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Phy 241
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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 pendelum by creating a vector from the origin of the x-y axis. The terminal point on the vector is 10 cm to the left of the vertical y-axis.
The vector has a magnitude of 5N. The angle the the vector makes is found by arctan(200cm/-10cm) + 180° = 92.9°
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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: ->->->->->->->->->->->-> :
92.9°
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What is the direction of the tension force exerted on the mass?
answer/question/discussion: ->->->->->->->->->->->-> :
the direction of the tension force is 92.9°
In order to find the direction of the tension you can find the sum of all the forces. Since the mass is at the origin and gravity is creating a force, in order
to negate this force, you find the tension, which is opposite that of the gravitational force. Therefore the vector point up and to the left is the tension.
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What therefore are the horizontal and vertical components of the tension?
answer/question/discussion: ->->->->->->->->->->->-> :
Sum of all the forces in the x direction
0 = -5sin(2.9) + T
T = -.25 N
y-direction
0 = 5cos(2.9) - T
T = 5N
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What therefore is the weight of the pendulum, and what it its mass?
answer/question/discussion: ->->->->->->->->->->->-> :
w = m*g = 5N
m = w/g
= 5N / 9.81m/s^2
= 0.51 kg
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What is its acceleration at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
acceleration in the y direction is -9.81 m/s^2
acceleration in the x- direction
F = m*a
a = F/m
= -.25N/.51 kg
= .49 m/s^2
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&#Good responses. Let me know if you have questions. &#