Phy 231
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 angle of the gravitational force, from this perspective, is 90 degrees. The magnitude of the y component of the gravitational force is much greater. This can be found by using a vector to represent the x and y components. (49cos60, 49sin60).
• 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: ->->->->->->->->->->->-> :
Using vectors, I get (49cos60, 49sin60) for the x and y components. This gives me 24.5 N for the horizontal force and 42.44 N for the vertical force.
• 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'm not sure what kind of force they are referring to. I do know that there has to be a normal force that is opposing the weight of the cart that should be perpendicular to the surface and equal to the weight.
• If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
Assuming that the horizontal force found was correct at 24.5 N. Then using the equation F =ma, we find acceleration to be 4.9 m/s^2.
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30 min
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I'm not sure if I found the x and y components of the force correctly. I used an angle of 60 degrees but shouldnt the downward force be 49N? Or is that the force that is perpendicular to the surface?
49 N is downward, which is at an angle of 240 degrees relative to this system (reference angle would indeed be 60 degrees), which resolves the weight vector into x and y components according to cosine and sine of 240 deg.
You've got most of it, but to be sure you understand the orientation of the system check out the link:
&#Please compare your solutions with the expanded discussion at the link
Solution
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