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Const@ntine

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## Homework Statement

A small object with mass m is dragged without friction to the highest point of a semicircle with a radius of R, by a weightless rope.

a) If the magnitude of his velocity is constant, then his acceleration that is parallel to the semicircle, is zero. Prove that F = mgcosθ

b) Integrate the following swiftly W = ∫ F*dr, to calculate the work that is produced when the object is moved from the highest point, to the lowest.

## Homework Equations

## The Attempt at a Solution

(a) So, first up I set the direction of the force F as the Y axis, and then created the net force (I don't know the proper term yet, but you get the gist of it from the pic). Like this:

**
**

Thus: ΣF

_{y}= ma

_{t}= 0 <=> F = F

_{gy}= F

_{g}cosθ = mgcosθ

(b) Now's the part where I can't quite figure it out. I didn't do much intergals at school, so it's pretty new to me, and I haven't reached that part in my math book. I glanced at the back and found the basic ones (eg ∫cosθdθ = sinθ + c), but I've never come across an intergal with both x & y coordinates. I took a look at other examples from the solution manual, but only one other problem was intergals, and it's quite different.

The book's answer is "mgR", and I kinda sort of found the same, but from lowest to highest, not the opposite, like the book's asking. If anyone could help me with the intergal, I'd appeciate it!