what force does the rail exert at the top ?

Question

at six flags there is a roller coaster shaped like a tear drop. the cars ride on the inside of the loop. the loop is 35 meters high with a max speed of 31 m/s at the bottom and 18 m/s at the top and corresponding centripetal acceleration is 30.38 m/s^2. radius of the arc at the top is 10.664 m. If the mass of the people plus the cars is 2011 kg, what force does the rail exert on it at the top ? answer in units of newtons.

Answer 1

It is 41392 N to 5 (probably unjustified) significant figures, or 41000 N to the 2 sig. figs. justified by the severely limited velocity data.

There is a significant mismatch in the accuracy of the input data, with the radius of curvature given to 5 sig. figs., but the speed at the top (' v ') only to 2 sig. figs, and the mass to 4. Are we to assume that the 18m/s really means 18.0, 18.00, or 18.000m/s? If not, only 2 sig figs are justified.

Nevertheless, I'll evaluate the result initially to 5 sig. figs., wich includes calculating my own value for the centripetal acceleration from v^2/r (my value for that is 30.383... m/s^2).

With that input data, the answer is 41392 N. Here's how that is obtained:

The forces acting DOWNWARDs on the object are mg + R, where ' m ' is the mass, ' g ' is the "acceleration due to gravity" (I'll take that to be 9.8m/s^2; some might argue for 9.81) and R is the downward force of reaction exerted by the rail.

Then mg + R = mv^2/r, so that R = m (v^2/r - g). Thus

R = 2011 (18^2/10.664 - 9.8) N = 41392 N.

If we were to limit our result to only 2 sig. figs., it would be 41000 N, of course.

Live long and prosper.

Answer 2

A stress is significant to make something flow in a curved route (Newton each body will flow in a right now line at consistent % until eventually acted upon by technique of a stress) the quantity of that stress is m v^2 / r the completed of gravity + frequent reaction on the genuine substances this stress. If the stress of gravity is already more suitable than the stress required then the project can in reality artwork if the conventional reaction is upwards. that could require particular wheels on something such that the wheels CAN pull something upwards. If we had such wheels then a cart may be stopped on the genuine of a loop and it can't fall. without such wheels the article will fall even if it truly is transferring slowly sufficient so the stress required ( m v^2/r) is below the stress utilized ( mg) At a sufficiently severe % then the stress of gravity is below the stress needed so the conventional reaction substances the more suitable stress required.