Forces and couples generated by various elements-roller problem
Forces and couples generated by various elements-roller problem: Let us now solve the well known example of a roller of radius r being pulled over a step as shown in figure 1. The height of the step is h. What is minimum force F required if the roller is pulled in the direction shown and is about to roll over the step. What are the normal and frictional forces at that instant?
When the roller is about to roll over the step, there will be no normal reaction from the lower surface and therefore the roller will be under equilibrium under the influence of its weight W, the applied force F and the normal reaction N and the frictional force f applied by the edge of the step. To calculate the force F, we apply the torque equation about the edge to get
To find N and f we apply the force equation
That can be written in the component form a
Let us look at these equations.
Solving these equations gives
So in this situation, we do not require friction to keep the roller in equilibrium. On the other hand recall the problem in the previous lecture when we were trying to lift a 1000Nt weights by putting a rod on a brick edge. In that case we did require friction.