Question 1147860
.
if 300 pounds of {{{highlight(cross(face))}}} <U>force</U> is required to push 1000 pound safe up a ramp, 
then what is the angle of inclination of the ramp. 
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<pre>

    {{{drawing( 302, 210, 0.0, 10.1, -1.0, 6.0,
            
            line ( 0, 0, 10,    0), 
            line (10, 0,  9.7, -0.1), 
            line (10, 0,  9.7,  0.1), 
            locate(9.6,  -0.1,  x),

            line  (1.0,  -1.0, 1.0, 5.8),
            line  (1.0,   5.8, 0.9, 5.5),
            line  (1.0,   5.8, 1.1, 5.5),
            locate(0.4,   5.7, y),

            line  (2.0,   0.0, 9.5, 2.5),

            arc   (2.0, 0.0, 2.6, 2.6, 345, 360),
            arc   (2.0, 0.0, 2.8, 2.8, 345, 360),
            locate (3.5, 0.55, alpha),

            line  (5.0, 1.0, 4.8, 1.6),
            line  (6.5, 1.5, 6.3, 2.1),
            line  (4.8, 1.6, 6.3, 2.1),

        red(line  (5.65,  1.5, 5.65, -0.5)),
            line  (5.65, -0.5, 5.55, -0.2),
            line  (5.65, -0.5, 5.75, -0.2),
            locate(5.3,  -0.4, W),

      green(line  (5.65,  1.52, 4.9, 1.25)),
            line  (4.9,   1.25, 5.2, 1.5),
            line  (4.9,   1.25, 5.2, 1.25),

      green(line  (5.70,  1.5,  6.30, -0.3)),
            line  (6.30, -0.3,  6.35, -0.05),
            line  (6.30, -0.3,  6.17, -0.12),

            arc   (5.65,  1.5, 1.4, 1.4, 70, 90),
            arc   (5.65,  1.5, 1.6, 1.6, 70, 90),
            locate (5.68, 0.75, alpha),

      green (line (5.00,  1.25, 5.65, -0.5)),
      green (line (6.30, -0.3,  5.65, -0.5)),

             line (6.4, 1.8, 7.9, 2.3),
             line (7.9, 2.3, 7.58, 2.32),
             line (7.9, 2.3, 7.65, 2.07),
             locate (7.7, 2.9, F)
)}}}

    <B>Figure</B>. &nbsp;The body pulled up on the inclined plane
</pre>


From this plot,  F = {{{sin(alpha)*Weight}}}.


In your case,  300 = {{{sin(alpha)*1000}}}.


Hence,  {{{sin(alpha)}}} = {{{300/1000}}} = 0.3,


and  {{{alpha)}}} = arcsin(0.3) = 0.3947 radians = 17.5 degrees (approximately).
</pre>

Solved, answered, explained and plotted.


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