Looking for a specific product?

Make a search for products & suppliers, articles & news.

Finalist: Jon Wallem Anundsen

Jon Wallem Anundsen, 18 år, Kristiansand
Skole: Kristiansand Katedralskole, Gimle

Developing a theoretical model for the sliding motion of a frictionless object on a curve


The aim of this project was to develop a general theoretical model of the motion of a frictionless object sliding on a curved surface, where the shape of the surface is defined by a function of horizontal position.

Two approaches were used in attempting to find a model for the motion of the object. In the first approach, it was assumed that the instantaneous acceleration of the object at a point on the curve would be the same as the acceleration of an object placed on an inclined plane with the same slope as the curve at that point. From this assumption, horizontal acceleration was found as a function of horizontal position, and was used to find a function for the horizontal speed of the object.

The second approach was based on the assumption that the total mechanical energy of the object would be constant, and that any loss of gravitational potential energy would therefore cause an equivalent gain of linear kinetic energy, and vice versa. By considering the change in the vertical position of the object, its linear speed was found as a function of its horizontal position, and this function was modified to give the horizontal component of the speed. When the two functions for the horizontal speed of the object were compared, it was found that they produced different results. Therefore, it was concluded that the first approach is invalid, which indicates that the forces acting on an object sliding on a curved surface are not as simple as those acting on an object on an inclined plane.

The reciprocal of the object’s horizontal speed (as found from the second approach) was integrated with respect to horizontal position to find an expression for the time it takes for the object to slide to a given position. This expression was used to calculate the motion of an object sliding on the graph of the function f(x)=-ln|cos(x)|. Because the integral was difficult to evaluate analytically, a numerical approximation was used, and the results were visualised by graphing the horizontal and vertical positions of the object against time. Additionally, an expression for the horizontal acceleration of the object at any given point on the curve was found based on the function for horizontal speed found in the second approach, and this expression was compared with the one found in the first approach. The differences between the two expressions indicated that the normal force acting on an object on a curved surface depends on other factors than just the slope of the curve, and might be affected by the velocity of the object. For further study, it would be interesting to find out exactly what determines the normal force, as this knowledge might be useful in developing a more realistic model that accounts for the effects of friction.


Related news

Latest news

Trainee weekend in Hafjell and Bremanger daily life

First joint kick of seminar

Pentair and Stahl Tranberg had their first customer event presenting both companies heat tracing solutions for customers.

Untrue rumours about an on-going incident at the Halden Research Reactor in Norway

The Norwegian Radiation Protection Authority has become aware that stories about an ongoing incident involving a “meltdown” at the Norwegian Institute for Energy Technology (IFE) reactor situated in Halden are currently ci...

Gulf Notified Body meeting in Manama Bahrain

At the end of January, the GSO (Gulf Standards Organization) arranged the first meeting with the present group of 23 Notified Bodies. These Notified Bodies are authorised by GSO to certify the electrical products as curren...


During the spring thaw period in Sweden, many small roads are closed to traffic despite the fact that they are fit for use. The BiFi research project has analysed the roads’ bearing capacity in real time using Internet-con...

Children with poor vitamin B12 status early in life struggle more with tasks, recognition and interpreting feelings

Small children with low levels of vitamin B12 had more difficulties solving cognitive tests, such as the ability to do puzzles, recognize letters and interpret other children’s feelings.

BP Awards Schlumberger Contract for Mad Dog 2 Project

Export Conference 2017: A changing world

Register for this year’s most important conference for Norwegian exporters. We can promise you an interesting and inspirational day!

Meet Elkem Silicon Materials at the Ceramics Expo 2017

Elkem Silicon Metrials invites to meet their team at the Ceramics Expo 2017. This is North America’s largest, free-to-attend exhibition for Ceramic manufacturing and applications.