\nThe following is by my understanding.<\/p>\n
\nLet’s imagine one has to work on a slope of 22\u00b0 and another of 35\u00b0. How much more likely is it to slip down the steeper one, and why?<\/p>\n
\nThe acceleration due to gravity is given by gsin\u03b8, where \u03b8 is the angle of elevation (22\u00b0 or 35\u00b0 in this case). The grip of friction, holding the person in place on the slope, is calculated from gcos\u03b8.<\/p>\n
\nImportantly, to compare the 22\u00b0 slope with the 35\u00b0 one, the difference between sin\u03b8 on both slopes, then between cos\u03b8 on both, is key. To compare them, we will round to two decimal places.<\/p>\n
\nsin22\u00b0=0.37, while sin35\u00b0=0.57. Therefore, the acceleration down the slope increases by about 54 percent from 22\u00b0 to 35\u00b0.<\/p>\n
\ncos22\u00b0=0.93, while cos35\u00b0=0.82. Therefore, friction decreases between 22\u00b0 and 35\u00b0, but only by about 12 percent.<\/p>\n
\nTherefore, it seems that what makes the 35\u00b0 slope so much more challenging to stay in place on, compared to the 22\u00b0 one, is the increase in acceleration down the slope moreso than the accompanying decrease in friction.<\/p>\n
\nSource:<\/p>\n
Giancoli,D.C. (1998). Physics,<\/em> fifth edition. Prentice Hall.<\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.\n","protected":false},"excerpt":{"rendered":" Tutoring physics, you consider gravity against a slope. The tutor makes a comparison. The following is …<\/p>\n