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egrooker

a Physics question......help

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the Problem: In a stage production of Peter Pan, the 54.0 kg actor playing Peter has to fly in vertically, and to be in time with the music, he must be lowered a distance of 3.10 m in 2.90 s. Backstage, a smooth surface sloped at an angle of 59.0° with respect to the horizontal supports a counterweight of mass m. Calculate the mass of the counterweight. [img]http://www.nofx.com/users/SonOfDoDo/ppan.gif[/img] To (attempt to)solve this I used the equation: T-m1g sin (theta)=m1a T-56kg (9.81) sin 59d=59kg(1.07) <==acceleration from 3.10/2.90 worked out I got T=1049.7 solved for T, then I put T in this equation: m2g-T=m2a solve for m2: m2(9.81)-1049.7=m2(1.07) -1049=m2(1.07)-m2(9.81) -1049.7=m2(1.07-9.81) -1049.7/-8.74=120N So my final answer is m2=120N But my homework software says "YOU ARE INCORRECT" Any help? Any ideas on what went wrong? Any help would be appreciated.. For Reference, this is the notes my teacher gave me thats basically the same thing: [url]http://plato.phy.ohiou.edu/~elster/phys251/examples/ex9d.pdf[/url]

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"I don''t understand ... how can mass be in Newtons?"

Yeah, it looks like I messed up there on the end, but i took the 120 as kg (which should be correct) and multiplied it by it''s accel 1.07 and got 128.5 but that''s still incorrect.

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egrooker,

Although you posted a homework question, it is acceptable. Reason? You explained yourself and SHOWED YOUR WORK, . So I know you really want to understand this stuff! Thank you!

Regardless, this is homework, so I won''t give the answer, but I can point to a couple of errors. You''re almost on the right track in terms of approach, but you''re missing a couple of things.



Right off the bat, you''re solving for the wrong m in the end. Your teacher''s notes show that m1 is the mass of the counterweight, and m2 is the mass of Pan. You already know m2 = 54kg.

Your equations (which are coming directly from your teacher''s notes) are right. but you cannot solve your first set of equations before the second. Reason? The first equation has 3 unknown values, T, a, and m1, and you don''t have 3 equations yet. You know m2, and you know T and a are related (that gives you another equation) so you have to deal with m2g-T=m2a first. This equation has two unknowns and with two equations you can solve for T.

Second problem. You calculated acceleration wrong. Remember, distance/time is velocity , not acceleration. So your 1.07 is just the average velocity over the 3.1 seconds.

There''s a couple of ways to do this problem. One is to find an equation for distance in terms of mass and constant acceleration and use that together with m2g-T=m2a to find T. I don''t think this is how your teacher expects you to solve it, but it is an appraoch.

The second approach is to use the equations for a and T that your teacher gave you, together with your first equation. That gives you 3 equations and from there you can calculate T, a, and m1 using the system of equations. By substitution, you can get a new equation where m1 is the only thing you do not know.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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