A steel alloy specimen having a rectangular cross section of dimensions 18.1 mm × 3.0 mm ( 0.7126 in. × 0.1181 in.) has the stre
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Explanation:
<u>Forces</u><u> </u><u>on</u><u> </u><u>Block</u><u> </u><u>A</u><u>:</u>
Let the x-axis be (+) towards the right and y-axis be (+) in the upward direction. We can write the net forces on mass as
Substituting (2) into (1), we get
where , the frictional force on
Set this aside for now and let's look at the forces on
<u>Forces</u><u> </u><u>on</u><u> </u><u>Block</u><u> </u><u>B</u><u>:</u>
Let the x-axis be (+) up along the inclined plane. We can write the forces on as
From (5), we can solve for <em>N</em> as
Set (6) aside for now. We will use this expression later. From (3), we can see that the tension<em> </em><em>T</em><em> </em> is given by
Substituting (7) into (4) we get
Collecting similar terms together, we get
or
Putting in the numbers, we find that . To find the tension <em>T</em>, put the value for the acceleration into (7) and we'll get
. To find the force exerted by the inclined plane on block B, put the numbers into (6) and you'll get