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phy121
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 magnitude is 5kg * 9.8m/sec^2 = 49 newtons
measuring counterclockwise, a 240 degree rotation is required. The y component is greater 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: ->->->->->->->->->->->-> :
x componenet = 49 Newtons * cos 240 = -24.5 newtons
y componenet =49 newtons * sin240 = -42.44 newtons
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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 y component of gravitational force is -43 newtons. Since the y axis is perpendicular to the incline, this -43 newtons of force acts perpendicular to the incline. Thus the incline responds with the elastic or compressive force of 43 newtons.
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• If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
the net force would be -24.5 newtons in the x direction
a=Fnet /m = -24.5 newtons/5kg = -4.8 m/sec^2
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30 min
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&#Very good responses. Let me know if you have questions. &#