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MSD 210 Project: Sci-Enza: Mechanical Paradox: The Uphill Roller

The document summarizes a school project to explain the dynamics concept behind an uphill roller toy. The uphill roller consists of a double cone that appears to roll uphill between two angled rails. However, it only appears to move uphill, as the center of gravity of the cone actually decreases in height as the cone moves along the rails due to the geometry of the cone and rails. Diagrams are included to illustrate the angles and motion of the uphill roller.

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67 views5 pages

MSD 210 Project: Sci-Enza: Mechanical Paradox: The Uphill Roller

The document summarizes a school project to explain the dynamics concept behind an uphill roller toy. The uphill roller consists of a double cone that appears to roll uphill between two angled rails. However, it only appears to move uphill, as the center of gravity of the cone actually decreases in height as the cone moves along the rails due to the geometry of the cone and rails. Diagrams are included to illustrate the angles and motion of the uphill roller.

Uploaded by

gatkramp
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MSD 210 Project: Sci-Enza

Mechanical paradox: The uphill roller.

Group members:

22 May 2012

Contents
1 2 3 Introduction ............................................................................................................................................................................... 1 Concept behind the uphill roller................................................................................................................................................. 1 References ................................................................................................................................................................................. 2

ii

List of figures
Figure 1: Sci-Enza Uphill roller Figure 2: Graphical representation of uphill roller Figure 3: Side view of the uphill roller. Figure 4: Cone rolling uphill 1 1 1 2

iii

Introduction

The group were assigned a project to go to Sci-Enza and play with the toys. The group had to choose a toy that illustrates a dynamics concept. The group chose the uphill roller. The uphill roller is very interesting concept and wouldnt be that difficult to explain to a high school student.
Figure 1: Sci-Enza Uphill roller

The uphill roller consists of a double cone roller and a v shaped incline rails with the bottom of the v shape being the lowest. When the double cone is placed at the bottom of the incline rails, it appears to move uphill to the top part of the rails until it reaches the top part of the rails. As the cone moves uphill, the points where the rails connect with the cone move further apart. 2 Concept behind the uphill roller

Figure 2: Graphical representation of uphill roller Figure 2 Geometry of the double cone and rails. The three angles: , the semi-angle of the double cone; , the semi-angle of the two rails and the elevation angle are visible.

Figure 3: Side view of the uphill roller. Figure 3 Horizontal view in the direction of the symmetry axis of the body. We call x the horizontal axis, y the vertical axis.

A semi angle is an angle that is only the half of the whole angle. in relation to the x-axis.

is the incline of the ramp is the semi angle of the

is a semi angle formed by the rails while +

cone. For the cone the move uphill it is necessary for

< 90 and < 90 .

The centre of gravity is the point at which the entire weight of the double cone may be considered as concentrated so that if supported at this point the body would remain in equilibrium. The centre of gravity of the cone tends to move downwards because of the earths gravity field. The centre of gravity for the double cone is indicated by point on our figure. Now, when placing the cone at the bottom of the incline, its centre of gravity is moving down as the cone moves uphill. Thus, it looks like the cone is moving uphill but in effect its height is decreasing as it moves uphill. ( , )

Figure 4: Cone rolling uphill 3 References

European journal of physics: 2011 Eur. J. Phys. 32 1559. www.en.demo.phy.tw/experiments/mechanics/double-cone/ Papercraft.blogspot.com/2007/06/uphill-roller.html

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