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Phy 121
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, the y component should be greater I think
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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: ->->->->->->->->->->->-> :
Perpendicular to the incline the cart exerts a force:
F = 5 kg * 9.8 m/s/s = 49 Newtons.
Parallel to the incline we would want to use sin theta;the altitude of the incline, divided by the length of the incline.
Since it is 30 degrees above, 90 degrees downward (90+30=120 degrees, 360 degrees-120 degrees= 240 degrees)
x component*cos (theta)=49 N*cos(240)= -24.5 N
y component* sin (theta)= 49 N* cos(240)= -43 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: ->->->->->->->->->->->-> :
Since the y component is -43 N, the incline must exert +43 N to support the cart. ??Not sure what direction it is.
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The direction of the force exerted by the incline, in response to this force, is equal and opposite to the direction of this force.
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The -43 N force is in the y direction, so the force exerted by the incline is +43 N in the y direction.
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&#Good responses. See my notes and let me know if you have questions. &#