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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: ->->->->->->->->->->->-> :
The gravitational force forms an angle 240 degrees counterclockwise from the positive x axis. The x component is greater in magnitude.
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A vector at 270 degrees would have x component zero.
The x component of a vector at 180 degrees would have the same magnitude as the vector itself.
Is the current vector closer to the x or the y axis?
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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 x component of the carts weight is 42N because 49cos(30)=42 and the y component is 25N because 49sin(30)=25.
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The car's weight vector is at 240 degrees as measured counterclockwise from the positive x axis, per your previous answer.
The weight vector is not at 30 degrees from the positive x axis, and the given formulas for the components apply only when this is the case.
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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 incline must exert an upward force of 25N to support the cart.
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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 acceleration is 8m/s^2 because 40N = 5kg*a, so 8m/s^2.
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Your results don't match the picture of the 'tilted' xy coordinate system and the vector at 240 degrees.
Vectors are giving you a little trouble, as they do most students, but you'll soon be over it. It will 'click' for you very soon, hopefully as you revise your work on this problem.
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