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Phy 121
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.
• Sketch the system with the pendulum mass at the origin and the x axis horizontal.
answer/question/discussion: ->->->->->->->->->->->-> :
I drew a straight vertical line hanging from a horizontal line, that forms a perpendicular union. The pendulum has an arrow emanating from the right side, pulling up the pendulum. The horizontal displacement of this line is 10 cm.
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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: ->->->->->->->->->->->-> :
The direction would be in the positive x direction.
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The length vector would have a 10 cm component to the right or left along the x axis. A vector of length 2 meters with a positive y component and an x compoent of magnitude 10 cm makes an angle of either about 93 deg or 87 deg with the positive x axis (the 93 deg angle concides with your subsequent solution for the angle of the tension vector).
However note that your 93 degree angle would correspond to a negative 10 cm x component, not the positive x component you assert here.
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• What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
Angle=arctan(200cm/-10cm)=2.9 deg+90 deg= 92.9 deg tension force is along the string.
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• What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
The x component is : 5 N* cos (92.5 deg)= 0.25 N
The y component is: 5N*sin(92.9 deg)= 5 N
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• What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> :
m=weight/grams=5N/(9.8 m/s^2)=0.51 kg
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• What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
a=F_net/m
0.25 N/(0.51 kg)
=0.49 m/s^2
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Very good, but check my note.
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