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:
you should have estimated this from your sketch before calculating it in the next step
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 = 5cos(30) = .77kg, y = 5sin(30) = 4.94kg
The x component would indeed be weight * cos(30 deg).
However 5 kg is not a weight but a mass, and 5 cos(30 degrees) is not .77 (nor is 5 sin(30 degrees) equal to 4.94) . These results would not be compatible with a reasonable sketch of the situation, and the sketch is very important. I suspect the calculation error was because you had your calculator in radian mode rather than degree mode.
See the link at the end for more detail on the weight, the picture, and the calculation.
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: F = ma = .77kg * 9.8m/s^2 = 7.5N , F = ma = 4.94kg * -9.8m/s^2 = -48.4N, Fnet = -48.4N - 7.5N = -55.9N
You wouldn't add forces that are exerted in perpendicular directions.
If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: a = F/m = -55.9N / 5kg = -11.18m/s^2
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30min
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You're on the right track, but you should do as instructed below in order to put it all together into the big picture.
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
This link also expands on these topics and alerts you to many of the common errors made by students in the first part of this course. &#