Phy 121
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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: ->->->->->->->->->->->-> :
If I drew a picture of the pendulum, it would start off with the weight hanging perpendicular in the downward direction from the x axis. Because it would be hanging straight down it would start off with an angle of 90 degrees.
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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: ->->->->->->->->->->->-> :
When the pendulum gets pulled back 10 cm, it will change the angle (vector) of the pendulum. The hint says that the y component is practically the same as the length of the pendulum so I am assuming that the y component is approximately 2 meters.
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• What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
I think that the direction of the tension force is -5 N. I think this because if the normal tension force is 5 N and the pendulum is in equilibrium then it means that the pendulum has to be exerting a force in the negative direction.
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• What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
I am not 100 percent what the angle would be of the pendulum. I know that it starts by hanging at what I assume would be considered as a 90 degree angle. When it gets pulled back by 10 cm, it makes me wonder if that is the equivalent of 10 degrees? If so then we could figure out the horizontal and vertical components as follows:
5N * cos 100 degrees = -.9 degrees(This does not seem right to me though…)
5N * sin 100 degrees = 5 degrees (this does not seem right either…)
The angle isn't 100 degrees, but if it was your calculations would be correct, except for the units. For example,
5N * cos 100 degrees = -.9 N, not -.9 degrees.
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• What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> :
If we are solving for the mass of the pendulum I am assuming that we use 5N = m * 9.8 m/s^2. To solve for the mass we divide each side by 9.8 m/^2 and it gives us .51 kg. From here I am not sure how to solve for the weight of the pendulum.
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• What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
I am assuming that the acceleration is 9.8 m/s ^2 which is the standard rate of acceleration for gravity being exerted in an object- in this case it is being exerted on the pendulum mass.
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35-40 minutes
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You've got a lot of this. Check the discussion and let me know if you have questions.
&#Please compare your solutions with the expanded discussion at the link
Solution
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