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: ->->->->->->->->->->->-> :
The gravitational force makes a 240 degree angle with the positive x axis. The y component of the force is going to have a greater magnitude than the x component.
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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: ->->->->->->->->->->->-> :
parallel: 49N cos 240 = -24.5N
perpendicular: 49N sin 240 = -42.4N
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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: ->->->->->->->->->->->-> :
The compressive force has to be 42.4N and it is in the opposite direction from gravity, so it is going up.
The compressive force is perpendicular to the incline. Since the magnitude of this force is less than that of the gravitational force, the two are not equal and opposite.
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• If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
-24.5N = 5kg * a
A = -4.9 m/s^2
The motion cart will be slowing down if it were going forward, or it will now be rolling backward if the initial velocity was 0m/s
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20 minutes
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Very good. Take a look at the additional discussion (and of course see my note).
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your 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. &#