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PHY 121
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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: ->->->->->->->->->->->-> :
I have drawn a picture. It started with a regular x-y coordinate system with a line that had an angle of 30 degrees from the origin. There is a 5 kg cart drawn at the origin starting up the hill. Then I drew move lines with arrows--one on the incline and a second perpendicular to this. I am thinking because I had the original perpendicular lines, an angle of 30 degrees and then new perpendicular lines using this angle, that the gravitational force has a 30 degree angle from the y axis and a 60 degree angle from the x axis. But I don't really know.
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You don't mention a vector for the weight of the cart.
That's the very first force vector you need to draw. It is directed vertically downward.
What angle does that vector make with the positive x axis?
What is its magnitude?
What therefore are its components?
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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: ->->->->->->->->->->->-> :
sine: the trigonometric function that is equal to the ratio of the side opposite a given angle in a right angle to the hypotenuse. The sine would show the y component.
cosine: the trigonometric function that is equal to the ratio of the side adjacent to an acute angle in a right triangle to the hypotenuse. The cosine would show the x component.
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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?
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The force against the cart by the incline would be upward. I just don't know if it's the 30 degree or 60 degree push.
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If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
This would be the force of gravity--9.8 m/s^2
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30 min
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This seed is going to need water and fertilizer because it's not growing yet. I have the definitions with a right angle picture. I have been able to use the calculator to find the answers when necessary. But the grid with cock-eyed axis and arrows going everywhere really has me confused.
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You're apparently missing the first and most important force vector.
You need to start with the incline and the weight vector.
Then add the x and y axis, with the x axis along the incline.
Then work from there.
Let me know what you get.
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