A uniform ladder is 10 m long and is 200 N. the ladder leans against a vertical, frictionless at a point 8.0 m

A uniform ladder is 10 m long and is 200 N. the ladder leans against a vertical, frictionless at a point 8.0 m above the ground as shown in the figure. A horizontal force F is applied to the ladder at a point 2 m from the base of the ladder (as measured from the base of the ladder). (a) if F = 50 N, what is the force of the ground on the ladder, in terms of the Unit vectors shown? (b) if F = 150 N, what is the force of the ladder on the ground in unit vector form? (c) Suppose the coefficient of static friction between the ladder and the ground is 0.38; for what minimal value of F will the base of the ladder just start to move toward the wall?.

A uniform ladder is 10 m long and is 200 N. the ladder leans against a vertical, frictionless at a point 8.0 m
I will not provide you with a step-by-step solution to your problem because I strongly believe that is not going to benefit your learning. However, I would give you some advice as to how one may effectively approach a physics problem of this nature.





This particular problem is quite apparently an exercise dealing with concepts of statics. Statics problems are typically straightforward because nothing moves and everything is in a state of static equilibrium. All forces are in equilibrium and all moments generated by all forces about any point in the system are also in equilibrium.





You may like to follow these steps in your working:


(1) Draw a free body diagram (of the ladder). It is not necessary to draw the wall or the ground because our main focus is just the ladder, inclined so that it is as if you are looking at one of its sides.





(2) Add to your free body diagram All forces acting On the ladder. Be careful not to miss out any. In this problem, you should have these forces:


(a) the weight of the ladder, W, acting vertically downwards from the centre of the ladder,


(b) the normal force on the ladder by the wall, N1, acting at the top of the ladder normal to the wall surface,


(c) the normal force on the ladder by the ground, N2, acting at the base of the ladder normal to the ground surface,


(d) the frictional force on the ladder by the ground, F2, acting at the base of the ladder parallel to the ground surface,


(e) the horizontal force F acting at 2m from the base of the ladder.





(3) Identify the unknowns. In the first two parts of the problem, N1, N2 and F2 are unknown. In the last part of the problem, N1, N2 and F are unknown.





(4) Establish the equations to solve for the unknowns. Theoretically, 3 equations are needed to solve for 3 unknowns. Based on force and moment equilibrium, we sum forces horizontally and vertically, as well as moment about a selected point and equate them to zero.


ΣFx = 0


ΣFy = 0


ΣM = 0

balsam