Phy 231
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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 cart on the incline and the x axis 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.
answer/question/discussion: Since the slope is less than 45 degrees I would estimate it that gravity still has a strong force along the x-axis and the y-axis force would be much less. For values I would esimate 50 N times .8 in the x and 50 N times .4 in the y or 40 N in the x-component, and 20 N in the y-component.
Using the definitions of the sine and cosine, find are the components of the cart's weight parallel and perpendicular to the incline.
answer/question/discussion: x-component produced by gravitational force = 5 kg * 9.8 m/s^2 * sin(30) = 24.5 N, and y-component produced by gravitational force = 5 kg * 9.8 m/s^2 * cos(30) = 42.44 N.
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 provide at least force equal to the y-component of gravity acting upon the cart; therefore, it must provide at least 24.5 N of force.
If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: Since there is 24.5 N acting downwards, we can ignore the horizontal force, we know that 24.5 N/ 5 kg = 4.9 m/s^2 = a.
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12 minutes
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&#Your work looks good. Let me know if you have any questions. &#