A velodrome is built for use in the Olympics (the figure below). The radius of curvature of the surface is 15.7 m. At what angle should the surface be banked for cyclists moving at 15 m/s? (Choose an angle so that no frictional force is needed to keep the cyclists in their circular path. Large banking angles are indeed used in velodromes
the angle answers should be in degrees, please besides answering it, explain the problem to me, I dont know where to start or anything, thank you!
2007-10-19 05:03:04 · 3 answers · asked by ? 2 in Science & Mathematics ➔ Physics
In order to keep an object moving in a circle there must be a force acting on the object that continuously pushes it towards the center of the circle. Without this force the object would run off the circle in a straight line. This force is called the centripetal force. This force is caused by a centripetal acceleration.
The other main force that will be acting on the cyclist is gravity. So the angle of the velodrome banking must be the same as the angle of the combined force of gravity and the centripetal force, such that the combined forces on the cyclist will be perpendicular to the surface of the velodrome. (Sketching it out might help you visualize it as you work the problem.)
Since no mass of the rider is given we can assume that it will not change the answer in this problem. So let's assume a mass of rider and bike to be 100kg (I know that's pretty high, but it's a nice round number).
The centripetal force for the given radius and speed is:
Fc = 1433N
The weight of our hypothetical rider:
Fw = 981N
Now is when you really need to sketch to help you determine what angle you need to calculate with these forces. The centripetal force is horizontal and towards the inside of the banking. The weight of the rider is vertical towards the earth.
tan(theta) = Fc/Fw
theta = 55.6 deg
You can now see that the 100kg mass we arbitrarily picked does not matter because it ends up being the same mass in Fc divided by the same mass in Fw, thus canceling out.
2007-10-19 05:52:41 · answer #1 · answered by endo_jo 4 · 0⤊ 0⤋
To keep on the track while going in a circle you need to accelerate towards the centre of the circle, if there is no friction they can not push against a horizontal surface to accelerate. The track needs to be banked so that they can push against the track and have the normal force accelerate them towards the centre.
2007-10-19 05:44:12 · answer #2 · answered by Blank 2 · 0⤊ 0⤋
Consider the banked road to be a ramp for sideways motion and forces. The angle should be such that centripetal accel along the ramp = grav. accel along the ramp.
v^2/r*cos(theta) = g*sin(theta)
tan(theta) = v^2/(rg); theta = arctan(v^2/(rg)) in rad
I'll bet you can convert rad to deg.
2007-10-19 05:42:15 · answer #3 · answered by kirchwey 7 · 0⤊ 0⤋