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Phy 231
Your 'cq_1_17.2' 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 5 kg cart rests on an incline which makes an angle of 30
degrees with the horizontal.
Sketch this situation with the incline rising as you move to the
right and the cart on the incline. Include an x-y coordinate
system with the origin centered on the cart, with the x axis
directed up and to the right in the direction parallel to the
incline.
The gravitational force on the cart acts vertically downward, and
therefore has nonzero components parallel and perpendicular to
the incline.
Sketch the x and y components of the force, as estimate the
magnitude of each component.
What angle does the gravitational force make with the positive x
axis, as measured counterclockwise from the positive x axis?
Which is greater in magnitude, the x or the y component of the
gravitational force?
answer/question/discussion: ->->->->->->->->->->->-> :
60 degrees
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Using the definitions of the sine and cosine, find the components
of the cart's weight parallel and perpendicular to the incline.
answer/question/discussion: ->->->->->->->->->->->-> :
5 kg * cos30 * 9.8 m/sec^2
= 42.44 N
5 kg * 9.8 m/sec^2 * sin 30
= 24.5 N
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How much elastic or compressive force must the incline exert to
support the cart, and what is the direction of this force?
answer/question/discussion: ->->->->->->->->->->->-> :
25.5 N + 42.44 N = 67.94 N
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If no other force is exerted parallel to the incline, what will
be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
F = m * a
42.44 = 5 * a
a = 8.49 m/sec^2
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*#&!*#&!
@& For the situation as described the gravitational force makes an angle of 240 degrees with the positive x axis, resulting in components
49 N * cos(240 deg) = -24.5 N in the x direction
and
49 N * sin(240 deg) = -42.4 N in the y direction.
That is, the gravitational force has a component of 24.5 N down the incline, and 42.4 N 'directly into' the incline (i.e., perpendicular to the incline).*@
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&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
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