Find the force of static friction of the ground on the...

Find the force of static friction of the ground on the ladder, if a man climbs a distance d = 10m up an L = 25m long ladder. Assume the coefficient of static friction is 0.4 between the ladder and the ground, the angle of the ladder is 70°, the mass of the ladder is 13kg, and the mass of the man is 85kg. Assume the ladder is uniform, and that g = 9.8m/s^2. Friction on the vertical wall can be neglected.

Transcript

00:01 For this problem, we are given a ladder and we are told that this man rests on this ladder.

00:11 We're giving this angle at 70 degrees.

00:16 The distance from where the man is, how far he has climbed is 10 meters.

00:23 The length of the entire ladder all the way to the end is 25 meters.

00:32 Now i will put the weight of the man here.

00:35 Of course weight of the ladder will act just in the middle now because of there will be a frictional force here preventing this ladder from sliding and there will be a normal reaction here there will also be another reaction here which i'll call n1 to find this frictional force all we have to do is to use the condition for equilibrium and that is the sum of all the x forces is equal to the of all the y forces which is equal to the sum of all the moments which is zero now if i take the sum of all the x forces you will simply see that f is equal to n1 let us skip that so once we can find n1 we found f what about the sum of all the y forces i can simply see again that n is simply equal to mass of the ladder plus the mass of the man multiplying all that by the acceleration due to gravity and so n is equal to 85 plus 13 multiplying g and i'll just say that that is 98g for now i'll put the value of g later what about the sum of all the moments i'll say taking the moment about the pivot on the ground if i take the moment about this pivot about this point let us see this force here will cause a moment in that direction.

02:29 You will make that one to rotate in the anticlockwise direction.

02:34 While these two forces will cause a clockwise rotation.

02:39 Now what is the distance from here? from the line of action of this force to that point, we have to bring that in.

02:48 We can see again and we also have to do that for this other one.

02:55 Other one...

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