Direction of the net force acting on a pendulum

[songoku]

Homework Statement

The picture shows a pendulum in its upward swing, that is, the velocity vector for the pendulum is pointing in the direction of E. What is the direction of the net force acting on the pendulum?

Relevant Equations

Not sure

I imagine y - axis is parallel to direction of A and x - axis is parallel to direction of E. There are two forces acting on the pendulum: tension in direction of A and weight in direction of D.

I break the weight into 2 components: W sin θ in opposite direction to tension and W cos θ in direction of C (where θ is angle between D and C). Tension should be bigger than W sin θ to provide centripetal force so the resultant of force in y - axis is in the direction of A and resultant of force in x - direction is in direction of C hence the direction of net force will be B.

But the answer is C. Where is my mistake?

Thanks

 

[haruspex]

Tension should be bigger than W sin θ to provide centripetal force so the resultant of force in y - axis is in the direction of A

Yes.

resultant of force in x - direction is in direction of C

Yes.

hence the direction of net force will be B.

You seem to be showing B as horizontal. The direction could be anywhere between A and C.

But the answer is C.

Only if it is at the peak of the swing.

 

[songoku]

You seem to be showing B as horizontal. The direction could be anywhere between A and C.

But for this case, B is the only logical answer, right?

Only if it is at the peak of the swing.

So the answer key (C) is wrong because from the diagram it is not at its peak?

Thanks

 

[PeroK]

But for this case, B is the only logical answer, right?
So the answer key (C) is wrong because from the diagram it is not at its peak?

Thanks

Yes, I'd say that if it's a multiple choice and it has to be one of the answers, then the pendulum must (logically) be just at the point where the acceleration is horizontal.

Either that or it is supposed to be at the top of its swing, when the answer would be C.

I suspect the question setter forgot that acceleration is not necessarily in the instantaneous direction of motion.

 

[songoku]

Yes, I'd say that if it's a multiple choice and it has to be one of the answers, then the pendulum must (logically) be just at the point where the acceleration is horizontal.

Either that or it is supposed to be at the top of its swing, when the answer would be C.

I suspect the question setter forgot that acceleration is not necessarily in the instantaneous direction of motion.

Yes it is multiple choice question.

By " top of its swing" you mean when the string is horizontal?

Thanks

 

[PeroK]

By " top of its swing" you mean when the string is horizontal?

No. When it reaches its highest point.

 

[songoku]

No. When it reaches its highest point.

When the string is horizontal, the tension will be directed to the left and weight downwards so the resultant will also be C, right?

Thanks

 

[PeroK]

When the string is horizontal, the tension will be directed to the left and weight downwards so the resultant will also be C, right?

Thanks

If the string reaches the horizontal just as the pendulum stops, there will be no tension.

Anyway, the diagram clearly shows the pendulum at an intermediate point (which is what you would expect). With the string neither vertical nor horizontal.

Also, the statement about the velocity vector pointing in the direction of E infers that the pendulum is still moving upwards.

 

[jbriggs444]

Also, the statement about the velocity vector pointing in the direction of E infers that the pendulum is still moving upwards.

Nicely noticed.

However "implies" is what the writer does while "infers" is what the reader does. The former would be appropriate here.

 

[songoku]

If the string reaches the horizontal just as the pendulum stops, there will be no tension.

I see, miss this point. No tension if it stops and there is tension if it keeps moving

Thank you very much for the help Perok and haruspex

 

[PeroK]

Nicely noticed.

However "implies" is what the writer does while "infers" is what the reader does. The former would be appropriate here.

Yes, I thought it didn't sound quite right.