# ROLLING RESISTANCE

Fig. 3.37 (a) shows a hard roller moving without slipping on a horizontal surface while supporting a load W at the centre. If the roller is moving with uniform velocity, due to horizontal force P, then some sort of resistance must be present so that the net force in the × Acc. As due to uniform motion of roller, acceleration is zero, hence net force is zero. But net force = P-resisting force]. The resistance to the motion of the roller in such cases is known as rolling resistance.

Hence rolling resistance is the resistance to the motion of the roller moving without slipping on a horizontal surface while supporting a load W at the centre.

The rolling resistance can be understood if we imagine the surface to be yielding as shown in Fig. 3.37 (b). The same result may be if the roller is assumed to be yielding and moving over a rigid surface or both the roller and surface are yielding. The ground in front of the roller is depressed, causing the normal reaction (RN) to act ahead of the line of action of the weight W as shown in Fig. 3.37 (b). Now for equilibrium of the roller, the three forces i.e., W, P and RN must be concurrent. As W and P intersect at B, hence RN will also pass through B, making an angle Φ with the vertical direction as shown in Fig. 3.37 (b)

. This means with the increase of W, the value of P also increases. Also for a given material of constant radius of roller, the value of ‘a’ (i.e., value of co-efficient of rolling resistance) is constant.

Problem 3.29. A railroad freight car is having a weight of 80 metric tons. The diameter of the wheels is 0.75 m and co-efficient of rolling resistance between wheel and track is 0.025 mm. Find the horizontal force required to maintain uniform speed.

What will be the horizontal force for the truck and trailer of weight 80 metric tons if the diameter of the tires is 1.2 m and co-efficient of rolling resistance between the truck tires and road is 0.625 mm? In which case, the horizontal force is minimu.

Sol. Given: