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## Vertical semicircular guide uniformly accelerated

Problem text A vertical semicircular guide, with radius and without friction, is constrained to a platform that moves with constant acceleration along the horizontal direction (see figure). A point body of mass , initially...

## Conic sections: an introduction from space

The conic sections (or simply conics) are those curves that are obtained as the intersection of the surface of a cone with a plane. Here, we discuss what kind of curves are achieved by varying the characteristics of the plane...

## Minimum speed to throw down a parallelepiped

Problem text Let us consider an object shaped as a parallelepiped and placed on a horizontal plane with friction (see figure). In particular, let us suppose that the object has a mass , a...

## Fractions LCM: Mathway vs WolframAlpha

What is the Least Common Multiple (LCM) of two or more fractions? Probably, one can ask himself “What do I need this calculation for?” or maybe one thinks that it is equal to the...

## Periodic decimal numbers as series: generating fractions

The periodic decimal numbers as every kind of decimal numbers have own generating fraction. In this post, we provide a general proof of the method usually used for converting them to fractions. Let us...

## Solved problem: a ball moving around a vertical circle

Solved problem A ball is tied to one end of a string. The other end of the string is held fixed. The ball is set moving around a vertical circle without friction, and with...

## The parabolic mirror and its remarkable reflection property

A parabolic mirror is a mirror that has the shape of a rotating paraboloid. The latter one is  a space surface of equation (see example in the figure below for ), obtained by rotating the...

## What is the Cartesian equation of a round cartoons cloud?

What is the Cartesian equation of a round cartoons cloud? What do we mean for a cartoons cloud? Of course, I do not mean a real cloud made by water steam and floating in...

## What mark do you need to get the desired average?

What mark do you need to get the desired average? In details, let us consider a student that up to date received in a discipline the following sequence of marks Moreover, let us assume that...

## Speed-time graph of a skydiver using GeoGebra

Today, we will study the motion of a skydiver with the aim to obtain its speed-time graph. For this purpose, we will use both a spreadsheet and the graphics of the didactic software GeoGebra. As...

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