welcome to our lecture line here we have a very practical application of the screw and of course we're dealing with a square threaded screw that is connected to a clamp which pushes two blocks together we're applying a force to the edge of the handle which is 10 centimeters away from the from the centre of the screw and we're applying a force of 400 Newton's trying to tighten that screw the lead of the screw threading is four millimeters in the diameter of the screw is 10 millimeters so what we're trying to do here is find out what the applied forces to the block based upon these parameters also knowing that the static coefficient of friction is equal to 0.3 which gives us an angle fee of sixteen point seven degrees what we've done so far is taking a look at this is the thread of the screw this is the object that would be the thread inside the bracket here and of course these are the forces at play what we're looking for is the force on the block which is the same as the weight on the block and so that would be represented by the W right here - weight on the block even though the screw weight is not really what's causing the force is the force applied to the blocks that will be represented by W the force F is the force applied to the turning of the screw and of course is a relationship between this force F which is applied to the screw and the moment here which is 400 Newtons applied over radius of 10 centimeters so the relationship between F here and FP there can be done as follows the force applied to the screw is equal to the ratio of the moment arm are divided by the average radius of the screw multiplied time F sub P since f CP is 400 Newtons we can say that F is equal to the ratio of 10 centimeters which is a hundred millimeters divided by the radius of the screw now the diameter is 10 millimeters which means the radius is only 5 millimeters so we divided by 5 millimeters and multiply that times 400 Newtons so it goes in there 20 times 20 times this we have a force applied of 8,000 Newtons to the screw alright now what we're going to do is we're going to draw a triangle summing all these forces together so we have the weight of the screw which is what we're looking for that's a W now we also have the force applied to the screw which we calculated right here and then we have the reactionary force right here which is caused by the normal force on the surface and the friction so it's the vector sum of the friction and the normal force on the surface and so that's going to be the reaction force right here now notice that the angle between the reaction force and the vertical here is going to be the sum of theta plus feet so this is the case where you have to add the two together and fee is larger than theta and well in this case it doesn't matter if it's larger or not it's simply the sum of the two which means that this angle here it's going to be the sum of theta plus fee that's the lead angle plus the angle caused by the friction and the lead angle let's see we don't have the lead angle yet we need to calculate the lead angle so let's go ahead and do that how do we find theta well theta can be found by the ratio of the lead to the circumference of the thread so that would be theta is equal to the arctangent of the opposite side which is the lead which is 4 millimeters divided by the adjacent side which is 2 pi times the radius which is 5 millimeters and let's take the arctangent of that so we get four divided by two divided by pi divided by five then we take the arctangent of that and we get seven point two six degrees close enough seven point two six degrees that's theta let's see if we got that right so that's four divided by two pi times our correct and so we add the two angles together so that would be seven point two six degrees plus fee which is sixteen point seven degrees so that would be twenty three point nine six degrees that's the sum of the angles that says angle right there now to find w what do we know we know f so f is a known quantity and we're looking for w so we're going to use these two sides and we have this angle that means that the tangent of the sum of the two angles theta plus V is equal to the opposite side which is f divided by the adjacent side which is W and since we're looking for W we could say that W is equal to F divided by the tangent of the sum of the two angles which is twenty three point nine six degrees and F is a known quantity that's 8,000 Newton's a thousand Newton's divided by the tangent of twenty three point nine six degrees and let's see what we get so we add that to plus sixteen point seven take the tangent of that and take the inverse and multiply that times eight thousand and that means we have a total force of very close to 18,000 Newtons applied to the clamp which is quite a bit of force so you can see that because the diameter of the screw is so small and the moment arm is relatively large with a fairly 9 amount of force a small amount of 400 Newtons is not that large by applying a foreigner Newton force we can apply a force clamping to two pieces put together of 18,000 Newtons which is quite a large force you can see again it's the advantage of using a screw gives you the mechanical advantage and we use the very same principles here to calculate the force required or the force of between the two blocks and the ND and the clamp by using the same concept as the wedge and that's how it's done and by the way Part B how to find a torque required to loosen the clamp we'll do another video for that so it'll be video 29 so you didn't forget about that it's a simply coming up on the next video because after all I'm not a bird space