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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: ->->->->->->->->->->->-> :
+225 degrees angle (gravitational force) Both components are negative, as the force is in the third quadrant.
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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 component will be zero since the cart rests on the incline. Parallel weight component is weight* slope.
@& For small slopes, the parallel component is weight * slope.
If the perpendicular component was zero, then there would be no force between the object and the incline. This isn't the case.
You say that the gravitational force is at 225 degrees to the x axis. You're close. If the angle of the incline was 45 degrees then 225 degrees would be correct.
However the incline is at 30 degrees, not 45 degrees. What therefore is the correct angle?
What is the magnitude of the gravitational force on a 5 kg mass?
If the incline was at 45 deg, then you would have this force acting at 225 deg. What would the x and y components of this force therefore be?
The incline is at 30 deg, so the angle isn't 225 deg. Using the correct angle, what are the components?
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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 inlcine must exert a force equal and opposite to that of what is placed on it by the weight of 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: ->->->->->->->->->->->-> :
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Accel = Fnet/mass
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10 minutes
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