Phy 231
Your 'cq_1_26.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A simple pendulum has length 2 meters. It is pulled back 10 cm from its equilibrium position and released. The tension in the string is 5 Newtons.
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Sketch the system with the pendulum mass at the origin and the x axis horizontal.
answer/question/discussion: ->->->->->->->->->->->-> sion: OK
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Sketch a vector representing the direction of the pendulum string at this instant. As measured from a horizontal x axis, what is the direction of this vector? (Hint: The y component of this vector is practically the same as the length; you are given distance of the pullback in the x direction. So you know the x and y components of the vector.)
answer/question/discussion: ->->->->->->->->->->->-> sion: This vector would be just slightly more than 90 degrees in the second quadrant, or you could get the actual value by tan^-1(2m/-.1m) =~ -87.14 deg, and adding 180 deg = 92.86 deg.
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What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> sion:
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Ahhh, I think it would just be the same... Since it's in the string it'd also be ~ 93 deg, unless you have to flip it or something, but I don't remember doing that.
What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> sion:
5N(cos(93)) =~ -.26N
5N(sin(93) =~ 4.99N
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What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> sion:
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So, the y-comp is 5N (or close enough), which is balanced, so the magnitude of the weight is 5N, and
5N = 9.8m/s^2(m), and m = .51kg
What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> sion:
acceleration is in the horizontal direction, so a = -.26/(.51kg) =~ -.51m/s^2 or I guess it should actually be .51m/s^2 if the direction of motion is positive.
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15 min
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The displacement from equilibrium is positive; when released the pendulum is pulled back toward equilibrium by the -.26 N x component of the tension, and its acceleration is -.51 m/s^2, as you said originally.
&#Very good work. Let me know if you have questions. &#