm pretty sure both are conserved. momentum is, and it doesn't mention the stone is inelasticly deforming into anything after it's released, so kinetic energy should be conserved.

2) I think contact area does affect force of friction. while it is not in the friction equation, normal force is. what's the normal force? force=pressure*area. if you increase contact area, you increase the force. normal force increases, which increases frictional force.

3) yep, same direction, and there is definitely changing acceleration in a pendulum. why? because the pendulum is not only accelerating based on MG. it's accelerating based on MG and M(v^2)/r. don't forget the pendulum has rotational motion. you have to factor in the centripetal force. if the velocity is increasing, the centripetal acceleration is increasing.

 

[oldenough2know]

nevermind, i was wrong

 

[yessira]

1. Yes, both momentum and energy are conserved because nothing is happening such that either one of them are affected. (This will change once the stone hits the ground, however.)

2. Frictional force is equal to the friction coefficient (a constant) times the normal force. Normal force is given as mg. Because neither the mass nor the force of gravity is changing, the frictional force does not change either. As for what rocketbooster said, force is pressure/unit area, not pressure*area.

3. If acceleration was in the same direction as velocity, the pendulum bob would constantly be accelerating in one direction. This does not happen in a pendulum, therefore they are not in the same direction. Also worth mentioning is that when acceleration is opposite velocity, the object slows down. In this case, they are perpendicular to each other (centripetal acceleration and tangental velocity).

 

[Fort]

2. Frictional force is equal to the friction coefficient (a constant) times the normal force. Normal force is given as mg. Because neither the mass nor the force of gravity is changing, the frictional force does not change either. As for what rocketbooster said, force is pressure/unit area, not pressure*area.

Other way around. Pressure is force per unit area; force is pressure multiplied by the area.

 

[KiwiBruin]

I came across this question in one my Physics books.
1) when a stone is swinging on the thread and the string suddenly breaks
Momentum and Energy conserved (reasons like others stated)
Energy only conserved
momentum only
Neither both conserved

Other random facts that i am a bit confused

2)As the surface of the contact area increases what happens to force of friction
I think the force of friction stays the same as long as the mass isn't changing. (just like other people said above).

3) Is acceleration of the pendulum, the same direction as velocity?
Think of this problem this way. Acceleration is 0 at the bottom of the path(goes from speeding up while going to the bottom and then speeds down once you pass the bottom) while greatest at the ends (think of this in terms of velocity, goes in one direction getting to the end then goes in the other direction after it gets to the end which causes the greatest instantaneous acceleration change) while we can easily picture that velocity is greatest at the bottom and 0 at ends.
I think if you can relate springs and pendulums together that would help. They both work in the same ways in terms of velocity and acceleration

Hopefully I haven't said anything wrong...

 

[amikhchi]

As for the friction debate... if you took a 10kg mass that had a surface area of 10m^2, and a coefficient of friction was .5, then frictional force would be 50N

if you took a 10kg mass that had a surface area of 1m^2 (much more dense), the frictional force would still be 50N, it is independent of area

 

[MD2BEEE]

I'm going to have to go with Walker and "Physics Volume I, 3rd ed." Both kinetic and static friction are "independent of the area of contact between the surfaces."

Good example from the book:

Take a brick and lay it on its side, then pull on it. Now, take the same brick and stand it on its end so that it has a smaller area in contact with the table and pull on it. Force remains the same regardless of the area of contact.

 

[Ari1584]

i thought momentum is not conserved when gravity is an external force? or am i confusing this with something else...

 

[premed101]

Momentum is NOT conserved in that first problem because there is an external force being applied, namely gravity and even air resistance

 

[BerkReviewTeach]

Momentum is certainly NOT conserved in that first problem because there is an external force being applied, namely gravity and even air resistance

Not sure why you resurrected this thread, but you might want to reconsider the certainty with which you are presenting your answer.

If we consider just the stone, then you are correct. There is an external force acting on the stone (namely gravity), so it will gain momentum as it falls.

However, if you consider the stone on the string at the lowest point of the swing, there is a point where the net acceleration of the ENTIRE system is zero (gravity and centripetal are offset by the tension in the string). If it breaks at that very instance (which is probably what the question is getting at), then the ball will accelerate down and the string will accelerate up, but the net momentum of the ENTIRE system will not experience a change (the up momentum gain will balance the down momentum gain) unless there is friction.

In my opinion, you can't answer this question without a little more information.

 

[Jeff85]

Not sure why you resurrected this thread, but you might want to reconsider the certainty with which you are presenting your answer.

If we consider just the stone, then you are correct. There is an external force acting on the stone (namely gravity), so it will gain momentum as it falls.

However, if you consider the stone on the string at the lowest point of the swing, there is a point where the net acceleration of the ENTIRE system is zero (gravity and centripetal are offset by the tension in the string). If it breaks at that very instance (which is probably what the question is getting at), then the ball will accelerate down and the string will accelerate up, but the net momentum of the ENTIRE system will not experience a change (the up momentum gain will balance the down momentum gain) unless there is friction.

In my opinion, you can't answer this question without a little more information.

WHy would the acceleration of the string be upward? And why would that exactly balance gravity? It seems you're assuming gravity is the centripetal force?

 

[Jeff85]

Is there any other case besides inelastic collisions that energy would not be conserved?

 

[ccoonen]

Agreed, the only force minus air resistance is gravity - so the old 9.8 m/s/s comes into play but it seems worded weirdly.