# Uniform circular motion, trapeze artists problem

Lewis is a trapeze artist. He is hanging upside down on a swing bar; he is holding on to the swing bar with his knees. Lewis is holding his partner Amanda below him, who weighs 475 Newtons. Assume that Amanda moves on a circle that has a radius of 6.50 meters. At a swinging speed of 4.00 m/s, what force must Lewis apply to his partner Amanda when she is in the straight down position?

Relevant equations
ac = v2/r
Fc = (mv2)/r

The attempt at a solution
Lewis has to provide the force that holds up Amanda's weight of 475 Newtons AND also the centripetal force Fc that accelerates Amanda through the circle.

The total force that Lewis has to provide is: Ftotal = Weightamanda + Fc

What I did to find Fc was to plug and chug:
Fc = mv2/r
Fc = [48.46938776 kg * 42m/s]/6.5
Fc = 119.3092622

Then I used this value to plug into Ftotal = Weightamanda+ Fc

Ftotal = 475 + 119.3092622 = 594.3092622 N

HOWEVER, on some discussions on this problem, they are saying that the circle is horizontal when Amanda is at the straight down position, and thus, the Fc is horizontal which requires that we use the horizontal component????? ....Firstly, I do not know what they are implying here...Secondly, there are others who solved the problem as I did. Can somebody please tell me which is correct? Here is the discussion on a similar problem but with different values: http://answers.yahoo.com/question/index?qid=20081018232148AABuLGD

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PeterO
Homework Helper
Lewis is a trapeze artist. He is hanging upside down on a swing bar; he is holding on to the swing bar with his knees. Lewis is holding his partner Amanda below him, who weighs 475 Newtons. Assume that Amanda moves on a circle that has a radius of 6.50 meters. At a swinging speed of 4.00 m/s, what force must Lewis apply to his partner Amanda when she is in the straight down position?

Relevant equations
ac = v2/r
Fc = (mv2)/r

The attempt at a solution
Lewis has to provide the force that holds up Amanda's weight of 475 Newtons AND also the centripetal force Fc that accelerates Amanda through the circle.

The total force that Lewis has to provide is: Ftotal = Weightamanda + Fc

What I did to find Fc was to plug and chug:
Fc = mv2/r
Fc = [48.46938776 kg * 42m/s]/6.5
Fc = 119.3092622

Then I used this value to plug into Ftotal = Weightamanda+ Fc

Ftotal = 475 + 119.3092622 = 594.3092622 N

HOWEVER, on some discussions on this problem, they are saying that the circle is horizontal when Amanda is at the straight down position, and thus, the Fc is horizontal which requires that we use the horizontal component????? ....Firstly, I do not know what they are implying here...Secondly, there are others who solved the problem as I did. Can somebody please tell me which is correct? Here is the discussion on a similar problem but with different values: http://answers.yahoo.com/question/index?qid=20081018232148AABuLGD

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I haven't checked whether your arithmetic is correct, but the logic in the "answers.yahoo.com" best solution is rubbish. It should be calculated the way you set out.
btw.
I would have found the centripetal acceleration [v2/r] and expressed it in terms of g. - giving 0.25 * g.
The upward force [Weightamanda+ Fc] is thus 1.25 * mg.

mg = 475N, so 1.25 * 475 = 594 N
Same answer - a different way of expressing it.

EDIT: It is assumed that 6.5m is the radius of the circle through which Amanda's Centre of Mass rotates.

NascentOxygen
Staff Emeritus
The yahoo solution is quite perplexing. I think the phrase in the straight-down position is being interpreted there as meaning that the partner is facing downwards, i.e., has swung out into the horizontal position so he is momentarily facing straight down. That's not how I interpret it, but I can see that an ESL person may readily take it that way.

This illustrates how careful one must be when setting exam questions for a class with diverse backgrounds. There may turn out to be more than one correct answer!

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PeterO
Homework Helper
The yahoo solution is quite perplexing. I think the phrase in the straight-down position is being interpreted there as meaning that the partner is facing downwards, i.e., has swung out into the horizontal position so he is momentarily facing straight down. That's not how I interpret it, but I can see that an ESL person may readily take it that way.

This illustrates how careful one must be when setting exam questions for a class with diverse backgrounds. There may turn out to be more than one correct answer!
Or indeed that you must be careful about referring to a trapeze, given that not everyone will know what a trapeze is, and how people swing on them!!

Thank you all :)