 Hello everyone, I am Sachin Rathod working as an assistant professor in mechanical engineering department from wall chain stop technology, Solaplu. So, today we will see the numericals on single block or shoe break, the learning outcome of this session is student will be able to calculate forces on single block or shoe break. So, you can think about this, so why there is a necessity to calculate how much amount of the force will be the get apply on the lever to stop the rotating drum, you can think about this. So, there is a need to calculate the forces means how much amount of the force is required for rotating, stopping the rotating drum, so it is easy for designing the length of the levers or how much distance will be kept in between the position of the fulcrums and the center of the disc or how much distance we have to keep in between the fulcrum position to the frictional lining force. So, for that purpose means ultimately if you are going to design the single shoe break or single block break, we require to calculate how much amount of the force is required on the lever to stop the rotating drum, we will see how to calculate this. So, before to going to the numericals, we will see what are the conditions of the position of the block or shoe on the drum. So, already we have seen this is a rotating drum, it may be rotates in the clockwise or anticlockwise direction on which the shoe is placed and here is a lever is rigidly fixed to this shoe, the fulcrum positions may be along the lines, it may be the below the center points or it may be the above the frictional lining and here the P force is applied on this lever. So, in that case the angle of block with the center of the disc, it matters lot, so this angle 2 theta is a angle of the block or the shoe from the center of the disc. So, this 2 theta, if 2 theta is less than or equal to the 60 degree at the times the uniform pressure will get distributed over this contacting surface and if the angle 2 theta is greater than 60 degree at that time the maximum pressure will get observed at the center of this point and the minimum pressure will get observed at the end of this shoe. So, for that purpose we have to consider the mu dash, that is a coefficient of friction if angle of the block is more than 60 degree, so the coefficient of friction mu dash is equal to mu that is the actual coefficient of friction in bracket 4 sin theta divided by 2 theta plus sin of 2 theta by using this equation wherever the mu is there that we can replace with the mu dash. So, we have to use this formula if the angle of the block is greater than 60 degree, so by considering this concept we will see how to solve the numerical. So, one numerical psi or taken that is a single block break is shown in the figure the diameter of the drum is 250 mm and the angle of the contact is 90 degree if the operating force of 700 Newton is applied at the end of the lever and the coefficient of friction between the drum and the lining is 0.35 determine the torque that may be the transmitted by the block break. So, we will write the given data given thing that the diameter of the drum that is the d is equal to 250 mm is equal to 0.25 meter therefore radius of the drum is equal to 0.125 mm meter. The angle of the contact is 90 degree, so the angle of the contact this is nothing but the 2 theta therefore 2 theta is equal to 90 degree therefore theta is equal to 45 degree. So, as the angle 2 theta is greater than 60 degree we have to consider the value of mu dash again they are given the force P is equal to 700 Newton is applied at the end of the line the coefficient of friction mu is equal to 0.35 we have to calculate the T b value. So, as the angle 2 theta is greater than 60 degree we have to calculate the value of mu dash this is a actual coefficient of friction between drum and lining this is drum and lining this is the actual coefficient of friction mu as the angle 2 theta is greater than 60 degree we have to find out the mu dash value as the pressure is not going to be distributed uniformly through this block. So, mu dash is equal to mu in bracket 4 sin theta divided by 2 theta plus sin of 2 theta. So, mu is equal to 0.35 in bracket 4 sin 45 divided by 2 into 45 plus sin of 90 degree. So, we have to calculate this force 1 2 theta that is a 90 that 90 it is in the degree we have to convert into the radial. So, 90 into by 180 plus sin 90. So, we are getting the answer 2.57079 it is equal to 2.828 divided by answer into 0.35. So, we are getting that 0.385. So, this is a new coefficient of friction that as the angle is greater than 60 degree. So, now we have to calculate the value of T b that we are knowing the value of the T b T b is equal to mu into R n into the radius of the drum R. So, we have to calculate the value of R n for that purpose we have to take the moment about this fulcrum. So, the take the moment about fulcrum O. Therefore, 700 into the distance total distance is 200 plus 250 it is in the mm. So, into 0.45 meter and this rodent in the clockwise direction only in the same direction of this. So, plus f t into this distance 50 that is a 0.05 and this normal reaction it is in the minus R n into this distance 200 that is a 0.2 it is equal to 0. Therefore, we have to calculate the value of R n. Therefore, 700 into the 700 into 0.45315 plus f t into 0.5 that is f t is equal to mu R n that is we have to consider the value of mu dash into the R n into the 0.05 minus R n into 0.2 it is equal to 0. Therefore, we will solve here 315 is equal to you have to take the mu dash is equal to minus mu dash into the R n into 0.05 plus 0.2 into R n. So, put the value of mu dash minus 0.385 0.05 into the R n plus 0.2 R n it is equal to take the R n term common. So, 0.385 to 0.05 plus 0.2 it is equal to this answer we are getting 0.18075 R n therefore, R n is equal to 315 we are getting the answer. So, this is the value of R n. So, you have to calculate the T b therefore, T b is equal to that mu is nothing but the mu dash the mu dash value is 0.385 into the value of R n 1742.73 into the radius of the drop that is a 0.125 it is equal to value into 0.385 into 0.125. So, we are getting 83.869 Newton meter. So, this is the required answer that is a breaking torque T b is equal to 83.869. So, like this way you can easily calculate the breaking torque acting by the drop these are my references. Thank you.