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Phy 201
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: ->->->->->->->->->->->-> :
30 degrees
I would say the x component is greater.
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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: ->->->->->->->->->->->-> :
The parallel weight is sine(theta). The perpendicular is the cos(theta).
If theta is the angle with horizontal, that's right (as long as you remember to multiply sine and cosine by 49 N). If theta is the angle of the weight with respect to the x axis (which would be either 240 deg or 300 deg) then the components would be 49 N * cos(theta) and 49 N * sin(theta), in that order.
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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: ->->->->->->->->->->->-> :
I would say that we would use the equation: .5(m)(v^2)= .5(5kg)(9.8m/s/s)=24.5N. The force is going up.
.5 m v^2 wouldn't come out in Newtons, it would come out in Joules.
9.8 m/s^2 is not a velocity, nor is it the square of a velocity.
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• If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
w(sin)(theta)
2.5m/s/s
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Check my notes, as well as the link. You can ignore the part about a revision, unless you think that would be benficial for you.
&#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. &#