An insect is crawling up on the concave surface of a hemispherical bowl of radius R. if the coefficient of friction is 1/3 then the height upto which the insect can crawl is _______?
please explain the answer with steps
please explain the answer with steps
-
1.) First, ask yourself, if the coefficient of static friction is 1/3, what must be the angle at which the insect will begin to slide? The bug can crawl until the slope of the tangent line on the bowl is 1/3.
2.) When is the slope of the tangent line 1/3? Find the formula for the shape of the bowl: x^2+y^2=R^2
Derive the equation: dy/dx=-x/y. Find the point at which 1/3=-x/y. This requires you to find the point at which both x^2+y^2=R^2 and 1/3=-x/y are true. You can solve the system yourself; the answers are x = R/sqrt(10), y = -(3R)/sqrt(10) in addition to their addititive inverses. However, you must choose this one, as the other points do not exist on the bowl because those are up in the air, and you have semicircle (hemisphere).
3.) Now, notice that the y value is the height, but it is the distance from the top of the bowl. You need to find the distance from the bottom, i.e., -r. That gives you (-3R)/sqrt(10)-(-R).
4.) You must simplify, though. This gives you an answer of "R-3R/sqrt(10)" or 0.051R.
I would be shocked if this is for a high school physics class in the US.
2.) When is the slope of the tangent line 1/3? Find the formula for the shape of the bowl: x^2+y^2=R^2
Derive the equation: dy/dx=-x/y. Find the point at which 1/3=-x/y. This requires you to find the point at which both x^2+y^2=R^2 and 1/3=-x/y are true. You can solve the system yourself; the answers are x = R/sqrt(10), y = -(3R)/sqrt(10) in addition to their addititive inverses. However, you must choose this one, as the other points do not exist on the bowl because those are up in the air, and you have semicircle (hemisphere).
3.) Now, notice that the y value is the height, but it is the distance from the top of the bowl. You need to find the distance from the bottom, i.e., -r. That gives you (-3R)/sqrt(10)-(-R).
4.) You must simplify, though. This gives you an answer of "R-3R/sqrt(10)" or 0.051R.
I would be shocked if this is for a high school physics class in the US.
-
Like regular ed, high school physics or AP Physics C?
Report Abuse