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PHY 231
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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 sketched the system, with the origin centered on the pendulum on the x-axis.
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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: ->->->->->->->->->->->-> :
Knowing that its x-component is .1 meters and its y-component is approximately 2 meters, we can use Pythagorean theorem to find the magnitude of the vector. 2^2 + .1^2 = c^2, which is about 4.01. C is approximately a little over 2 meters. Its direction is equal to the inverse tangent of y/x; the degrees with respect to the positive x-axis are 87.14.
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• What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
Tension is semi-perpendicular to the downward gravitational pull; it is a product of the circular/centripetal motion. At this instant, it is ( 90 - 87.14 ) 2.86 degrees east of north.
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• What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
x-component = 5 * cos ( 87.14 degrees ) = .999 ( est. )
cos(87.14 deg) = .05, very roughly.
y-component = 5 * sine ( 87.14 degrees ) = 4.99 ( est. )
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• What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> :
The mass of pendulum is approximately .510 kg ( F / a = m ), which equals a weight of about 1.124 pounds ( 2.20 lbs. = 1 kg ).
pounds do measure force, but the pound is not a metric unit and won't articulate with other metric units
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• What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
The acceleration is 9.8 m/s/s.
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25 Minutes
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Solution
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