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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: ->->->->->->->->->->->-> :
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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: ->->->->->->->->->->->-> :
We can look at the tension in terms of a vector.
The vertical component of the vector is 2 meters, the horizontal component is 0.1m.
The magnitude of direction isn’t a useful quantity to us here I don’t believe but we do need the angle, which we find by:
Angle= arctan(2m/0.1m) = 87.1 deg
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• What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
The vertical component of our tension force is 5N, and we know our angle to be 87.1 deg, we can say this as follows:
Ty(5N) = T sin(87.1)
We can find the magnitude of the tension by dividing by the sin of 87.1
T = Ty(5N) / sin(87.1 = 5N
To find the x component we would then say
Tx = 5N Cos(87.1) = 0.3N
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• What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
T = 5N
Tx = 0.3N
Ty = 5N
Theta= 87.1
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• What therefore is the weight of the pendulum, and what it its mass?
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weight is equal to mass times gravity. The weight is given to use at 5N. This means that some mass multiplied by the acceleration of gravity equals 5N
5N = (m) (9.8m/s^2)
Divide by 9.8m/s^2
M = 5N / 9.8m/s^2 = 0.5kg.
A half kilogram mass exerts a vertical force of 5 N against gravity.
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• What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
The net force of the pendulum raised 0.1m is the 5N - 0.3N = 4.7N
4.7N / 0.5kg = 9.4m/s^2
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The 0.3 N force is in the x direction and the only 5 N forces are in the y direction. You wouldn't use simple addition to combine them.
However you don't need to combine them in the first place. The vertical component of the tension is equal and opposite to the 5 N weight.
Only the horizontal component of the tension remains, so the net force is 0.3 N in the horizontal direction.
This results in an acceleration of
0.3 N / (0.5 kg) = 0.6 m/s^2.
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